The Mechanism behind Superinsulation

From Left to Right: Valerii Vinokur, Tatyana Baturina and Nikolai Chtchelkatchev (photo courtesy: Argonne National Laboratory)

Scientists at the U.S. Department of Energy's Argonne National Laboratory have discovered the microscopic mechanism behind the phenomenon of superinsulation, the ability of certain materials to completely block the flow of electric current at low temperatures.

The essence of the mechanism is what the authors termed "multi-stage energy relaxation" in a recent paper [1] published in Physical Review Letters. An earlier paper [2] on the discovery of superinsulation was published in Nature in April, 2008.

Traditionally, energy dissipation accompanying current flow is viewed as disadvantageous, as it transforms electricity into heat and thus results in power losses. In arrays of tunnel junctions that are the basic building units of modern electronics, this dissipation permits the generation of current.

Argonne scientist Valerii Vinokour, along with Russian scientists Nikolai Chtchelkatchev (Moscow Institute of Physics and Technology) and Tatyana Baturina (Institute of Semiconductor Physics, Novosibirsk), found that at very low temperatures the energy transfer from tunneling electrons to the thermal environment may occur in several stages.

An electron microscopy image of titanium nitride, on which the effect of superinsulation was first observed [image courtesy: Argonne National Laboratory]

“First, the passing electrons lose their energy not directly to the heat bath; they transfer their energy to electron-hole plasma, which they generate themselves,” Vinokour said. “Then this plasma 'cloud' transforms the acquired energy into the heat. Thus, tunneling current is controlled by the properties of this electron-hole cloud.”

As long as the electrons and holes in the plasma cloud are able to move freely, they can serve as a reservoir for energy—but below certain temperatures, electrons and holes become bound into pairs. This does not allow for the transfer of energy from tunneling electrons and impedes the tunneling current, sending the conductivity of the entire system to zero.

“Electron-hole plasma disappears from the game and electrons cannot generate the energy exchange necessary for tunneling,” Vinokour said. Because the current transfer in thin films and granular systems that exhibit superinsulating behavior relies on electron tunneling, the multistage relaxation explains the origin of the superinsulators.

Superinsulation is the opposite of superconductivity; instead of a material that has no resistivity, a superinsulator has a near-infinite resistance. Integration of the two materials may allow for the creation of a new class of quantum electronic devices. This discovery may one day allow researchers to create super-sensitive sensors and other electronic devices.

Reference
[1] N. M. Chtchelkatchev, V. M. Vinokur, and T. I. Baturina, "Hierarchical Energy Relaxation in Mesoscopic Tunnel Junctions: Effect of a Nonequilibrium Environment on Low-Temperature Transport", Physical Review Letters, 103, 247003 (2009). Abstract.
[2] Valerii M. Vinokur, Tatyana I. Baturina, Mikhail V. Fistul, Aleksey Yu. Mironov, Mikhail R. Baklanov and Christoph Strunk, "Superinsulator and quantum synchronization", Nature, 452, 613-615 (3 April 2008). Abstract.

[We thank Argonne National Laboratory, IL, USA for materials used in this report]

Interference-Induced Terahertz Transparency in a Semiconductor Magneto-plasma

Junichiro Kono

[This is an invited article based on recently published work by the author and his collaborators from Rice University, Texas A&M University, and Los Alamos National Laboratory -- 2Physics.com]

Author: Junichiro Kono
Affiliation: Dept of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA.

Maximum modulation of light transmission occurs when an initially opaque medium is suddenly made transparent. This dramatic phenomenon, induced transparency, indeed occurs in atomic and molecular gases through different mechanisms [1,2], while there remains much room for further studies in solids. A plasma is an illustrative system exhibiting opacity, where light is completely reflected if its frequency is smaller than the plasma frequency. Light-plasma interaction theory provides a universal framework to describe such diverse phenomena and systems as radiation in space plasmas, diagnostics of laboratory plasmas, and collective excitations in condensed matter. However, quite surprisingly, induced transparency in plasmas is a rather uncharted area of research.

In a paper published online in Nature Physics on December 6, 2009, researchers at Rice University, Texas A&M University, and Los Alamos National Laboratory reported a novel type of thermally- and magnetically-induced transparency in a semiconductor plasma, revealed by coherent terahertz (THz) magneto-spectroscopy [3]. They observed a sudden appearance and disappearance of transmission through a slab of electron-doped InSb over narrow temperature and magnetic field ranges.

To explain these striking observations, the researchers developed a theoretical model based on coherent interference between the left- and right-circularly polarized eigenmodes of the low-density magneto-plasma in InSb. Detailed simulations demonstrated how the observed THz modulation and interference effects depend sensitively on the magnetic field, as well as on the temperature through the intrinsic carrier density of narrow-gap semiconductors. Excellent agreement between experiment and theory demonstrated surprisingly long-lived coherence of magnetoplasmon excitations.

The free electrons in the conduction band of doped narrow-gap semiconductors, e.g., InSb, InAs, and HgCdTe, behave as classic solid-state plasmas and have been examined through a number of infrared spectroscopy studies [4,5]. Due to the low electron densities achievable in these materials and to the electrons’ small effective mass and high mobility, most of the important energy scales (the cyclotron energy, the plasma energy, the Fermi energy, intra-donor transition energies, etc.) can all lie within the same narrow energy range from ~1 to 10 meV, or the THz frequency range (1 THz = 4.1 meV). The interplay between these material properties, which are tunable with magnetic field, doping density, and/or temperature, make doped narrow-gap semiconductors a useful material system in which to probe and explore novel phenomena that can be exploited for future THz technology.

The Rice researchers used a time-domain THz magneto-spectroscopy system [6] with a linearly-polarized, coherent THz beam to investigate magneto-plasmonic effects in a lightly n-doped InSb sample that exhibits a sharp plasma edge at ~0.3 THz at zero magnetic field as well as sharp absorption and dispersion features around the cyclotron resonance. These spectral features can be sensitively controlled by changing the magnetic field and temperature due to the very small effective masses of electrons and low thermal excitation energy in this narrow-gap semiconductor. Furthermore, long decoherence times (< 40 ps) of electron cyclotron oscillations give rise to sharp interference fringes and coherent beating between different normal modes (coupled photon-magneto-plasmon excitations) of the semiconductor plasma.

Figure 1 (click on the image to see hi resolution version) Temperature dependence of THz transmittance spectra for lightly-doped InSb in a magnetic field. a, Transmittance versus temperature at 0.25 THz at a magnetic field of 0.9 T (corresponding to a horizontal cut in the contour map of b), showing thermally induced transparency. b, Measured and c, calculated transmittance contour as a function of temperature (2-240 K) and frequency (0.12-2.6 THz) at a fixed magnetic field of 0.9 T. d, Transmittance versus magnetic field at 0.25 THz at a temperature of 40 K (corresponding to a horizontal cut in the contour map of e), showing magnetically induced transparency. e, Measured and f, calculated transmittance contour as a function of magnetic field (0-2 T) and frequency (0.12-2.6 THz) at a fixed temperature of 40 K.

As an example, the temperature (Figs. 1a, 1b, and 1c) and magnetic field (Figs. 1d, 1e, and 1f) dependence of THz transmittance spectra are shown. A striking feature in both Figs. 1a and 1d is a narrow range of temperature (1a) and magnetic field (1d) where the transmission of THz light is high. Figure 1b shows a full contour map of the transmittance as a function of frequency and temperature at a fixed magnetic field. Figure 1c shows a calculated contour plot of the transmittance, based on their model. A horizontal cut of the contour at 0.25 THz is shown in Fig. 1a. Similarly, Figs. 1e and 1f show, respectively, measured and calculated contour plots of the transmittance as a function of frequency and magnetic field. A horizontal cut of the contour at 0.25 THz is shown in Fig. 1d.

At zero magnetic field, the only spectral feature appearing in our InSb samples is the plasma edge at the plasma frequency (0.3 THz). When a magnetic field is applied along the wave propagation direction, the incident linearly-polarized THz wave propagates in the sample as a superposition of the two transverse normal modes of the magneto-plasma: the left-circularly-polarized mode, called the ‘extraordinary’ or cyclotron resonance active (CRA) wave, and the right-circularly-polarized mode, called the ‘ordinary’ or cyclotron resonance inactive (CRI) wave. The CRA mode couples with the cyclotron motion of electrons. With increasing magnetic field, the plasma edge splits into the two magnetoplasmon frequencies for the CRA and CRI modes.

