Quantum Ratchet in Graphene: One-way Electron Traffic at Atomic Scale

S.D. Ganichev (Left) and S.A. Tarasenko (Right)

Authors: 
S.D. Ganichev¹ and S.A. Tarasenko²

Affiliation:
¹Terahertz Center, University of Regensburg, Germany
²Ioffe Physical-Technical Institute, St. Petersburg, Russia

A mechanical or electronic system driven by alternating force can exhibit a directed motion facilitated by thermal or quantum fluctuations. Such a ratchet effect occurs in systems with broken spatial inversion symmetry. Canonical examples are the ratchet-and-pawl mechanisms in watches, electric current rectifying diodes and transistors in electronics, and Brownian molecular motors in biology [1,2]. The ratchet suggests one-way traffic. One can pull it back and forth, but it moves predominantly in a certain direction. Therefore, the effect has fascinating ramifications in engineering and natural sciences.

Now an international consortium consisting of research groups from Germany, Russia, Sweden, and the U.S. has demonstrated that electronic ratchets can be successfully scaled down to one-atom thick layers [3]. Specifically, it has been shown that graphene layers support a ratchet motion of electrons when placed in a static magnetic field. The ac electric field of terahertz radiation [4] was applied to push the Dirac electrons back and forth, while the magnetic field acted as a valve letting the electrons move in one direction and suppressing the oppositely directed motion. The resulting magnetic quantum ratchet transforms the ac power into a dc current, extracting work from the out-of-equilibrium Dirac electrons driven by undirected periodic forces.

Graphene, a one-atom-thick layer of carbon with a honeycomb crystal lattice [5], is usually threated as a spatially symmetric structures, as far as its electric or optical properties are concerned. Driven by a periodic electric field, no directed electric current can be expected to flow. However, if the space inversion symmetry of the structure is broken due to the substrate or chemisorbed adatoms on the surface, an electronic ratchet motion can arise. In Ref.[3], we and our colleagues report on the observation and experimental and theoretical study of quantum ratchet effects in single-layer graphene samples, proving and quantifying the underlying spatial asymmetry.

Figure 1: Alternating electric field drives a ratchet current in graphene.

The physics behind the magnetic quantum ratchet effect in graphene is illustrated in Fig. 1. The alternating electric field E(t) drives Dirac electrons back and forth in the graphene plane. Due to the Lorentz force, the applied static magnetic field B deforms the electron orbitals such that the right-moving electrons have their centre of gravity shifted upwards, while the left-moving electrons are shifted downwards. (In quantum mechanical consideration, the shift is caused by the magnetic-field-induced coupling between σ- and π-band states). For spatial symmetric systems the net dc current would vanish. However, in a graphene layer with spatial asymmetry, e.g., caused by top adsorbates, the electrons shifted upwards feel more disorder and exhibit a lower mobility than the electrons shifted downwards and moving in the opposite direction. This difference in the effective mobility for the right- and left-moving carriers results in a net dc current. The current scales linearly with the magnetic field, changes a sign by switching the magnetic field polarity, and proportional to the square of the amplitude of the ac electric field. The linear dependence on B comes from the Lorentz force. The electric field appears twice: on the one hand, it causes the oscillating motion of carriers in the plane, and on the other, the Lorentz force itself is proportional to the electron velocity.

The ratchet motion implies that the particle flow depends on the orientation of the ac force with respect to the direction of built-in spatial asymmetry. In the case of magnetic quantum ratchets, where the asymmetry stems from the magnetic field, the relevant parameter is the angle β between the ac electric field E(t) and the static magnetic field B. Shown in Fig. 2 is the measured dependence of the dc current on the angle β. The current reaches a maximum for the perpendicular electric and magnetic fields and remains finite for the co-linear fields. The whole angular dependence is well described by the equation

j_x(β) = j₁ Cos(2β) + j₂

with two contributions j₁ and j₂, which is in agreement with the developed theory [see Ref.3]. It has also been shown that the ratchet transport can be induced by a force rotating in space. By exciting the graphene samples with a clockwise or counterclockwise rotating in-plane electric field E(t), the dc current is detected. Interestingly, the current measured along the static magnetic field turns out to be sensitive to the radiation helicity being of the opposite sign for the clockwise and counterclockwise rotating fields.

Figure 2: Dependence of the ratchet current on the orientation of ac electric field. Experimental data (dots) are obtained for an epitaxial graphene on SiC at temperature 115K, magnetic field 7T, and electric field amplitude 10 kV/cm. Solid line is a theoretical fit.

Graphene may be the ultimate electronic material, possibly replacing silicon in electronic devices in the future. It has attracted worldwide attention from physicists, chemists, and engineers. The discovery of the ratchet motion in this purest possible two-dimensional system known in nature indicates that the orbital effects may appear and be substantial in other two-dimensional crystals such as boron nitride, molybdenum dichalcogenides and related heterostructures. The measurable orbital effects in the presence of an in-plane magnetic field provide strong evidence for the existence of structure inversion asymmetry in graphene.

References:
[1] R. P. Feynman, R. B. Leighton, and M. Sands, "The Feynman Lectures on Physics, Vol. 1" (Addison-Wesley, 1966).
[2] Peter Hänggi and Fabio Marchesoni, "Artificial Brownian motors: controlling transport on the nanoscale", Review of Modern Physics, 81, 387 (2009). Abstract.
[3] C. Drexler, S. Tarasenko, P. Olbrich, J. Karch, M. Hirmer, F. Müller, M. Gmitra, J. Fabian, R. Yakimova, S. Lara-Avila, S. Kubatkin, M. Wang, R. Vajtai, P. Ajayan, J. Kono, and S.D. Ganichev: "Magnetic quantum ratchet effect in graphene", Nature Nanotechnology 8, 104 (2013). Abstract.
[4] S.D. Ganichev and W. Prettl, "Intense Terahertz Excitation of Semiconductors" (Oxford Univ. Press, 2006).
[5] A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, "The electronic properties of graphene". Review of Modern Physics, 81, 109 (2009). Abstract.

Quantum Flutter: A Dance of an Impurity and a Hole in a Quantum Wire

[Clockwise from Top left]: Charles J. M. Mathy, Eugene Demler, Mikhail B. Zvonarev.

Authors: 
Charles J. M. Mathy^1,2, Mikhail B. Zvonarev^2,3,4, Eugene Demler²

Affiliation:
¹ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts, USA
³Université Paris-Sud, Laboratoire LPTMS, UMR8626, Orsay, France,
⁴CNRS, Orsay, France.

What happens when a particle moves through a medium at a velocity comparable to the speed of sound? The consequences lie at the heart of several striking phenomena in physics. In aerodynamics, for example, an object experiencing winds close to the speed of sound may experience a vibration that grows with time called flutter, which can ultimately have dramatic consequences such as the destruction of aeroplane wings or the iconic Tacoma Narrows bridge collapse. Other examples of physics induced by fast motion include acoustic shock waves and Cerenkov radiation. What we addressed in our work [1] was the effect of fast disturbances in strongly interacting quantum systems of many particles, in a case where the particles are effectively restricted to move in one dimension known as a quantum wire.