The THz response of the InSb sample was modeled through a dielectric tensor for a classical magneto-plasma for both electrons and holes, including the effect of conduction band non-parabolicity. The CRA wave experiences strong absorption and dispersion, while the transmission of the CRI mode is nearly flat and featureless everywhere except at very low frequencies. Simple addition of the two, however, does not produce any of the experimentally observed spectral features. What is measured experimentally is a superposition of the two fields, which contains the interference between the CRA and CRI modes. The interference term depends on the index difference between the two modes, and its inclusion in the simulation indeed totally modified the spectra at finite magnetic fields. The agreement between theory and experiment is outstanding. The positions and shapes of all the transmission peaks, plateaus, and dips in the spectra are accurately reproduced in great detail, confirming the accuracy of our interpretation and theoretical model and indicating the long coherence times of coupled photon-magnetoplasmon excitations reaching tens of ps.

The dominant process affecting the temperature dependence of the dielectric tensor at elevated temperatures is the thermal excitation of intrinsic carriers across the band gap given, which leads to an exponentially growing plasma frequency. The density of intrinsic carriers eventually exceeds the doping density at ~180 K. Therefore, one would expect a weakly temperature-dependent transmittance below ~180 K that would abruptly decrease above this temperature due to the exponentially growing plasma frequency. The intensities of individually-transmitted CRA and CRI modes indeed exhibit this expected temperature dependence.

However, again, one has to include the interference term in calculating the transmission. With realistic parameters for the sample and experimental conditions, this interference term is negative and almost exactly cancels the other two terms below 160 K, leading to interference-induced opacity. As the temperature increases above 160 K, the difference between the refractive indices of the two modes starts growing exponentially, causing strong oscillations in the total transmittance due to interference. These oscillations, however, are strongly damped above 200 K due to the exponentially growing absorption coefficient for both normal modes. As a result, only one strong peak remains prominent, followed by a few progressively smaller peaks, explaining the existence of the observed transparency bands. This is further illustrated by the excellent agreement between the observed and calculated temperature dependence of transmittance in Figs. 1b and 1e (experiment) and 1c and 1f (theory).

These results demonstrate that free carrier plasmas in lightly-doped narrow-gap semiconductors are promising materials systems for THz physics, exhibiting huge magnetic anisotropy effects and plasmon excitations in the THz range that are highly tunable with external fields, temperature, and doping. In particular, coherent interference phenomena, which are commonly observed and used in the visible and near-infrared range, can be extended into the THz regime. Moreover, the observed novel interference phenomena depend sensitively on plasma properties and carrier interactions, and thus, can be used to study solid-state plasmas over a vast range of external fields and temperatures from the classical limit to the ultra-quantum limit. This experimental finding may open up further new opportunities for using coherent THz methods to probe more exotic phenomena in condensed matter systems that occur due to many-body interactions and disorder.

References
[1] Harris, S. E. "Electromagnetically induced transparency". Phys. Today 50, 36-42 (1997). Abstract.
[2] McCall, S. L. & Hahn, E. L. "Self-induced transparency by pulsed coherent light", Phys. Rev. Lett. 18, 908-911 (1967). Abstract.
[3] X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-Induced Terahertz Transparency in a Semiconductor Magneto-plasma,” Nature Physics, published online on December 6, 2009. Abstract. Rice University Press Release.
[4] Palik, E. D. & Furdyna, J. K. "Infrared and microwave magnetoplasma effects in semiconductors". Rep. Prog. Phys. 33, 1193-1322 (1970). Abstract.
[5] McCombe, B. D & Wagner, R. J. in "Advances in Electronics and Electron Physics", Vol 37 (eds Marton, L.) 1-79 (Academic Press, 1975).
[6] Wang, X., Hilton, D. J., Ren, L., Mittleman, D. M., Kono, J. & Reno, J. L. "Terahertz time-domain magnetospectroscopy of a high-mobility two-dimensional electron gas". Optics Lett. 32, 1845-1847 (2007). Abstract.

Observation of Magnetic Monopoles in Spin Ice

Hiroaki Kadowaki, Yuji Aoki and Naohiro Doi of Tokyo Metropolitan University


[This is an invited article based on recently published work of the authors -- 2Physics.com]






Authors: H. Kadowaki¹, Y. Aoki¹, T. J. Sato², J. W. Lynn³

Affiliations: ¹Department of Physics, Tokyo Metropolitan University, Tokyo, Japan,
²NSL, Institute for Solid State Physics, University of Tokyo, Tokai, Japan,
³NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA

From the symmetry of Maxwell's equations of electromagnetism, magnetic charges or monopoles would be expected to exist in parallel with electric charges. About 80 years ago, a quantum mechanical hypothesis of the existence of magnetic monopoles was proposed by Dirac [1]. Since then, many experimental searches have been performed, ranging from a monopole search in rocks of the moon to experiments using high energy accelerators [2]. But none of them was successful, and the monopole is an open question in experimental physics. Theoretically, monopoles are predicted in grand unified theories as topological defects in the energy range of the order 10¹⁶ GeV [2]. However these enormous energies preclude all hope of creating them in laboratory experiments.

Taku J. Sato of University of Tokyo

Alternatively, recent theories predict that tractable analogs of the magnetic monopole might be found in condensed matter systems [3,4,5]. One prediction [4] is for an emergent elementary excitation in the spin ice compound Dy₂Ti₂O₇ [6], where the strongly competing magnetic interactions exhibit the same type of frustration as water ice [7]. In addition to macroscopically degenerate ground states [6], the excitations from these states are topological in nature and mathematically equivalent to the Dirac monopoles [1,4]. We have successfully observed [8] the signature of magnetic monopoles in the spin ice Dy₂Ti₂O₇ using neutron scattering, and find that they interact via the magnetic inverse-square Coulomb force. In addition, specific heat measurements show that the density of monopoles can be controlled by temperature and magnetic field, with the density following the expected Arrhenius law.

Jeffrey W. Lynn of NIST, USA

In Fig. 1 we illustrate creation of a magnetic monopole and antimonopole pair in spin ice under applied magnetic field along a [111] direction. This excitation is generated by flipping a spin, which results in ice-rule-breaking "3-in, 1-out" and "1-in, 3-out" tetrahedral neighbors, simulating magnetic monopoles, with net positive and negative charges sitting on the centers of tetrahedra. The monopoles can move and separate by consecutively flipping spins in the kagome lattice.

Fig. 1. Spins of Dy₂Ti₂O₇ occupy a cubic pyrochlore lattice, which is a corner -sharing network of tetrahedra, and consists of a stacking of triangular and kagome lattices. The competing magnetic interaction brings about a geometrical constraint where the lowest energy spin configurations on each tetrahedron follow the ice rule, in which two spins point inward and two point outward on each tetrahedron. (A) By applying a small magnetic field along a [111] direction, the spins on the triangular lattices are parallel to the field, while those on the kagome lattices retain disorder under the same ice rules. This is referred to as the kagome ice state [9]. (B) Creation of a magnetic monopole (blue sphere) and antimonopole (red sphere) pair in the kagome ice state.

A straightforward signature of monopole-pair creation is an Arrhenius law in the temperature (T) dependence of the specific heat (C). This Arrhenius law of C(T) is clearly seen in Fig. 2 at low temperatures, indicating that monopole-antimonopole pairs are thermally activated from the ground state, and that the number of monopoles can be tuned by changing temperature and magnetic field.

Fig. 2. Specific heat of Dy₂Ti₂O₇ under [111] magnetic fields is plotted as a function of 1/T. In intermediate temperature ranges these data are well represented by the Arrhenius law denoted by solid lines.