When the interactions between particles are weak, quantum systems can sometimes be described by a simple hydrodynamic equation. For example, the Gross-Pitaevskii Equation (GPE) describes the evolution of a weakly coupled gas of bosons at low temperatures when it forms a Bose-Einstein condensate. The GPE is analogous to equations found in hydrodynamics, which explains why one can see analogs of classical hydrodynamical effects such as shock waves and solitons in these systems [2,3]. But what if the interactions are too strong and such an approximation breaks down?

We have found a model that shows interesting physics induced by supersonic motion which goes beyond a hydrodynamical description [1]. The system is a one-dimensional gas of hardcore bosons known as a Tonks-Girardeau gas (TG) [4]. We start the system in its ground state and inject a supersonic impurity that interacts repulsively with the background particles. We obtained exact results on what happens next using an approach from mathematical physics called the Bethe Ansatz approach, coupled with large-scale computing resources [5]. Thus we track the impurity velocity as a function of time and find two main surprising features. Firstly, the impurity does not come to a complete stop, instead it only sheds part of its momentum and keeps on propagating at a reduced velocity forever (Fig 1a). Secondly, the impurity velocity oscillates a function of time, a phenomenon we call quantum flutter as it arises from nonlinear interactions of a fast particle with its environment (see Fig. 1b).

Figure 1: Impurity momentum evolution and quantum flutter:
a, Schematic picture of our setup. Top: We start with a one-dimensional gas of hardcore bosons of mass m known as a Tonks Girardeau (TG) gas (red arrows), in its ground state. We then inject an impurity also of mass m with finite momentum Q (green arrow). Middle: The impurity loses part of its momentum by creating a hole around itself (sphere) and emitting a sound wave in the background gas (blue arrow). However it retains a finite momentum Q_sat after this process and carries on propagating without dissipation. Bottom: legend of the different characters in the story.
b, Time evolution of the expected momentum of the impurity, <P̂_↓(t)>. The momentum decays to a finite value Q_sat, and shows oscillations around Q_sat at a frequency we call ω_osc. The background gas has density ρ_↑, and we define a Fermi momentum k_F = πρ_↑, a Fermi energy E_F = k_F²/(2m) where m is the mass of the particles, and a Fermi time t_F = 1/E_F. Inset: zoom into the plot of <P̂_↓(t)> showing the oscillations we call quantum flutter.
c, Time evolution of the density of the background gas in the impurity frame. More precisely, shown is the density-density correlation function G_↓↑(x,t) = <ρ_↓(0,t) ρ_↑(x,t)> in units of ρ_↑/L where L is the system size, and the position along the wire is written in units of the interparticle distance ρ_↑^-1 in the background gas. Here ρ_↑ is the density of the background gas, and ρ_↓ the density of the impurity. G_↓↑(x,t) is effectively the density of the background gas with respect to the impurity position. We see the formation of the correlation hole around x ρ_↑ = 0 (blue valley), and the emission of the sound wave (red ridge). Underneath a schematic illustration of the dynamics is given: the blue arrow represents the emitted sound wave, the sphere is the hole, and the green arrow the impurity (see a). Inside the correlation hole the impurity and hole are dancing, meaning that they are oscillating with respect to each other, the phenomenon we denote as quantum flutter.

Using the exact methods just mentioned we were able to look in detail at the dynamical processes underlying quantum flutter. The time evolution of the impurity in the gas of bosons can be broken down into several steps. First the impurity carves out a depletion of the gas around itself, called a correlation hole. It expels the background density into a sound wave that carries away a large part of the momentum of the impurity, but not of all it (fig 1c). In fact the impurity retains part of its momentum and no longer sheds momentum because of kinematic constraints: there are no sound waves it can emit in the background gas while conserving momentum and energy.

After formation of the correlation hole, the impurity momentum starts to oscillate. When the dynamics of a quantum system shows a feature that is periodic in time, typically the frequency of the feature corresponds to an energy difference between two states of the system. Examples include light emission of an atom, or spin precession in response to a magnetic field, which underlies Nuclear Magnetic Resonance. In our case, the two states are an exciton and a polaron. The exciton corresponds to the impurity binding to a hole, since if the impurity repels the background gas, it is attracted to a hole (i.e. a missing particle in the background). The polaron is an impurity dressed due to interactions with the background particles, which affects its properties such as its effective mass: it becomes heavier as it carries a cloud of displaced background particles around it [6]. Thus we arrive at the following picture, as shown schematically in Fig. 2: first the impurity causes the emission of a sound wave in the background gas and creation of a hole close to it. It can bind to this hole and form an exciton, or not bind to it and form a polaron instead. In fact the impurity does both in the sense that it forms a quantum superposition of a polaron and an exciton. This quantum superposition leads to oscillations in the impurity velocity, a phenomenon called quantum beating, which is analogous to Larmor precession of a spin in a magnetic field. The difference here is that the two states that are beating, the exciton and polaron, are strongly entangled many-particle states. That we observe long-lived quantum coherence effects in a system composed of infinitely many particles is surprising. Namely, typically such systems exhibit decoherence, such that if one puts a particle in a quantum superposition of two states, the superposition decays because of interactions with other particles.

Figure 2: Origin of quantum flutter:
a, The quantum flutter oscillations originate from the formation of a superposition of entangled states of the impurity with its environment. After the impurity is injected in the system is creates a hole around itself. It can then bind to this hole and form an exciton, or not bind to it and form a state that is dressed with its environment called a polaron. In fact the system forms a coherent superposition of these two possibilities, which then leads a quantum beating and oscillations in the impurity momentum with a frequency given by the energy difference between these two possibilities.
b, Comparison between the frequency ω_osc of oscillations in the impurity momentum, and the energy difference between the polaron E(Pol(0)) and the exciton E(Exc(0)) (the zero between brackets refers to the exciton and polaron having momentum zero). The x-axis denotes the interaction strength between the impurity and the background particles: the interaction between a background particle at position x_i and the impurity at position x_↓ is a contact interaction of the form g δ(x_i - x_↓), and one defines the dimensionless interaction parameter γ = m g/ρ_↑. ℏω_osc and E(Pol(0))-E(Exc(0)) are in quantitative agreement, which motivates the interpretation of quantum flutter as quantum beating between exciton and polaron.

To see quantum flutter in the laboratory directly, one can use methods from the field of ultracold atoms, in which neutral atoms are cooled and trapped using a combination of lasers and magnetic fields. The trapping potential can be chosen to restrict the atoms to move along 1D tubes, and effectively behave like a TG gas [7,8]. The interaction between the particles can be tuned using a Feshbach resonance. Impurity physics in one-dimensional TG gases has already been studied [9,10,11]. The only added ingredient needed for quantum flutter is to create impurities at finite velocities, which can be done using two-photon Raman processes. Quantum flutter can be observed by measuring the expected impurity velocity as a function of time. Thus cold atom experiments could confirm our predictions, and one could vary different parameters of the model so see how robust quantum flutter is. Our preliminary calculations suggest that quantum flutter survives within a certain window of varying all the parameters in the theory such as the interaction between background particles, the relative mass of the impurity and the background particles, and the form of the interactions.