A microscopic experimental method of observing monopoles is to perform magnetic neutron scattering using the neutron's dipole moment as the probe. One challenge to the experiments is to distinguish the relatively weak scattering from the monopoles from the very strong magnetic scattering of the ground state. By choosing appropriate field-temperature values, we have successfully observed scattering by magnetic monopoles, diffuse scattering close to the (2,-2,0) reflections, and that by the ground state (Fig. 3) [8].

Fig. 3. Intensity maps of neutron scattering at T = T_c + 0.05 K in the scattering plane perpendicular to the [111] field are shown for H = 0.5 T and H = H_c. The kagome ice state at H = 0.5 T (A) compared with the MC simulation (C). The weakened kagome-ice state scattering plus the diffuse monopole scattering (B) at H = H_c agree with the MC simulation (D).

Typical elementary excitations in condensed matter, such as acoustic phonons and (gapless) magnons, are Nambu-Goldstone modes where a continuous symmetry is spontaneously broken when the ordered state is formed. This contrasts with the monopoles in spin ice, which are point defects that can be fractionalized in the frustrated ground states. Such excitations are unprecedented in condensed matter, and now enable conceptually new emergent phenomena to be explored experimentally [10].

References:
[1] "Quantised singularities in the electromagnetic field",
P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931). Article.
[2] "Theoretical and experimental status of magnetic monopoles",
K. A. Milton, Rep. Prog. Phys. 69, 1637 (2006). Abstract.
[3] "The anomalous Hall effect and magnetic monopoles in momentum space", Zhong Fang, Naoto Nagaosa, Kei S. Takahashi, Atsushi Asamitsu, Roland Mathieu, Takeshi Ogasawara, Hiroyuki Yamada, Masashi Kawasaki, Yoshinori Tokura, Kiyoyuki Terakura, Science 302, 92 (2003). Abstract.
[4] "Magnetic monopoles in spin ice"
C. Castelnovo, R. Moessner, S. L. Sondhi, Nature 451, 42 (2008). Abstract.
[5] "Inducing a magnetic monopole with topological surface states"
X-L. Qi, R. Li, J. Zang, S-C. Zhang, Science 323, 1184 (2009). Abstract.
[6] "Spin ice state in frustrated magnetic pyrochlore materials"
S. T. Bramwell, M. J. P. Gingras, Science 294, 1495 (2001). Abstract.
[7] "The structure and entropy of ice and of other crystals with some randomness of atomic arrangement" , L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935). Abstract.
[8] "Observation of Magnetic Monopoles in Spin Ice", H. Kadowaki, N. Doi, Y. Aoki, Y. Tabata, T. J. Sato, J. W. Lynn, K. Matsuhira, Z. Hiroi, J. Phys. Soc. Jpn. 78, 103706 (2009). Abstract.
[9] "A new macroscopically degenerate ground state in the spin ice compound Dy2Ti2O7 under a magnetic field" K. Matsuhira, Z. Hiroi, T. Tayama, S. Takagi and T. Sakakibara, J. Phys. Condens. Matter 14, L559 (2002). Article; "Kagome ice State in the dipolar spin ice Dy2Ti2O7" Y. Tabata, H. Kadowaki, K. Matsuhira, Z. Hiroi, N. Aso, E. Ressouche, and B. Fåk, Phys. Rev. Lett. 97, 257205 (2006). Abstract.
[10] In Oct. 2009, in addition to [8], three experimental papers on the magnetic monopoles in spin ice have been published: "Measurement of the charge and current of magnetic monopoles in spin ice" S. T. Bramwell, S. R. Giblin, S. Calder, R. Aldus, D. Prabhakaran & T. Fennell, Nature 461, 956 (2009), Abstract; "Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7" D. J. P. Morris, D. A. Tennant, S. A. Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czternasty, M. Meissner, K. C. Rule, J.-U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, R. S. Perry, Science 326, 411 (2009) Abstract; "Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7" T. Fennell, P. P. Deen, A. R. Wildes, K. Schmalzl, D. Prabhakaran, A. T. Boothroyd, R. J. Aldus, D. F. McMorrow, S. T. Bramwell, Science 326, 415 (2009). Abstract.

Topological Insulators : A New State of Quantum Matter

M. Zahid Hasan

[This is an invited article based on a series of recent works by the author and his collaborators -- 2Physics.com]

Author: M. Zahid Hasan

Affiliation: Joseph Henry Laboratories of Physics, Department of Physics,
Princeton University, USA

Most quantum states of condensed-matter systems or the fundamental forces are categorized by spontaneously broken symmetries. The remarkable discovery of quantum Hall effects (1980s) revealed that there exists an organizational principle of matter based not on the broken symmetry but only on the topological distinctions in the presence of time-reversal symmetry breaking [1,2]. In the past few years, theoretical developments suggest that new classes of topological states of quantum matter might exist in nature [3,4,5]. Such states are purely topological in nature in the sense that they do not break time-reversal symmetry, and hence can be realized without any applied magnetic field : "Quantum Hall-like effects without magnetic field".

Research Team at Princeton University: [L to R] David Hsieh, Dong Qian, L. Andrew Wray, YuQi Xia

This exotic phase of matter is a subject of intense research because it is predicted to give rise to dissipationless (energy saving) spin currents, quantum entanglements and novel macroscopic behavior that obeys axionic electrodynamics rather than Maxwell's equations [6]. Unlike ordinary quantum phases of matter such as superconductors, magnets or superfluids, topological insulators are not described by a local order parameter associated with a spontaneously broken symmetry but rather by a quantum entanglement of its wave function, dubbed topological order. In a topological insulator this quantum entanglement survives over the macroscopic dimensions of the crystal and leads to surface states that have unusual spin textures.

Topologically ordered phases of matter are extremely rare and are experimentally challenging to identify. The only known example was the quantum Hall effect discovered in the 1980s by von Klitzing (Nobel Prize 1985). It was identified by measuring a quantized magneto-transport in a two-dimensional electron system under a large external magnetic field at very low temperatures, which is characterized by robust conducting states localized along the one-dimensional edges of the sample. Two-dimensional topological insulators, on the other hand, are predicted to exhibit similar edge states even in the absence of a magnetic field because spin-orbit coupling can simulate its effect (Fig.1A) due to the relativistic terms added in a band insulator's Hamiltonian.

Remarkably, three-dimensional topological insulators, an entirely new state of matter with no charge quantum Hall analogue, are also postulated to exist. And its topological order or exotic quantum entanglement is predicted to give rise to unusual conducting two-dimensional surface states (Fig.1B) that have novel spin-selective energy-momentum dispersion relations. Utilizing state-of-the-art angle-resolved photoemission spectroscopy, an international collaboration led by scientists from Princeton University have studied the electronic structure of several bismuth based spin-orbit materials [7,8,9]. By systematic tuning of the incident photon energy, it was possible to isolate surface quantum states from the bulk states, which confirmed that these materials realized a three-dimensional topological insulator phase.

Figure 1. (A) Schematic of the 1D edge states in a 2D topological insulator. The red and blue curves represent the edge current with opposite spin character. (B) Schematic of the 2D surface states in a 3D topological insulator. (C) Most elemental topological Insulators exhibit odd number of Dirac cones on their surface unlike the even numbers observed in graphene. Topological insulator Dirac cones are spin polarized where as Dirac cones in graphene are not.

The remarkable property of the surface states of a 3D topological insulator is that its Fermi surface supports a geometrical quantum entanglement phase, which occurs when the spin-polarized Fermi surface encloses the Kramers' points and on the surface Brillouin zone an odd number of times in total (Fig.2B). ARPES intensity map of the (111) surface states of bulk insulating Bi1-xSbx (Fig.2A) shows that a single Fermi surface encloses . However, determination of the degeneracy of the additional Fermi surface around requires a detailed study of its energy-momentum dispersion. ARPES spectra along the - direction (Fig.2C) reveal that the Fermi surface enclosing is actually composed of two bands, therefore two Fermi surfaces enclose , leading to a total of seven and Fermi surface enclosures.

Figure 2. (A) ARPES surface state (SS) Fermi surface of insulating Bi1-xSbx showing spin polarization directions as indicated by red and blue arrows. (B) Schematic of the SS Fermi surface of a 3D topological insulator. (C) ARPES energy-momentum dispersion of the surface states. The shaded areas denote the bulk bands while the dashed white lines are guides to the eye for surface state dispersions. (D) A single Dirac cone is observed in Bi2Te3.