In summary, we have found an example of a system of many particles where injecting a supersonic impurity leads to the spontaneous formation of a long-lived quantum superposition state which travels through the system at a finite velocity. The question of which systems allow transport of quantum coherent states is important for quantum computing applications [12], and has surfaced in recent studies of quantum effects in biology [13]. Thanks to the advent of exact methods and the development of precise experiments in the study of many-particle quantum dynamics, we expect to see progress being made on this question in the near future.

References
[1] Charles J. M. Mathy, Mikhail B. Zvonarev, Eugene Demler. "Quantum flutter of supersonic particles in one-dimensional quantum liquids". Nature Physics, 8, 881 (2012). Abstract.
[2] A.M. Kamchatnov and L.P. Pitaevskii. "Stabilization of solitons generated by a supersonic flow of a bose-einstein condensate past an obstacle". Physical Review Letters, 100, 160402 (2008). Abstract.
[3] I. Carusotto, S.X. Hu, L.A. Collins, and A. Smerzi. "Stabilization of solitons generated by a supersonic flow of a bose-einstein condensate past an obstacle". Physical Review Letters, 97, 260403 (2006). Abstract.
[4] M. Girardeau. "Relationship between systems of impenetrable bosons and fermions in one dimension". Journal of Mathematical Physics, 1, 516 (1960). Abstract.
[5] Jean-Sébastien Caux. "Correlation functions of integrable models: a description of the abacus algorithm". Journal of Mathematical Physics, 50, 095214 (2009). Abstract.
[6] A.S. Alexandrov, S. Devreeze, and T. Jozef. "Advances in Polaron Physics". Springer Series in Solid-State Sciences, Vol. 159 (2010).
[7]  Toshiya Kinoshita, Trevor Wenger and David S. Weiss. "A quantum newton's cradle". Nature, 440, 900 (2006). Abstract.
[8] Toshiya Kinoshita, Trevor Wenger and David S. Weiss. "Observation of a one-dimensional tonks-girardeau gas". Science, 305, 1125 (2004). Abstract.
[9] Stefan Palzer, Christoph Zipkes, Carlo Sias, Michael Köhl. "Quantum transport through a tonks-girardeau gas". Physical Review Letters, 103, 150601 (2009). Abstract.
[10] P. Wicke, S. Whitlock, and N.J. van Druten. "Controlling spin motion and interactions in a one-dimensional bose gas". ArXiv:1010.4545 [cond-mat.quant-gas] (2010).
[11] J. Catani, G. Lamporesi, D. Naik, M. Gring, M. Inguscio, F. Minardi, A. Kantian, and T. Giamarchi. "Quantum dynamics of impurities in a one-dimensional bose gas". Physical Review A, 85, 023623 (2012). Abstract.
[12] D.V. Averin, B. Ruggiero, and P. Silvestrini. "Macroscopic Quantum Coherence and Quantum Computing". Plenum Publishers, New York (2000).
[13] Gregory S. Engel, Tessa R. Calhoun, Elizabeth L. Read, Tae-Kyu Ahn, Tomá Manal, Yuan-Chung Cheng, Robert E. Blankenship, Graham R. Fleming. "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems". Nature, 446, 782 (2007). Abstract.

Evidence of Majorana States in an Al Superconductor – InAs Nanowire Device

[From left to right] Moty Heiblum, Yuval Oreg, Anindya Das, Yonathan Most, Hadas Shtrikman, Yuval Ronen

Authors: Yuval Ronen, Anindya Das, Yonatan Most, Yuval Oreg, Moty Heiblum, and Hadas Shtrikman

Affiliation: Dept. of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

When a bridge between fields in physics is created, exciting physics can emerge. In 1962 Anderson walked on a bridge connecting condensed matter physics with particle physics, by introducing the Anderson mechanism in superconductivity to explain the Meissner effect. A similar idea was used on the other side of the bridge by Higgs in 1964, to explain the mechanism that generates the mass of elementary particles known as the Higgs mechanism. Nowadays, another bridge is formed between these two fields emanating from an idea first originated by Ettore Majorana in 1937 – where spin 1/2 particles can be their own anti-particles[1]. Back then, Majorana suggested the neutrino as a possible candidate for his prediction, and experiments such as double-beta decay are planned to test his prediction.

A link between Majorana’s prediction of new elementary particles and the field of condensed matter physics was formed already more than a decade ago. Quasi-particle excitations, which are equal to their anti-quasi-particle excitations, are predicted to be found in the solid. Specifically, in vortices that live in an esoteric two-dimensional P-wave spinless superconductor. Moreover, these excitations are expected to be inherently different from their cousins the elementary particles: they have non-abelian statistics. The non-abelian statistics is one of the beautiful triumphs of the physics of condensed matter.

This so far unobserved quasi-particle, that has non-abelian statistics, has for a while been a ‘holy grail’ in the fractional quantum Hall effect regime; with filling factor 5/2 being the most promising candidate for its observation. Lately, another realization of Majorana quasi-particles is pursued. It follows a 1D toy model presented by Kitaev in 2001, showing how one can isolate two Majorana states at two widely separated ends of a 1D P-wave spinless superconductor [2]. These two Majorana states are expected to sit in the gap of the superconductor (at the Fermi energy) for a wide range of system parameters. Seven years later, Fu and Kane [3] found that a P-wave spinless superconductor can be induced by an S-wave superconductor in proximity to a topological insulator, occurring in a semiconductor with an inversion gap. It was thus not long before two theoretical groups [4,5] provided a prescription for how to turn a 1D semiconductor nanowire into an effective Kitaev 1D spinless P-wave superconductor.

The prescribed system is a semiconductor nanowire, with strong spin-orbit coupling, coupled to an S-wave superconductor (a trivial superconductor, with Cooper pairs in a singlet state). Electrons from the semiconductor undergo Andreev reflections, a process which induces S-wave superconductivity in the nanowire. The induced superconductivity opens gaps in the nanowire spectrum around the Fermi energy, at momentums k=0 and k=k_F (the Fermi momentum), due to the two spin bands being separated by spin-orbit coupling. An applied magnetic field quenches the gap at k=0 while hardly affecting the gap at k_F (the Zeeman splitting competes with superconductivity at k=0, where spin-orbit coupling, being proportional to k, plays no role), creating an effective gap different from the one induced by superconductivity. A gate voltage is used to tune the chemical potential into the effective gap. When the Zeeman energy is equal to the induced superconducting gap, the effective gap at k=0 closes; it then reopens upon further increase of the magnetic field, bringing the nanowire into a so called ‘topological phase’. Kitaev’s original toy model of a 1D P-wave superconductor is then implemented (Fig. 1).