These results constitute the first direct experimental evidence of a topological insulator in nature which is fully quantum entangled. The observed spin-texture in BiSb is consistent with a magnetic monopole image field beneath the surface. It shows that spin-orbit materials are a new family in which exotic topological order quantum phenomena, such as dissipationless spin currents and axion-like electrodynamics, may be found without the need for an external magnetic field. The results presented in this study also demonstrate a general measurement algorithm of identifying and characterizing topological insulator materials for future research which can be utilized to discover, observe and study other forms of topological order and quantum entanglements in nature. A detailed study of topological order and quantum entanglement can potentially pave the way for fault-tolerant (topological) quantum computing [10].

Figure 3: A new type of quantum matter called a topological insulator contains only half an electron pair (represented by just one Dirac cone in schematic crystal structure at top left), which is observed in the form of a single ring (red) in the center of the electron-map (top right) with electron spin in only one direction. This highly unusual observation shows that if an electron is tagged "red" and then undergoes a full 360-degree revolution about the ring, it does not recover its initial face as an ordinary everyday object would, but instead acquires a different color "blue" (represented by the changing color of the arrows around the ring). This new quantum effect can be the basis for the realization of a rare quantum phase that had been a long-sought key ingredient for developing quantum computers that can be highly fault-tolerant.

References:
[1] K. von Klitzing, G. Dorda, M. Pepper, "New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance", Phys. Rev. Lett. 45, 494-497 (1980). Abstract.
[2] D.C. Tsui, H. Stormer, A.C. Gossard, "Two-dimensional magnetotransport in the extreme quantum limit", Phys. Rev. Lett. 48, 1559-1562 (1982). Abstract.
[3] L. Fu, C. L. Kane and E. J. Mele, "Topological insulators in three dimensions", Physical Review Letters 98, 106803 (2007). Abstract.
[4] J. E. Moore and L. Balents, "Topological invariants of time-reversal-invariant band structures", Physical Review B 75, 121306(R) (2007). Abstract.
[5] S.-C. Zhang, "Topological states of quantum matter", Physics 1, 6 (2008). Abstract.
[6] M. Franz, "High energy physics in a new guise", Physics 1, 36 (2008). Abstract.
[7] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava and M. Z. Hasan, "A topological Dirac insulator in a quantum spin Hall phase", Nature 452, 970 (2008). Abstract.
[8] Y. Xia, D. Qian, L. Wray, D. Hsieh, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of a large-gap topological insulator class with single surface Dirac cone”, Nature Physics 5, 398 (2009). Abstract.
[9] D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of Unconventional Quantum Spin Textures in Topological Insulators", Science 323, 919 (2009). Abstract.
[10] A. Akhmerov, J. Nilsson, C. Beenakker, “Electrically detected interferometry of Majorana fermions in a topological insulator”, Phys. Rev. Lett. 102, 216404 (2009). Abstract.

Ferrofluidic Deformable Mirrors for Adaptive Optics

Ermanno F. Borra (left) and Denis Brousseau (right)



[This is an invited article. The authors have built the first deformable liquid mirror from a magnetic liquid or “ferrofluid”, which is set to find wide range of applications including correction of aberration in the images of telescopes and many other optical devices. -- 2Physics.com]



Authors: Denis Brousseau and Ermanno F. Borra
Affiliation: Université Laval, Département de physique, de génie physique et d’optique and Centre d’Optique, Photonique et Laser (COPL), Québec, Canada.

For roughly the last 25 years, adaptive optic (AO) systems were primarily used for astronomical applications. In the last 10 years, the range of scientific applications of AO has soared and now includes vision science, medical imaging and free space optical communications to name only a few. These new applications have stimulated research for low-cost, high-stroke deformable mirrors with a large number of actuators. Most actual deformable mirrors are expensive, costing about $1000 US per actuator. Current high-stroke deformable mirrors like the Imagine Optics 52-actuator MIRAO DM can produce large deformations (50 µm peak-to-valley tilt) but having a larger number of actuators would greatly increase its cost. Micro-Electro-Mechanical Systems (MEMS) deformable mirrors having large numbers of actuators (over 1000) and fabricated by a technique similar to surface micromachining have a great potential for low cost, but are currently limited to strokes of only a few microns.

It is well known that a liquid follows an equipotential surface to a high degree of precision. For example, the surface of a rotating pool of mercury takes a parabolic shape which can be used as a the primary mirror of a low cost telescope (http://wood.phy.ulaval.ca/what.html and http://www.astro.ubc.ca/lmt/lm/index.html). During the last few years, we have developed a new type of deformable mirror made of a ferrofluid whose surface is shaped by an array of magnetic coils. A ferrofluid is a liquid that contains a suspension of small ferromagnetic particles (Ø ~ 10 nm) within a water- or oil- based carrier liquid. In the presence of an external magnetic field, the magnetic particles react with the field and the fluid surface takes a shape that is determined by the equilibrium between the magnetic, gravitational and surface tension forces. The equation that describes the shape of the surface can be derived using equations found in [1]

where µ_r and ρ are the relative permeability and density of the ferrofluid respectively, n is a unit vector perpendicular to the liquid surface and B is the external magnetic field vector at the liquid-air interface. The external magnetic field B can be produced by an array of small current carrying coils located just under the surface of the liquid. Based on this principle, we built a 37-channel deformable mirror prototype, made of a ferrofluid whose surface is actuated by a hexagonal array of small current carrying coils.

In standard modal control of deformable mirrors, the mirror surface is shaped by the linear addition of the individual response function of the actuators. We see, from the preceding equation, that in the case of a ferrofluid deformable mirror (FDM), the liquid surface deformation is non-linear with respect to the external magnetic field, and also depends on the individual orientation of the external magnetic field components. Consequently, conventional modal control of a FDM is impossible; however we have successfully developed a custom algorithm that is able to compute the currents that must be assigned to the coils for a given mirror surface shape.

Using a commonly available ferrofluid we found that a maximum deformation of over a millimeter can be achieved before reaching instability [2]. In theory, much larger deformations (several mm) could be obtained with magnetic fields having components mostly parallel to the liquid surface and/or using ferrofluids having different physical properties.

Fig. 1. A custom ferrofluid developed in our labs is shown coated with a reflective layer of MeLLF and under the influence of a magnetic field from a permanent magnet located under the container. Picture clearly shows the very large deformation amplitudes that can be obtained.

Ferrofluids have a low reflectivity similar to motor oil and for many applications must be coated with a reflective layer. This can be done using reflective liquids based on interfacial films of silver particles known as Metal Liquid-Like Films or MeLLFs [3]. MeLLFs combine the properties of metals and liquids, can be deformed and are therefore well adapted to applications in the field of liquid optics. MeLLFs are not compatible with currently available commercial ferrofluids, which are hydrophobic, and for compatibility with MeLLFs we had to developed a custom hydrophilic ferrofluid (see Fig. 1) [4]. Our team is also considering the deposition of a chemical membrane on the ferrofluid.

Our prototype consists of 37 custom made coils (actuators) closely packed in a hexagonal array 35 mm in diameter (see Fig. 2). Each coil is made of about 200 loops of AWG28 magnet wire and has an external diameter of 5 mm. A small ferrite core is placed at the center of each coil to lower the current requirement of the device. An aluminum container (not seen) filled with a one-millimetre-thick layer of ferrofluid is placed on top.

Fig. 2. Our 37-channel prototype showing the hexagonal array of 37 coils of 5-mm diameter.

Total cost of the FDM was estimated at about $100 per actuator, including materials, electronics and shop time. Costs can certainly be reduced further with improved technology.

Using our algorithm, we have computed the required currents to produce standard Zernike polynomials (http://en.wikipedia.org/wiki/Zernike_polynomials). Those currents were then fed to the FDM and the resulting wavefronts were measured using a wavefront sensor (see Fig. 3).

Fig. 3. Experimental wavefronts representing Zernike polynomials reproduced by the FDM and measured using a Shack-Hartmann wavefront sensor. Each wavefront has a PV wavefront amplitude of about 5 μm.

Because of the vector-dependent response of our device, we suspected that trying to fit real wavefronts made from combining several Zernike polynomials would result in lower wavefront residual errors than by adding the residuals of each Zernike that made up the original wavefront. We performed experiments to test this assumption. We purposely introduced optical aberrations of 0.58 µm RMS wavefront amplitude and 2.42 µm PV wavefront amplitude in our wavefront measurement setup. PSFs before and after correction can be seen in Fig. 4. The achieved Strehl ratio of the corrected wavefront is 0.84 at a wavelength of 659.5 nm.

We also introduced much greater amplitude aberrations with PV and RMS wavefront amplitudes of 11.43 and 2.58 µm respectively. The RMS residual error of the corrected wavefront was measured to be 0.15 µm. We found that this error drops to 0.05 µm if we consider only the low order aberration terms. Correction for high spatial frequency Zernike polynomials would improve if the FDM had a greater number of actuators.

Fig. 4. Experimental result showing the PSF (log scale) of an aberrated wavefront (left) corrected by using our deformable mirror (right). Strehl ratio of corrected wavefront is 0.84 (659.5 nm).

Although we got promising results, some drawbacks remain. We need to bias the surface of the liquid to allow for a push-pull effect as the amplitude varies as the square of the current applied to a given actuator (deformations can only be positive). This reduces the available stroke of the mirror and also adds a surface residual error.

A novel way to control those liquid mirrors has recently been introduced by Iqbal and Amara, and solves most of these drawbacks [5]. The technique consists of adding a constant and uniform magnetic field whose orientation is along the direction perpendicular to the surface of the liquid. The amplitude of this constant magnetic field is about 10 times greater than what is produced by the coils (~ 2.5 gauss). The magnetic field of the actuators acts as a small perturbation of the uniform field and this linearizes the response of the liquid (as shown in Fig. 5). This also has the effect of amplifying the stroke produced by the coils, reducing the required currents, so that ferrite cores in the actuators are no longer necessary, and making negative deformations possible.

Fig. 5. Measured amplitudes of the deformations produced by a single actuator in the presence of an external uniform magnetic field, as a function of current in the coil. The red and blue curves correspond to external magnetic fields of 25 and 30 gauss respectively. Negative deformations can be produced by inverting the current flow. The actuator used in the experiment has no ferrite core.

Until recently, we thought that those liquid mirrors were limited to a time response of only a few tens of hertz, because when driven at frequencies higher than about 20 Hz, we saw a rapid loss in amplitude response of the liquid and a phase lag of over 90 degrees appeared between the driving signal and the resulting liquid deformation, quite similar to the response of a low-pass RLC filter.

We demonstrated that the amplitude loss can be overcome by overdriving the coils with a very short and high amplitude current pulse launched at the beginning of each driving signal. By using this technique, a desired surface deformation is reached faster and the remaining signal stabilize the liquid shape.

We also demonstrated that the phase lag can be countered by increasing the viscosity of the ferrofluid. The critical frequency (a 90 degrees phase lag) was improved from 20 to 450 Hz by increasing the viscosity of the ferrofluid from 6 cP to 450 cP (viscosity of water is 1 cP and SAE 50 motor viscosity is about 500 cP). Since a single square wave signal sent to the liquid corresponds to two corrections (rise and fall), this actually implies a frequency response of 900 Hz. But increasing the viscosity also increases the time required for the liquid to stabilize. However, a solution to this problem is to use overdriving pulses that give an initial velocity to the liquid as discussed in the preceding paragraph.

To conclude, we have demonstrated a liquid deformable mirror prototype that can produce standard aberration terms, and we successfully corrected a 11 µm PV amplitude aberrated wavefront, yielding a residual RMS wavefront error of 0.05 µm. A new technique linearizes the response of these new deformable mirrors and allows the use of regular control algorithms. This will simplify our goal to demonstrate closed-loop operation of these new mirrors.

We have also shown the counterintuitive result that using a liquid having a sufficiently high viscosity improves their frequency response up to 900 Hz. By using both overdriving pulses and a higher viscosity ferrofluid, utilizing these mirrors in closed-loop at a running frequency of hundreds of hertz, appears to be possible. This will enable these mirrors to be used in many more applications than we previously thought. Ongoing tests on the chemical deposition of thin chemical membranes on ferrofluids could also improve the response of FDMs. We are now building a new prototype having 91 actuators of 2-mm diameter, thus reducing the footprint and allowing a higher density of actuators.

References
[1] "Interaction of a magnetic liquid with a conductor containing current and a permanent magnet"
V. V. Kiryushin and A. V. Nazarenko, Fluid Dynamics, 23, 306–311 (1988). Abstract.
[2] R. E. Rosensweig, "Ferrohydrodynamics". (Dover, 1997).
[3] "Nanoengineered astronomical optics",
E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva and H. Yockell-Lelievre, Astron. Astrophys. 419, 777-782 (2004). Abstract.
[4] "Ethylene Glycol Based Ferrofluid for the Fabrication of Magnetically Deformable Liquid Mirrors"
J. -P. Déry, E. F. Borra, and A. M. Ritcey, Chem. Mater. 20 (2008). Abstract.
[5] "Modeling of a Magnetic-Fluid Deformable Mirror for Retinal Imaging Adaptive Optics Systems"
A. Iqbal and F. B. Amara, International Journal of Optomechatronics 1, 180-208 (2007). Abstract.

Up to 400-fold Improvement in Magnetic Field Detection

W.F. Egelhoff, Jr. (photo courtesy: NIST)

A team of researchers at the National Institute of Standards and Technology (NIST) has reported
dramatically enhanced sensitivity -- a 400-fold improvement in some cases -- in a carefully built magnetic flux concentrator that draw in external magnetic field lines and concentrate them in a small region. The flux concentrator is a kind of magnetic sandwich that interleaves layers of a magnetic alloy with a few nanometers of silver “spacer”. They are used to amplify fields in compact magnetic sensors used for a wide variety of applications from weapons detection and non-destructive testing to medical devices and high-performance data storage.

Those applications and many others are based on thin films of magnetic materials in which the direction of magnetization can be switched from one orientation to another. An important characteristic of a magnetic film is its saturation field, the magnitude of the applied magnetic field that completely magnetizes the film in the same direction as the applied field—the smaller the saturation field, the more sensitive the device.

The saturation field is often determined by the amount of stress in the film—atoms under stress due to the pull of bonds with neighboring atoms are more resistant to changing their magnetic orientation. Metallic films develop not as a single monolithic crystal, like diamonds, but rather as a random mosaic of microscopic crystals called grains. Atoms on the boundaries between two different grains tend to be more stressed, so films with a lot of fine grains tend to have more internal stress than coarser grained films. Film stress also increases as the film is made thicker, which is unfortunate because thick films are often required for high magnetization applications.

Transmission electron microscope (TEM) images show sections of a continuous 400-nanometer-thick magnetic film of a nickle-iron-copper-molybdenum alloy (top) and a film of the same alloy layered with silver every 100 nanometers (bottom). By relieving strain in the film, the silver layers promote the growth of notably larger crystal grains in the layered material as compared to the monolithic film (several are highlighted for emphasis). Electron diffraction patterns (insets) tell a similar story—the material with larger crystal grains display sharper, more discrete scattering patterns. (Color added for clarity). Image credit: J. Bonevich, NIST

The NIST research team discovered that magnetic film stress could be lowered dramatically by periodically adding a layer of a metal, having a different crystal structure or lattice spacing, in between the magnetic layers. Although the mechanism isn’t completely understood, according to lead author William Egelhoff Jr., the intervening layers disrupt the magnetic film growth and induce the creation of new grains that grow to be larger than they do in the monolithic films. The researchers prepared multilayer films with layers of a nickel-iron-copper-molybdenum magnetic alloy each 100 nanometers (nm) thick, interleaved with 5-nm layers of silver. The structure reduced the tensile stress (over a monolithic film of equivalent thickness) by a factor of 200 and lowered the saturation field by a factor of 400.