Figure 1: Energy dispersion of the InAs nanowire excitations (Bogoliubov-de Gennes spectrum), in proximity to the Al superconductor. Heavy lines show electron-like bands and light lines show hole-like bands. Opposite spin directions are denoted in blue and magenta (red and cyan) for the spin-orbit effective field direction (perpendicular direction), where a relative mixture denotes intermediate spin directions. (a) Split electronic spin bands due to spin-orbit coupling in the InAs wire. Spin-orbit energy defined as Δ_so, with the chemical potential μ measured with respect to the spin bands crossing at p=0. (b) With the application of magnetic field, B, perpendicular to the spin-orbit effective magnetic field, B_so a Zeeman gap, E_z= gμ_BB/2, opens at p=0. (c) Light curves for the hole excitations are added, and bringing into close proximity a superconductor opens up superconducting gaps at the crossing of particle and hole curves. The overall gap is determined by the minimum between the gap at p=0 and the gap at p_F, while for μ=0 and E_z close to Δ_ind the gap at p=0 is dominant. (d) As in (c) but E_z is increased so that the gap at p_F is dominant. (e) B is rotated to a direction of 30^o with respect to B_so. The original spin-orbit bands are shifted in opposite vertical directions, and the B component, which is perpendicular to B_so is diminished. (f) The evolution of the energy gap at p=0 (dotted blue), at p_F (dotted yellow), and the overall energy gap (dashed black) with Zeeman energy, E_z, for μ=0. The overall gap is determined by the minimum of the other two, where the p=0 gap is dominant around the phase transition, which occurs at E_z=Δ_ind. At high E_z the p_F gap, which is decreasing with E_z, becomes dominant.

Seventy five years after Majorana’s monumental paper, we may be close to a realization of a quasi-particle that is identical to its anti-quasi-particle, possessing non-abelian statistics. Several experimental groups [6,7,8] follow the prescribed recipe for a 1D P-wave spinless superconductor[4,5], with our group being one of them. A zero energy conductance peak, at a finite Zeeman field, had been seen now in InSb and InAs nanowires in proximity to Nb and Al superconductors, respectively. This peak is considered a signature for the existence of a Majorana quasi-particle, since the Majorana resides at the Fermi energy.

Figure 2: Structure of the Al-InAs structures suspended above p-type silicon covered with 150nm SiO₂. (a) Type I device, the nanowire is supported by three gold pedestals, with a gold ‘normal’ contact at one edge and an aluminum superconducting contact at the center. The conductive Si substrate serves as a global gate (GG), controlling barrier as well as the chemical potential of the nanowire. Two narrow local gates (RG and LG), 50nm wide and 25nm thick, displaced from the superconducting contact by 80nm, also strongly influence the barrier height as well as the chemical potential in the wire. (b) Type II device, similar to type I device, but without the pedestal under the Al superconducting contact. This structure allows control of the chemical potential under the Al contact. (c) SEM micrograph of type II device. A voltage source, with 5 Ohm resistance, provides V_SD, and closes the circuit through the ‘cold ground’ (cold finger) in the dilution refrigerator. Gates are tuned by V_GG and V_RG to the desired conditions. Inset: High resolution TEM image (viewed from the <1120> zone axis) of a stacking faults free, wurtzite structure, InAs nanowire, grown on (011) InAs in the <111> direction. TEM image is courtesy of Ronit Popovitz-Biro. (d) An estimated potential profile along the wire. The two local gates (LG and RG) and global gate (GG) determine the shape of the potential barriers; probably affect the distance between the Majoranas.

Our work, with MBE grown InAs nanowire in proximity to an Al superconductor [8] (Fig 2), demonstrated a zero bias peak and several more interesting features in the parameters' space. First, the closing of the gap at k=0 was clearly visible when the Zeeman energy was equal to the induced gap. Second, splitting of the zero-bias-peak was observed at low and high Zeeman field; likely to result from spatial coupling of the two Majorana states. Third, the zero-bias-peak was found to be robust in a wide range of chemical potential (assumed to be within the k=0 gap). While these observations agree with the presence of a Majorana quasi-particle (though the peak height is much smaller than expected, maybe due to the finite temperature of the experiment), the available data does not exclude other effects that may result with a similar zero bias peak (such as, interference, disorder, multi-bands, Kondo correlation).

Quoting Wilczek: “Whatever the fate of these particular explorations, there is no doubt that Majorana's central idea, which long seemed peripheral, has secured a place at the core of theoretical physics"[9].

References:
[1] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
[2] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
[3] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Physical Review Letters 100, 096407 (2008). Abstract.
[4] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[5] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[6] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science 336, 1003 (2012). Abstract. 2Physics Article.
[7] M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, H. Q. Xu, "Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device", arXiv: 1204.4130 (2012).
[8] Anindya Das, Yuval Ronen, Yonathan Most, Yuval Oreg, Hadas Shtrikman, Moty Heiblum, "Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions", Nature Physics, 8, 887–895 (2012). Abstract.
[9] Frank Wilczek, "Majorana Returns", Nature Physics, 5, 614 (2009). Abstract.

Disordered photonics: A New Strategy for Light Trapping in Thin Films

Left to right: Kevin Vynck, Matteo Burresi, Francesco Riboli, and Diederik S. Wiersma

Authors: 
Kevin Vynck, Matteo Burresi, Francesco Riboli, and Diederik S. Wiersma

Affiliation: 
European Laboratory for Non-linear Spectroscopy (LENS) &
National Institute of Optics (CNR-INO), Florence, Italy

Thin-film solar cells nowadays represent a promising alternative to more conventional, thick, silicon panels. Using less material for solar cells allows for a significant saving of natural resources and a lowering of the production costs. A counter-effect of using thinner films is that the amount of light that is absorbed and eventually converted into electricity is significantly reduced. For this reason, improving the absorption of light by thin dielectric films constitutes a challenge of paramount importance in the development of high-efficiency, cost-effective, photovoltaic technologies [1].

Significant efforts have been made in recent years to design structures on the scale of the wavelength that are able to efficiently “trap” light in thin films. Among the various techniques proposed [2], great attention has been given to so-called photonic crystals, made, for instance, by creating a periodic array of holes in the film. At well-defined frequencies and angles of incidence, light impinging on the film can couple to the optical modes created by the nanostructuring and be trapped in the absorbing medium for a long time, thereby significantly increasing the light absorption [3]. Alternatively, randomly textured surfaces have been designed to efficiently spread light in the film on broad spectral and angular ranges, leading as well to an overall increase of the light absorption [4].

In a recent Letter published in Nature Materials [5], our team has presented a new strategy for light trapping thin films that takes advantage of both the efficient light trapping of photonic structures and the broadband/wide-angle properties of random media. The solution that we proposed relies on the use of two-dimensional disordered photonic structures, such as that shown in Figure 1 (higher panel), which exhibit complex electromagnetic modes to which coupling from free space is possible.

Figure 1: (Upper panel) Schematic view of a thin film containing a random pattern of holes. (Lower panel) Top and side views of the electromagnetic energy density in a randomly-nanopatterned film at two different frequencies (where t is the film thickness and λ, the wavelength of light). Light is efficiently trapped in the film, due to the light coupling to disordered optical modes. (Figures adapted from Ref. [5])

To understand the physical process involved, it is instructive to consider how light behaves in such a film. The dielectric film naturally acts as a waveguide for light, confining it in the plane of the film and preventing any out-of-plane loss. Placing holes at random positions in the film makes such that light is multiply-scattered in the plane, in a similar way as a two-dimensional random walk. Multiple scattering and wave interference lead to the formation of optical modes, the characteristics of which (e.g., their spatial extent) are intimately related to the structural properties of the disordered system. A key feature of these modes is that they are leaky, due to the finite thickness of the film, meaning that they are accessible from the third dimension, and thus, can be used for light trapping purposes.

For illustration, the electromagnetic energy density produced by a plane wave at normal incidence on a thin film containing a random pattern of holes (air filling fraction of 30%) is shown in Figure 1 (lower panel) at two different frequencies. The very high energy density in the film is a clear indication of an efficient light trapping effect. The speckle patterns observed arise from the interference between the multiply-scattered waves in the plane of the film, as described above.

The main results of our work are given in Figure 2, showing the absorption spectra of a bare (unpatterned) film with a moderate absorption efficiency (< 5%) and of the same film containing the random pattern of holes considered above. A strong enhancement of the absorption efficiency is observed over a broad range of frequencies, as well as for wide incidence angles and both polarizations of light (see the inset). These are very important properties for solar panels since they should ideally be efficient in all circumstances.

Figure 2: Absorption spectra of the bare (unpatterned) film (black curve) and the films containing random and amorphous patterns of holes (blue and gray curves, respectively). The inset shows the angular dependence of the absorption of the randomly-nanopatterned film at t/λ=0.15 for both polarizations of light. The random pattern of holes leads to a large absorption of the incident light over broad spectral and angular ranges. Disorder correlations in the amorphous pattern allow for a fine-tuning of the absorption spectrum. (Figure adapted from Ref. [5])

Since, as stated above, the coupling process is mediated by the optical modes, which intrinsically depend on the type of disorder considered, we further investigated the possibility to tune the light absorption by engineering the disorder. More particularly, we considered the case of an “amorphous” structure, characterized by a short-range correlation in the position of the holes, as periodic patterns, yet lacking any long-range order. The results on the absorption efficiency, shown in Figure 2, are remarkable: while the absorption is diminished at lower frequencies, becoming quite close to that of the bare slab, it is significantly increased at higher frequencies. The absorption enhancement occurs when the wavelength in the material approximately equals the typical distance between holes, proving that disorder correlations provide us with an important degree of control over the light absorption spectrum.

A final test to conclude our work has been to simulate the absorption of a film of amorphous silicon in the red part of the solar spectrum, where efficient light trapping is generally needed. We observed that the absorption efficiency of the films containing the disordered hole patterns (random and amorphous) was at least as high as that of the film containing the periodic hole pattern. This is an important result as it shows that periodic nanostructuring does not necessarily guarantee the best possible outcome. The lack of periodicity in photonic structures and the robustness of the properties of the films to structural imperfections could lead to the development of low-cost solar panels with a higher efficiency.

References:
[1] Albert Polman and Harry A. Atwater, "Photonic design principles for ultrahigh-efficiency photovoltaics", Nature Materials, 11, 174-177 (2012). Abstract.
[2] Shrestha Basu Mallick, Nicholas P. Sergeant, Mukul Agrawal, Jung-Yong Lee and Peter Peumans, "Coherent light trapping in thin-film photovoltaics", MRS Bulletin 36, 453-460 (2011). Abstract.
[3] Xianqin Meng, Guillaume Gomard, Ounsi El Daif, Emmanuel Drouard, Regis Orobtchouk, Anne Kaminski, Alain Fave, Mustapha Lemiti, Alexei Abramov, Pere Roca i Cabarrocas, Christian Seassal, "Absorbing photonic crystals for silicon thin-film solar cells: design, fabrication and experimental investigation", Solar Energy Materials and Solar Cells, 95, S32-S38 (2011). Abstract.
[4] C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, F. Lederer, "Comparison and optimization of randomly textured surfaces in thin-film solar cells", Opics Express, 18, A335-A341 (2010). Abstract.
[5] Kevin Vynck, Matteo Burresi, Francesco Riboli, Diederik S. Wiersma, "Photon management in two-dimensional disordered media", Nature Materials, 11, 1017-1022 (2012). Abstract.

Topological States and Adiabatic Pumping in Quasicrystals

Left to right: Kobi E. Kraus, Oded Zilberberg, Yoav Lahini, Zohar Ringel and Mor Verbin

Authors: 
Yaacov E. Kraus¹, Yoav Lahini^2,3, Zohar Ringel¹, Mor Verbin², Oded Zilberberg¹

Affiliation:
¹Dept. of Condensed Matter Physics, Weizmann Institute of Science, Israel
²Dept. of Physics of Complex Systems, Weizmann Institute of Science, Israel
³Department of Physics, Massachusetts Institute of Technology, USA

The materials that make up our world have a variety of electrical properties. Some materials, such as metals, conduct electricity extremely well, while others are insulators, and are very efficient as shields from electric currents.

Recently, a new discovery revolutionized the prevailing paradigm of electrical properties of materials, when a new type of material was discovered [1, 2]. These materials are termed “topological insulators”, and have very unique electrical properties. For example, electricity would flow smoothly on the surface of a topological insulator, while the interior will be completely insulating. Interestingly, if one would cut this material in half, the new surface that is created, which was previously buried within the insulating interior, will suddenly become conducting. If the material is cut repeatedly, the same will happen each time.

Past 2Physics article by Yoav Lahini:
November 07, 2010: "Hanbury Brown and Twiss Interferometry with Interacting Photons"
by Yoav Lahini, Yaron Bromberg, Eran Small and Yaron Silberberg

In addition to this peculiar property, the electrical behavior on the surface itself reveals unique phenomena that are even expected to simulate bizarre new particle excitations [3]. As a result, these fascinating materials generated much activity in the condensed matter physics community, in an attempt to find new topological materials and to study their intriguing properties.

In a recent paper [4], we found that other unconventional materials, known as quasicrystals, are in fact also members of the topological materials family. Moreover, the topological behavior that they exhibit is similar to that of usual topological materials in some aspects, but differs from them in others.

Quasicrystals are materials in which the atoms are arranged in a distinct way. In most solid materials, the atoms are arranged in space either periodically or in a completely random fashion. Quasicrystals are an intermediate type of solid - they are neither periodic nor random. Rather, there is some non-repeating (i.e. non periodic) but well defined rule to the arrangement of their atoms [5, 6]. Despite the fact that quasicrystals have been experimentally observed already in 1982 [5], for a long time there was a debate between crystallographers whether they exist at all, as it was assumed that all crystalline materials are necessarily periodic. The conclusion that quasicrystals are a new type of solid revolutionized material science, updated the physical definition of what is a crystal, and culminated in the awarding of the Nobel Prize in Chemistry to its discoverer, Dan Shechtman from the Technion - Israel Institute of Technology [7].

Yet, many of the physical properties of quasicrystals, such as their electrical conductance, are not fully understood. The work recently published by our group in Physical Review Letters [4], discusses the electrical properties of surfaces of quasicrystals, and finds a new and surprising connection between quasicrystals and topological states of matter. Specifically, we show that a one-dimensional quasicrystal behaves, to some extent, like two-dimensional topological matter known as quantum Hall systems. We prove this claim theoretically and measure it experimentally.