Reference
"400-fold reduction in saturation field by interlayering",
W.F. Egelhoff, Jr., J. Bonevich, P. Pong, C.R. Beauchamp, G.R. Stafford, J. Unguris, and R.D. McMichael,
J. Appl. Phys. 105, 013921 (2009). Abstract.

[We thank Media relations, NIST for materials used in this report]

Field Effect Tuning of Superconductivity at Oxide Interfaces

Photo of the Geneva Group: (from Left to Right) Stefano Gariglio, Andrea Caviglia, Claudia Cancellieri, Nicolas Reyren and Jean-Marc Triscone

[This is an invited article based on recent work of this collaboration -- 2Physics.com]



Authors: A.D. Caviglia¹ , S. Gariglio¹, N. Reyren¹, C. Cancellieri¹, D. Jaccard¹, S. Thiel², G. Hammerl², J. Mannhart², J.-M. Triscone¹

Affiliation: ¹Département de Physique de la Matière Condensée, University of Geneva, Genève, Switzerland, >>Link to Group Homepage
²Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, Germany, >>Link to Group Homepage

Charge transfer in semiconductors interfaces has brought about exceptional technological progress, one of the best examples being the development of the Field Effect Transistor (FET). Applying the same principle to materials with a wider spectrum of electronic properties, such as complex oxides, is an exciting opportunity both for fundamental and applied physics. These oxide compounds often exhibit strong electronic correlations and complex phase diagrams. In such systems, the electric field effect can be used to tune the ground state of the system [1]. These materials also display a broad range of functional properties, such as high dielectric permittivity, piezoelectricity and ferroelectricity, superconductivity, spin polarised current, colossal magnetoresistance and ferromagnetism. Recent advances in growth methods have allowed the fabrication of atomically abrupt interfaces between these materials where novel electronic phases are created. Indeed the emerging field of complex oxide interfaces has a high potential impact for applications [2] and has been classified as one of the 10 breakthroughs of 2007 by the journal Science [3].

Fig.1 Photo of the device (courtesy of J. Mannhart)

The LaAlO3/SrTiO3 interface
A particularly interesting system is the interface between band insulators LaAlO3 and SrTiO3, which was reported to be conducting in 2004 in a seminal publication [4]. This result is indeed amazing: by depositing on top of an insulating crystal (SrTiO3) a thin film of a good insulator (LaAlO3), a metallic interface is generated. This immediately calls to mind the two dimensional (2D) electron gas generated by modulation doping in III-V semiconductors. Correlated oxide systems are however more complex than semiconductors and in fact, in 2007 we discovered that this metallic interface undergoes a 2D superconducting transition at around 200 mK [5]. The superconducting sheet is 10 nm thick and confined between two dielectrics. What a perfect opportunity to try modulating the superconducting state by applying an external electric field!

Fig.2: Atomic view of the interface (courtesy of J. Mannhart)

A complex phase diagram uncovered
Hence a gate electrode has been deposited on the backside of the SrTiO3 crystal and the sheet resistance as a function of temperature for different applied gate voltages has been measured down to 20 mK. For large negative voltages (typically less than -200 V), corresponding to the smallest accessible electron densities, the sheet resistance increases as the temperature is decreased, indicating an insulating ground state. No traces of superconductivity are left! As the electron density is increased the system becomes a superconductor. A further increase in the electron density produces first a rise of the critical temperature to a maximum of 310 mK. For larger voltages the critical temperature decreases again. This is a beautiful example of a quantum phase transition: a change of the electronic phase of matter driven not by a variation of temperature but by the application of an electric field. These findings have been reported recently in the journal Nature [6].

A bright future
This fascinating interface offers many possibilities, among them, fundamental studies of quantum phase transitions in low dimensions. This discovery also opens the way to the fabrication of new mesoscopic devices based on the ability to switch on and off the superconducting state at the nanoscale.

References
[1] "Electric field effect in correlated oxide systems", C. H. Ahn, J.-M. Triscone and J. Mannhart,
Nature 424, 1015-1018 (2003). Abstract.
[2] "When Oxides Meet Face to Face", Elbio Dagotto, Science 318, 1076 (2007). Abstract.
[3] Science 318, 1844 (2007). Link.
[4] "A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface",
A. Ohtomo and H. Y. Hwang, Nature 427, 423-426 (2004). Abstract.
[5] "Superconducting Interfaces Between Insulating Oxides", N. Reyren, S. Thiel, A. D. Caviglia, L. Fitting Kourkoutis, G. Hammerl, C. Richter, C. W. Schneider, T. Kopp, A.-S. Rüetschi, D. Jaccard, M. Gabay, D. A. Muller, J.-M. Triscone, J. Mannhart, Science 317, 1196-1199 (2007). Abstract.
[6] "Electric field control of the LaAlO3/SrTiO3 interface ground state", A. D. Caviglia, S. Gariglio, N. Reyren, D. Jaccard, T. Schneider, M. Gabay, S. Thiel, G. Hammerl, J. Mannhart & J.-M. Triscone,
Nature 456, 624-627 (2008). Abstract.

Optical Magnus Effect: Topological Monopole Deflects Spinning Light

Konstantin Y. Bliokh

[This is an invited article based on recent work of the authors -- 2Physics.com]

Authors: Konstantin Y. Bliokh, Avi Niv, Vladimir Kleiner, and Erez Hasman

Affiliation: Micro and Nanooptics Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel
>> Link to the Group Homepage

In an article published in the December 2008 issue of Nature Photonics a team from Micro- and Nanooptical Laboratory of Technion-Israel Institute of Technology has reported the first direct observation of the topological spin transport of photons, also known as the spin Hall effect of light or the optical Magnus effect [1]. The effect represents a polarization-dependent transverse deflection of the light beam upon a bending of its trajectory, and it can be attributed to a Coriolis effect or a spin-orbit coupling of light. Remarkably, the spin-orbit interaction of light has an inherent topological origin which is described by the Berry-phase monopole in the momentum space.

Vladimir Kleiner, Erez Hasman, and Avi Niv (left to right)

Two decades ago, the Berry phase brought a geometrical beauty to the description of quantum adiabatic evolution [2,3]. Afterwards, physicists realized that seemingly ‘passive’ geometrical concepts, such as Berry curvature, also manifest themselves dynamically, producing a real action on physical objects. As a result, the geometry-induced forces appear which affect the dynamics of quantum particles with some internal properties [4]. In particular, they describe the Magnus effect of quantum vortices [5] and spin Hall effect of spinning particles [6-8]. This offers a novel type of quantum transport which is robust against the details of the system and is determined solely by the geometry and intrinsic properties of the particles.

The spin-Hall effect was invented in the context of semiconductor spintronics, where it is expected to have promising applications [6]. The same effect also occurs within the fundamental equations of high-energy physics involving such intriguing mathematical objects as topological monopoles and space non-commutativity [8]. It seems that optics provides an ideal field for exploring this striking phenomenon. First, trajectory of light propagation can be directly observed in relatively clean and simple systems, and the accuracy of modern optics allows sub-wavelength resolution at nano-scales. Second, classical light captures all basic features of relativistic spinning particles, which enables one to extrapolate results to a diversity of physical systems, where such observations are impossible.

Fig. 1. The trajectories of left- and right-handed circularly polarized light beams propagating along the reflecting surface of a glass cylinder. The spin-orbit coupling between the intrinsic angular momentum of light and the curved propagation trajectory produces opposite deflections for the two beams. This is the spin Hall effect of light described by a Lorentz-force-type term from a topological monopole in momentum space [This figure is reprinted from "The dynamics of spinning light" by Franco Nori, Nature Photonics 2, 717 (2008). Our thanks to 'Nature Photonics']

The experiment of Ref. 1 was realized by launching a laser beam at a grazing angle to the internal surface of a glass cylinder, so that the light propagated along a smooth helical trajectory due to total internal reflection, Fig. 1. Such a helical path induces a spin-orbit interaction between the geometry of the trajectory and the intrinsic spin angular momentum carried by the polarized light. The theory and experiment of Ref. 1 provide a fairly complete picture of the geometrodynamical evolution of polarized light. On the one hand, the geometry of the trajectory determines the variations of the polarization of light. On the other hand, a spin-dependent perturbation of the trajectory occurs which deflects the right- and left-handed circularly polarized beams in opposite directions tangent to the cylinder surface (see Fig. 1).