The experiments were done on a novel type of quasicrystals, known as photonic quasicrystals [8, 9]. These systems are made of quasi-periodic arrangements of transparent materials, rather than atoms. In these systems, one studies the optical properties, rather than the electrical, but the underlying physics is very much the same. A major advantage of using photonic quasicrystals is the ability to fabricate one-dimensional materials, and to directly image the propagation of light within them.

In our experiments, we have realized a one-dimensional photonic quasicrystal, and measured the boundary (the surface of a one-dimensional system) properties of these quasicrystals. We found that the photonic states that reside at the boundary are localized -- meaning that light that is injected to that boundary will stay there. This is analogous to the electric currents on the surface of topological matter, which do not penetrate the interior of the material, but remain confined to the surface. This finding was surprising, as common wisdom was that -- generally, such a behavior is not supposed to occur in one-dimensional systems.

Our theory explains how that becomes possible in quasicrystals. In brief, the arrangement of atoms in a quasicrystal can be mathematically described as some type of projection of a periodic system on a system of lower dimension – for example, projection of a two-dimensional square lattice onto a one-dimensional line [10]. Note that this description defines the position of the atoms of the quasicrystal, but do not imply the properties of any electrons (or photons) moving through it. In our case, the one-dimensional quasicrystalline models we worked with can be described as another type of one-dimensional projection of a quantum Hall system, known as “dimensional reduction” [3]. Most importantly, the novel projection used to define our one-dimensional quasicrystals preserves the topological properties! Thus, we find that beyond their mere structure, quasicrystals can, in some sense, also “inherit” nontrivial topological properties from their higher-dimensional periodic “ancestors”.

Taking things a step forward, we have shown that the boundary states observed in the experiments indeed possess nontrivial topological properties, by demonstrating a topological “pumping” of light from one side of the quasicrystal to the other [4].

Figure 1: Experimental observation of adiabatic pumping via topologically protected boundary states in a photonic quasicrystal. (a) An illustration of the adiabatically modulated photonic quasicrystal, constructed by slowly varying the spacing between the waveguides along the propagation axis z. Consequently, the injected light is pumped across the sample. (b) Experimental results: Light was injected into the rightmost waveguide. The measured intensity distributions as a function of the position are presented at different stages of the adiabatic evolution, i.e., different propagation distances. It is evident that along the adiabatic evolution the light crossed the lattice from right to left.

This fascinating discovery appears to be just the beginning. Our results suggest that additional quasicrystals should exhibit topological states [11, 12], and that these states will always be linked to systems of a higher dimension. This approach might mean that three-dimensional quasicrystalline materials -- either photonic or electronic -- would exhibit strange surface properties, which can be explained as originating from a six-dimensional topological system. These subjects are currently under active investigation.

References:
[1] “Colloquium: Topological Insulators”, M.Z. Hasan and C.L. Kane, Reviews of Modern Physics, 82, 3045 (2010). Abstract.
[2] “Topological insulators and superconductors”, Xiao-Liang Qi and Shou-Cheng Zhang , Reviews of Modern Physics, 83, 1057 (2011). Abstract.
[3] “Topological field theory of time-reversal invariant insulators”, Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang, Physical Review B 78, 195424 (2008). Abstract.
[4] "Topological States and Adiabatic Pumping in Quasicrystals”, Yaacov E. Kraus, Yoav Lahini, Zohar Ringel, Mor Verbin, and Oded Zilberberg, Physical Review Letters, 109, 106402 (2012). Abstract.
[5] “Metallic Phase with Long-Range Orientational Order and No Translations Symmetry”, D. Shechtman, I. Blech, D. Gratias, and J.W. Cahn, Physical Review Letters, 53, 1951 (1984). Abstract.
[6] "Quasicrystals: A New Class of Ordered Structures", Dov Levine and Paul Joseph Steinhardt, Physical Review Letters, 53, 2477 (1984). Abstract.
[7] See http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/press.html .
[8] “Wave and defect dynamics in nonlinear photonic quasicrystals”, Barak Freedman, Guy Bartal, Mordechai Segev, Ron Lifshitz, Demetrios N. Christodoulides and Jason W. Fleischer, Nature, 440, 1166 (2006). Abstract.
[9] “Observation of a Localization Transition in Quasiperiodic Photonic Lattices”, Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson and Y. Silberberg, Physical Review Letters, 103, 013901 (2009). Abstract.
[10] “Algebraic theory of Penrose's non-periodic tilings of the plane”, N.G. de Bruijn, Kon. Nederl. Akad. Wetensch. Proc. Ser. A (1981).
[11] “Topological Equivalence Between The Fibonacci Quasicrystal and The Harper Model”, Yaacov E. Kraus and Oded Zilberberg, Physical Review Letters, 109, 116404 (2012). Abstract.
[12] “Observation of Topological Phase Transitions in One-Dimensional Photonic Quasicrystals”, M. Verbin, Y. E. Kraus, O. Zilberberg, Y. Lahini and Y. Silberberg, in preparation. 

Imperfections, Disorder and Quantum Coherence

Steve Rolston [Image courtesy: University of Maryland, USA]

A new experiment conducted at the Joint Quantum Institute (JQI, operated jointly by the National Institute of Standards and Technology in Gaithersburg, MD and the University of Maryland in College Park, USA) examines the relationship between quantum coherence, an important aspect of certain materials kept at low temperature, and the imperfections in those materials. These findings should be useful in forging a better understanding of disorder, and in turn in developing better quantum-based devices, such as superconducting magnets. The new results are published in the New Journal of Physics [1].

Most things in nature are imperfect at some level. Fortunately, imperfections---a departure, say, from an orderly array of atoms in a crystalline solid---are often advantageous. For example, copper wire, which carries so much of the world’s electricity, conducts much better if at least some impurity atoms are present.

In other words, a pinch of disorder is good. But there can be too much of this good thing. The issue of disorder is so important in condensed matter physics, and so difficult to understand directly, that some scientists have been trying for some years to simulate with thin vapors of cold atoms the behavior of electrons flowing through solids trillions of times more dense. With their ability to control the local forces over these atoms, physicists hope to shed light on more complicated case of solids.

That’s where the JQI experiment comes in. Specifically, Steve Rolston and his colleagues have set up an optical lattice of rubidium atoms held at temperature close to absolute zero. In such a lattice atoms in space are held in orderly proximity not by natural inter-atomic forces but by the forces exerted by an array of laser beams. These atoms, moreover, constitute a Bose Einstein condensate (BEC), a special condition in which they all belong to a single quantum state.

This is appropriate since the atoms are meant to be a proxy for the electrons flowing through a solid superconductor. In some so called high temperature superconductors (HTSC), the electrons move in planes of copper and oxygen atoms. These HTSC materials work, however, only if a fillip of impurity atoms, such as barium or yttrium, is present. Theorists have not adequately explained why this bit of disorder in the underlying material should be necessary for attaining superconductivity.

The JQI experiment has tried to supply palpable data that can illuminate the issue of disorder. In solids, atoms are a fraction of a nanometer (billionth of a meter) apart. At JQI the atoms are about a micron (a millionth of a meter) apart. Actually, the JQI atom swarm consists of a 2-dimensional disk. “Disorder” in this disk consists not of impurity atoms but of “speckle.” When a laser beam strikes a rough surface, such as a cinderblock wall, it is scattered in a haphazard pattern. This visible speckle effect is what is used to slightly disorganize the otherwise perfect arrangement of Rb atoms in the JQI sample.

In superconductors, the slight disorder in the form of impurities ensures a very orderly “coherence” of the supercurrent. That is, the electrons moving through the solid flow as a single coordinated train of waves and retain their cohesiveness even in the midst of impurity atoms.

In the rubidium vapor, analogously, the slight disorder supplied by the speckle laser ensures that the Rb atoms retain their coordinated participation in the unified (BEC) quantum wave structure. But only up to a point. If too much disorder is added---if the speckle is too large---then the quantum coherence can go away. Probing this transition numerically was the object of the JQI experiment. The setup is illustrated in figure 1.

Figure 1: Two thin planes of cold atoms are held in an optical lattice by an array of laser beams. Still another laser beam, passed through a diffusing material, adds an element of disorder to the atoms in the form of a speckle pattern. [Image courtesy: Matthew Beeler]

And how do you know when you’ve gone too far with the disorder? How do you know that quantum coherence has been lost? By making coherence visible.

The JQI scientists cleverly pry their disk-shaped gas of atoms into two parallel sheets, looking like two thin crepes, one on top of each other. Thereafter, if all the laser beams are turned off, the two planes will collide like miniature galaxies. If the atoms were in a coherent condition, their collision will result in a crisp interference pattern showing up on a video screen as a series of high-contrast dark and light stripes.

If, however, the imposed disorder had been too high, resulting in a loss of coherence among the atoms, then the interference pattern will be washed out. Figure 2 shows this effect at work. Frames b and c respectively show what happens when the degree of disorder is just right and when it is too much.

Figure 2: Interference patterns resulting when the two planes of atoms are allowed to collide. In (b) the amount of disorder is just right and the pattern is crisp. In (c) too much disorder has begun to wash out the pattern. In (a) the pattern is complicated by the presence of vortices in the among the atoms, vortices which are hard to see in this image taken from the side. [Image courtesy: Matthew Beeler]

“Disorder figures in about half of all condensed matter physics,” says Steve Rolston. “What we’re doing is mimicking the movement of electrons in 3-dimensional solids using cold atoms in a 2-dimensional gas. Since there don’t seem to be any theoretical predictions to help us understand what we’re seeing we’ve moved into new experimental territory.”

Where does the JQI work go next? Well, in figure 2a you can see that the interference pattern is still visible but somewhat garbled. That arises from the fact that for this amount of disorder several vortices---miniature whirlpools of atoms---have sprouted within the gas. Exactly such vortices among electrons emerge in superconductivity, limiting their ability to maintain a coherent state.

Another of the JQI scientists, Matthew Beeler, underscores the importance of understanding the transition from the coherent state to incoherent state owing to the fluctuations introduced by disorder: “This paper is the first direct observation of disorder causing these phase fluctuations. To the extent that our system of cold atoms is like a HTSC superconductor, this is a direct connection between disorder and a mechanism which drives the system from superconductor to insulator.”

Reference:
[1] M C Beeler, M E W Reed, T Hong, and S L Rolston, "Disorder-driven loss of phase coherence in a quasi-2D cold atom system", New Journal of Physics, 14, 073024 doi:10.1088/1367-2630/14/7/073024 (2012). Abstract. Full Article.

Rare Coupling of Magnetic and Electric Properties in a Single Material

Brookhaven physicists Stuart Wilkins (left) and John Hill (right) at NSLS beamline X1A2, where their research was performed with a new soft x-ray scattering facility.

Researchers at the U.S. Department of Energy’s Brookhaven National Laboratory have observed a new way that magnetic and electric properties — which have a long history of ignoring and counteracting each other — can coexist in a special class of metals. These materials, known as multiferroics, could serve as the basis for the next generation of faster and energy-efficient logic, memory, and sensing technology.

The researchers, who worked with colleagues at the Leibniz Institute for Solid State and Materials Research in Germany, published their findings in a recent issue of Physical Review Letters [1].

Co-authors Sven Partzsch (left) and Jochen Geck (right), researchers at the Leibniz Institute for Solid State and Materials Research in Germany

Ferromagnets are materials that display a permanent magnetic moment, or magnetic direction, similar to how a compass needle always points north. They assist in a variety of daily tasks, from sticking a reminder to the fridge door to storing information on a computer’s hard drive. Ferroelectrics are materials that display a permanent electric polarization — a set direction of charge — and respond to the application of an electric field by switching this direction. They are commonly used in applications like sonar, medical imaging, and sensors.

“In principle, the coupling of an ordered magnetic material with an ordered electric material could lead to very useful devices,” said Brookhaven physicist Stuart Wilkins, one of the paper’s authors. “For instance, one could imagine a device in which information is written by application of an electric field and read by detecting its magnetic state. This would make a faster and much more energy-efficient data storage device than is available today.”

But multiferroics — magnetic materials with north and south poles that can be reversed with an electric field — are rare in nature. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist.

Most models used by physicists to describe this coupling are based on the idea of distorting the atomic arrangement, or crystal lattice, of a magnetic material, which can result in an electric polarization.

The crystal structure of YMn₂O₅, which is made of yttrium, manganese, and oxygen. The oxygen atoms are shown in red and the yttrium atoms are gray. The magnetic moments on the manganese are shown as arrows. Ferroelectric polarization occurs between the oxygen and manganese atoms

Now, scientists have found a new way that electric and magnetic properties can be coupled in a material. The group used extremely bright beams of x-rays at Brookhaven’s National Synchrotron Light Source (NSLS) to examine the electronic structure of a particular metal oxide made of yttrium, manganese, and oxygen. They determined that the magnetic-electric coupling is caused by the outer cloud of electrons surrounding the atom.

“Previously, this mechanism had only been predicted theoretically and its existence was hotly debated,” Wilkins said.

In this particular material, the manganese and oxygen electrons mix atomic orbitals in a process that creates atomic bonds and keeps the material together. The researchers’ measurements show that this process is dependent upon the magnetic structure of the material, which in this case, causes the material to become ferroelectric, i.e. have an electric polarization. In other words, any change in the material’s magnetic structure will result in a change in direction of its ferroelectric state. By definition, that makes the material a multiferroic.

“What is especially exciting is that this result proves the existence of a new coupling mechanism and provides a tool to study it,” Wilkins said.

The researchers used a new instrument at NSLS designed to answer key questions about many intriguing classes of materials such as multiferroics and high-temperature superconductors, which conduct electricity without resistance. The instrument, developed by Wilkins and Brookhaven engineers D. Scott Coburn, William Leonhardt, and William Schoenig, will ultimately be moved to the National Synchrotron Light Source II (NSLS-II), a state-of-the-art machine currently under construction. NSLS-II will produce x-rays 10,000 times brighter than at NSLS, enabling studies of materials’ properties at even higher resolution.