In addition to fundamental interest, the spin Hall effect of light may have promising applications in photonics. Utilizing this effect in optical devices may lead to the development of a promising new area of research – spinoptics. The hope is that we will be able to control light in all-optical nanometer scale devices in ways that were impossible before [9,10]. While tiny wavelength-scale effects were negligible a decade ago, nowadays they can be crucial for numerous nano-optical applications.

References:
[1] “Geometrodynamics of Spinning Light”, K.Y. Bliokh, A. Niv, V. Kleiner, E. Hasman, Nature Photonics, 2, 748 (2008). Abstract.
[2] “Quantal Phase Factors Accompanying Adiabatic Changes”, M.V. Berry, Proc. R. Soc. A 392, 45 (1984). Abstract.
[3] “Geometric Phases in Physics”, A. Shapere, F. Wilczek (eds) (World Scientific, Singapore, 1989).
[4] “Origin of the Geometric Forces Accompanying Berry’s Geometric Potentials”, Y. Aharonov, A. Stern, Phys. Rev. Lett. 69, 3593 (1992). Abstract.
[5] “Transverse Force on a Quantized Vortex in a Superfluid”, D.J. Thouless, P. Ao, Q. Niu, Phys. Rev. Lett. 76, 3758 (1996). Abstract.
[6] “Dissipationless Quantum Spin Current at Room Temperature”, S. Murakami, N. Nagaosa, S.C. Zhang, Science 301, 1348 (2003). Abstract.
[7] “Topological Spin Transport of Photons: The Optical Magnus Effect and Berry phase”, K.Y. Bliokh, Y.P. Bliokh, Phys. Lett. A 333, 181 (2004). Abstract.
[8] “Spin Hall Effect and Berry Phase of Spinning Particles”, A. Bérard, H. Mohrbach, Phys. Lett. A 352, 190 (2006). Abstract.
[9] “Observation of the Spin Hall Effect of Light via Weak Measurements”, O. Hosten, P. Kwiat, Science 319, 787 (2008). Abstract. Related article in 2Physics.
[10] “Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect”, K.Y. Bliokh, Y. Gorodetski, V. Kleiner, E. Hasman, Phys. Rev. Lett. 101, 030404 (2008). Abstract.

World-record Performance using a Silicon-based Avalanche Photodetector

Mario Paniccia [Photo courtesy: Intel]

In an article published today in online version of Nature Photonics, a team led by Intel researchers reported a path-breaking advancement in the field of Silicon Photonics by achieving world-record performance with a silicon-based Avalanche Photodetector (APD), a light sensor that gains superior sensitivity by detecting light and amplifying weak signals as light is directed onto silicon. This could lower costs and improve performance as compared to commercially available optical devices.

Silicon Photonics is an emerging technology using standard silicon to send and receive optical information among computers and other electronic devices. The technology aims to address future bandwidth needs of data-intensive computing applications such as remote medicine and lifelike 3-D virtual worlds.

The photodetector developed by the team is Ge/Si-based and has built-in amplification, which makes it much more useful in instances where very little light falls on the detector. It is called an avalanche photodetector because an avalanche process occurs inside the device. First, a negative and a positive charge (electrons and holes in semiconductor terminology) are created when the light strikes the detector. The electron is accelerated by an electric field until it attains a high enough energy to slam into a silicon atom and create another pair of positive and negative charges. Each time this happens the number of total electrons doubles, until this “avalanche” of charges are collected by the detection electronics.

This amplification effect (called gain) is the key to the device, and it serves as the motivation for why anyone would try to do this in silicon and not just continue to use traditional InP (Indium phosphide)-based APDs. The materials properties of silicon inherently led to lower noise and better performance in this avalanche process.

Image: A ladybug crawls across an experimental Avalanche Photodetector chip containing silicon optical devices that are only a fraction of a millimeter [Photo courtesy: Intel]

The APD device developed by the Intel team used silicon and CMOS processing to achieve a "gain-bandwidth product" of 340 GHz -- the best result ever measured for this key APD performance metric. This opens the door to lower the cost of optical links running at data rates of 40Gbps or higher and proves, for the first time, that a silicon photonics device can exceed the performance of a device made with traditional, more expensive optical materials such as indium phosphide (InP).

"This research result is another example of how silicon can be used to create very high-performing optical devices," said Dr. Mario Paniccia, Intel Fellow and director of the company's Photonics Technology Lab. "In addition to optical communication, these silicon-based APDs could also be applied to other areas such as sensing, imaging, quantum cryptography or biological applications."

Reference
"Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–bandwidth product"
Yimin Kang, Han-Din Liu, Mike Morse, Mario J. Paniccia, Moshe Zadka, Stas Litski, Gadi Sarid, Alexandre Pauchard, Ying-Hao Kuo, Hui-Wen Chen, Wissem Sfar Zaoui, John E. Bowers, Andreas Beling, Dion C. McIntosh, Xiaoguang Zheng & Joe C. Campbell,
Nature Photonics (7 December 2008 doi:10.1038/nphoton.2008.247). Abstract.

Squeezing of Quantum Noise successfully used to develop First Tunable, ‘Noiseless’ Amplifier

Konrad Lehnert [Photo Courtesy: JILA, Boulder]

By significantly reducing the uncertainty in delicate measurements of microwave signals, a team of researchers from the National Institute of Standards and Technology (NIST) and Joint Institute of Laboratory Astrophysics (JILA) could successfully develop the first tunable “noiseless” amplifier which could boost the speed and precision of quantum computing and communications systems.

Conventional amplifiers add unwanted “noise,” or random fluctuations, when they measure and boost electromagnetic signals. Amplifiers that theoretically add no noise have been demonstrated before, but the JILA/NIST technology offers better performance and is the first to be tunable, operating between 4 and 8 GHz, according to JILA group leader Konrad Lehnert. It is also the first amplifier of any type ever to boost signals sufficiently to overcome noise generated by the next amplifier in a series along a signal path, Lehnert says, a valuable feature for building practical systems.

Noisy amplifiers force researchers to make repeated measurements of, for example, the delicate quantum states of microwave fields—that is, the shape of the waves as measured in amplitude (or power) and phase (or point in time when each wave begins). The rules of quantum mechanics say that the noise in amplitude and phase can’t both be zero, but the JILA/NIST amplifier exploits a loophole stipulating that if you measure and amplify only one of these parameters—amplitude, in this case—then the amplifier is theoretically capable of adding no noise. In reality, the JILA/NIST amplifier adds about half the noise that would be expected from measuring both amplitude and phase.

The JILA/NIST amplifier could enable faster, more precise measurements in certain types of quantum computers—which, if they can be built, could solve some problems considered intractable today—or quantum communications systems providing “unbreakable” encryption. It also offers the related and useful capability to “squeeze” microwave fields, trading reduced noise in the signal phase for increased noise in the signal amplitude. By combining two squeezed entities, scientists can “entangle” them, linking their properties in predictable ways that are useful in quantum computing and communications. Entanglement of microwave signals, as opposed to optical signals, offer some practical advantages in computing and communication such as relatively simple equipment requirements, Lehnert says.

[Image Credit: M. Castellanos-Beltran/JILA] In the JILA/NIST “noiseless” amplifier, a long line of superconducting magnetic sensors (beginning on the right in this photograph) made of sandwiches of two layers of superconducting niobium with aluminum oxide in between, creates a 'metamaterial' that selectively amplifies microwaves based on their amplitude rather than phase.

The new amplifier is a 5-millimeter-long niobium cavity lined with 480 magnetic sensors called SQUIDs (superconducting quantum interference devices). The line of SQUIDs acts like a “metamaterial,” a structure not found in nature that has strange effects on electromagnetic energy. Microwaves ricochet back and forth inside the cavity like a skateboarder on a ramp. Scientists tune the wave velocity by manipulating the magnetic fields in the SQUIDs and the intensity of the microwaves. An injection of an intense pump tone at a particular frequency, like a skateboarder jumping at particular times to boost speed and height on a ramp, causes the microwave power to oscillate at twice the pump frequency. Only the portion of the signal which is synchronous with the pump is amplified.

Reference
"Amplification and squeezing of quantum noise with a tunable Josephson metamaterial",
M.A. Castellanos-Beltran, K.D. Irwin, G.C. Hilton, L.R. Vale and K.W. Lehnert,
Nature Physics, published online: 5 Oct. 5 2008; doi:10.1038/nphys1090. Abstract

[We thank Media Relation, NIST for materials used in this posting]

Phase Transitions of Dirac Electrons in Bismuth in a High Magnetic Field

N. Phuan Ong

[This is an invited article based on recent works of the authors.
-- 2Physics.com]

Authors: N. P. Ong, Lu Li, Joseph G. Checkelsky and R. J. Cava

Affiliation: Dept of Physics, Princeton University
[Link to Ong Lab -->]

In most metals and semiconductors, the motion of an electron is well described by the Schrödinger equation. The kinetic energy increases as the square of the momentum just as for electrons in vacuum (Fig. 1a). However, in certain materials, the electronic energy increases linearly with the momentum (Fig. 1b). The linear dispersion is reminiscent of that of neutrinos and photons. Examples of such materials are graphene [1] (a single layer of carbon peeled from graphite), bismuth and antimony and their alloy BiSb, and a class of organic metals called “ET” salts. The quasiparticles (broken Cooper pairs) in the unconventional superconductors based on copper oxide and on strontium ruthenate also display a linear dispersion. In these “Dirac materials”, the electrons are accurately described by the Dirac Hamiltonian, except that the effective velocity of light is reduced by a factor of about 300. The effective fine structure constant is roughly 3 instead of 1/137.

Lu Li [Left], Joe Checkelsky [Right]

In comparison with relativistic electrons in vacuum, Dirac electrons living in solids have several distinguishing features. First, a magnetic field of a few Tesla is sufficient to quantize the orbits of Dirac electrons to form a series of Landau levels. To obtain similar effects in relativistic electrons in vacuum, one would need magnetic fields in excess of a million Tesla. As the applied field is increased, the Landau levels are successively emptied. This leads to the well-known quantum oscillations in curves of the resistivity and magnetization versus field (Fig. 1c) (the periods of these oscillations are routinely used to measure the caliper of Fermi Surfaces).

R. J. Cava

If the field is strong enough, all the Dirac electrons are forced into the lowest Landau Level. In this situation, the effects of mutual Coulomb repulsion between the electrons are greatly enhanced. This is particularly true for Dirac electrons which (unlike the Schrödinger case) do a poor job of screening each other’s Coulomb potential. Secondly, in solids, Dirac electrons occupy distinct but equivalent Fermi Surface pockets or “valleys”. The additional degree of freedom, akin to “flavor” in particle physics, is known as valley degeneracy. These ingredients suggest that, in a steadily increasing magnetic field, Dirac electrons may undergo a sudden phase transition to a collective state in order to relief the effects of mutual repulsion.

The Fermi surface of bismuth is comprised in part of 3 equivalent electron ellipsoids which are accurately described as Dirac electrons (the Fermi Surface encloses all occupied states in momentum space). Hence bismuth presents a gas of Dirac electrons which come in 3 flavors, corresponding to the 3 ellipsoids. The electrons coexist with an equal concentration of holes, which are positively charged carriers obeying the ordinary Schrödinger equation. If the electrons can be studied free from interference from the holes, we could investigate the question posed. Unfortunately, Nature has diabolically arranged matters so that the interference from the holes is a maximum when the magnetic field is pointed along the most interesting direction -- the trigonal axes (along this axis, strict equivalency between the 3 electron flavors is maintained). In this field direction, the period of the quantum oscillations is nearly the same for both holes and electrons. Because the hole oscillations have a larger amplitude, they completely obscure the electron oscillations. For 4 decades, this has prevented researchers from “seeing” what the Dirac electrons are doing in a magnetic field.

In Ref. 2, we extended torque magnetometry, a technique pioneered by David Shoenberg, to fields of 32 Tesla. In bismuth, the dynamics of the electrons are conveniently described in terms of effective-mass parameters which assume different values along the 3 symmetry axes. If the magnetic field is tilted at an angle to a symmetry axis, the mass anisotropy leads to a magnetic moment that is at an angle to the field. This immediately leads to a torque on the sample. As shown by Shoenberg, the torque signal provides a remarkably sensitive way to detect individual Landau Levels as they cross the chemical potential. By careful choice of the torque axes, we were able to tease out the torque signals of the Dirac electrons and distinguish them from the holes (see the low-field regions in Fig. 2). This solved the problem mentioned.

Fig. 1a: Quadratic energy dispersion of electrons obeying Schrödinger equation. Fig. 1b: Linear dispersion of Dirac electrons. Fig. 1c: Curves of the torque signal versus magnetic field in bismuth at 0.3 K at selected tilt angles of the field to the trigonal axis. Rapid oscillations at low fields are Landau Level crossings. The red and black arrows indicate sharp electronic transitions to a collective state [2].

With the ability to see what the Dirac electrons are doing, we proceeded to investigate their behavior in an intense magnetic field aligned nearly parallel with the trigonal axis. We found that at low temperature (below 2 K), the electrons exhibit a sharp transition to a collective state (red arrows in Fig. 1c). In contrast with the torque signal at lower fields which are replete with Landau oscillations (Fig. 2), the torque flat lines at a value close to zero above the transition field. In this region, which extends to very high fields over a narrow range of tilt angles, Landau levels are completely absent (upper right quadrant of Fig. 2). We have dubbed this the “dead zone”. Interestingly, when we exit the dead zone by further increasing the field at a finite tilt angle (see black arrows in Fig. 1c), the remaining Landau levels reappear.

Fig. 2 Curves of the derivative of the torque signal versus magnetic field at selected tilt angles q [2]. Peaks (labeled by 1+ or 0-) occur when Landau Levels cross the chemical potential. In the dead zone (upper right quadrant bounded by the gray curve), the curves assume flat-line behavior.

What is the state in the dead zone? Our best guess is that the Dirac electrons have transitioned to a collective state in which their total Coulomb energy is dramatically lowered. We may draw an analogy with ferromagnetism. In an ordinary metal, each electron can align its spin up or down. If the Coulomb repulsion is large compared with the kinetic energy, the electrons transition to the ferromagnetic state in which all spins are aligned up (say). The Pauli Principle then guarantees that the electrons are always kept maximally apart from each other. This results in a large lowering of the mutual repulsion energy (at the price of a small increase in kinetic energy). The 3 equivalent valleys for the Dirac electrons in bismuth constitute a degree of freedom that mimics the spin degree in a ferromagnet. We propose that, in the dead zone, all Dirac electrons occupy one of the valleys (or a linear combination of the 3) so that they can stay maximally apart from each other. This collective state, dubbed “valley ferromagnetism”, was previously proposed for bilayer GaAs in the quantum Hall effect state [3].

The present results share a common thread with recent developments in several areas of condensed matter physics. The Dirac electrons in (2 dimensional) graphene occupy 2 equivalent valleys. There is recent evidence [4] that, in an intense field, they also undergo a phase transition to a high-field state in which the degeneracy between the 2 valleys is lifted. Interesting Dirac states are predicted to exist on a 2D interface separating regions in which the Dirac mass has opposite signs. The massless Dirac states at the interface are chiral, i.e. they propagate in only one direction depending on the spin. The recent prediction [5] of quantized spin Hall currents carried by these chiral states has received strong support from experiments [6] on HgTe quantum wells. The 3-dimensional alloy Bi-Sb has recently drawn strong interest because of the prediction [7] that it harbors surface Dirac states that are chiral as well as “topological” in nature. Using angle-resolved photomission spectroscopy (ARPES), Hasan and collaborators recently observed directly the surface states [8]. Very recent spin-resolved ARPES experiments have confirmed the unique spin polarization of the surface states in both pure Sb and Bi-Sb [9]. Lastly, the possibility of Majorana fermions living at the edge of a p-wave superconductor has been discussed but the experimental situation is still uncertain.

References
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[9] M. Z. Hasan, private communication.