Reference
[1] S. Partzsch, S. B. Wilkins, J. P. Hill, E. Schierle, E. Weschke, D. Souptel, B. Büchner and J. Geck, "Observation of Electronic Ferroelectric Polarization in Multiferroic YMn₂O₅", Physical Review Letters, 107, 057201 (2011). Abstract.

[We thank Brookhaven National Laboratory for materials used in this report]

High Magnetic Fields Coax New Discoveries from Topological Insulators

James Analytis [Photo courtesy: Stanford U.]

Using one of the most powerful magnets in the world, a small group of researchers has successfully isolated signs of electrical current flowing along the surface of a topological insulator, an exotic material with promising electrical properties. The research, led by James Analytis and Ian Fisher of the Stanford Institute of Materials and Energy Sciences, a joint SLAC-Stanford institute, was published last Sunday in Nature Physics [1]. The results provide a new window into how current flows in these exotic materials, which conduct along the exterior, while acting as insulators at the interior. At least in theory.

"This is a difficulty people in the field have been struggling with for two years," Fisher said. "The topological part is there but the insulator part isn't there yet." Chemical imperfections in the materials being tested have meant that the interior, or bulk, portions of topological insulators have been behaving more like metals than insulators.

Ian Fisher [Photo courtesy: Stanford U.]

In other words, while researchers have been trying to decipher the behavior of the electrons on the surface by observing the way they conduct current (called electronic transport), the electrons in the interior have also been conducting current. The difficulty arises in telling the two currents apart.

But, according to Fisher, the promise of useful applications for these exotic new materials—not to mention possible discoveries of fundamental new physics—rests on the ability to measure and control the electric current at the surface. In order to do so, Analytis, Fisher, and their group first had to reduce the amount of current running through the bulk of the material until the surface current could be detected, and then probe the physical properties of the electrons responsible for that surface current.

Analytis tackled the first problem by replacing some of the bismuth in bismuth selenide, a known topological insulator, with antimony, a lighter relative with the same number of electrons in its valence, or chemically reactive, shell. This provided a way to reduce the number of charge-carrying electrons in the interior of the sample.

But even after removing hundreds of billions of electrons, "we still didn't have an insulator," Analytis said. That's when he turned to Ross McDonald and the pulsed magnets at the Pulsed Field Facility, Los Alamos National Laboratory's branch of the National High Magnetic Field Laboratory.

Ross McDonald [Photo courtesy: National High Magnetic Field Laboratory, Tallahassee, FL]

Electrons in a uniform magnetic field follow circular orbits. As the electrons are subjected to higher and higher magnetic fields, they travel in tighter and tighter orbits, which are quantized, or separated into discrete energy levels, called Landau levels. Using a high-enough magnetic field to trap the bulk electrons in their lowest Landau level enabled Analytis to differentiate between the bulk electrons and the surface electrons, or, as Fisher put it, "get the bulk under control."

With McDonald's help, Analytis used one of Los Alamos' multi-shot pulsed magnets, so called because they deliver their full field strength in pulses lasting thousandths of a second. Analytis discovered that a moderate field of four Tesla (about twenty thousand times the strength of a refrigerator magnet) was sufficient to force the bulk conduction electrons into their lowest Landau level. Then he pushed the magnetic field to 65T to see what the surface electrons on the topological insulator would do.

The 100 Tesla multi-shot pulsed magnet at Los Alamos National Laboratory. James Analytis used a slightly less powerful magnet for the research covered in this article [Photo courtesy: National High Magnetic Field Laboratory, Tallahassee, FL].

He saw a clear signature from the Landau levels of the surface electrons. And, at the very highest magnetic fields, at which the surface electrons are pushed most closely together, Analytis detected signs that the electrons interacted with each other, instead of behaving like independent particles.

"It's beautiful," Fisher said. "It's unambiguous evidence that we can probe electronic transport in the surface of these materials." However, much of the difficulty in creating a truly insulating topological insulator remains.

"It feels like we've opened a door to the place [experimenters] want to be," he said, "but there's a lot more work to be done."

In the meantime, Analytis is moving ahead with his latest experiment—hitting the antimony-doped bismuth selenide with a staggering 85T—the highest magnetic field available in a multi-shot magnet anywhere in the world.

Reference
[1] James G. Analytis, Ross D. McDonald, Scott C. Riggs, Jiun-Haw Chu, G.S. Boebinger & Ian R. Fisher, "Two-dimensional surface state in the quantum limit of a topological insulator", Nature Physics, Published online November 21 (2010), doi:10.1038/nphys1861. Abstract.

[The text is written by Lori Ann White of Stanford Linear Accelerator Laboratory (SLAC)]

New Technique Allows 3-D Mapping of the Magnetic Vector Potential

Amanda Petford-Long [Photo courtesy: Argonne National Laboratory]

Scientists at the U.S. Department of Energy’s (DOE) Argonne National Laboratory have developed a new technique [1] that maps the magnetic vector potential — one of the most important electromagnetic quantities and a foundation of quantum mechanics — in three dimensions. The vector potential is central to a number of areas of condensed matter physics, such as superconductivity and magnetism.

"The vector potential of magnetic structures is essential to the understanding of several areas in condensed matter physics and magnetism on a quantum level, but until now it has never been visualized in three dimensions,” Argonne Distinguished Fellow Amanda Petford-Long said. “If you want to understand the way magnetic nanostructures behave, then you have to understand the magnetic vector potential.”

According to Petford-Long, research into the creation and manipulation of magnetic nanostructures will enable the development of the next generation of data storage in the form of magnetic random access memory.

Charudatta Phatak [Photo Courtesy: Argonne National Laboratory]

Petford-Long and post-doctoral researcher Charudatta Phatak used a transmission electron microscope (TEM) to examine a series of different nanostructures. The theoretical and numerical reconstruction procedure was developed in collaboration with Prof. Marc De Graef at Carnegie Mellon University.

Using the TEM, the researchers were able to take images from several different angles and then rotate the structure by 90 degrees until they had several series of images. The scientists then extracted the vector potential by reconstructing how the electrons in the material shifted phase.

“The development of next generation magnetic sensors and devices requires studying the physics underlying the magnetic interactions at the nanoscale,” Phatak said. “This 3-D map is the first step to truly understanding those interactions.”

Marc De Graef [Photo courtesy: Carnegie Mellon University]

Funding for the research, including the TEM situated in the Materials Science Division, was provided by the U.S. Department of Energy’s Office of Science. The patterned structures were prepared at the Center for Nanoscale Materials with Alexandra Imre.

The Center for Nanoscale Materials at Argonne National Laboratory is one of the five DOE Nanoscale Science Research Centers (NSRCs), premier national user facilities for interdisciplinary research at the nanoscale, supported by the DOE Office of Science. For more information about the DOE NSRCs, visit http://nano.energy.gov/.

Reference
[1] Charudatta Phatak, Amanda K. Petford-Long, Marc De Graef, "Three-Dimensional Study of the Vector Potential of Magnetic Structures", Phys. Rev. Lett. 104, 253901 (2010). Abstract.

[We thank Argonne National Laboratory for materials used in this posting]