.comment-link {margin-left:.6em;}


2Physics Quote:
"Needless to say, these advantages would not only arise for antineutrino monitoring of the IR-40 but for any reactor with a power output in the 20-250 MWth range, which are the most likely candidates for being an entry point for a plutonium-based nuclear weapons program. Antineutrino reactor monitoring would not replace other techniques but in combination with those techniques can enhance the overall effectiveness and reliability of non-proliferation safeguards. A practical system appears feasible on a timescale of 1-2 years and the next step would be an actual antineutrino reactor monitoring experiment."
-- Eric Christensen, Patrick Huber, Patrick Jaffke, Thomas E. Shea
(Read Full Article: "Antineutrino Monitoring for the Iranian Heavy Water Reactor" )

Sunday, December 14, 2014

Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor

From Left to Right: (top row) Stevan Nadj-Perge, Ilya K. Drozdov, Jian Li, Hua Chen ; (bottom row) Sangjun Jeon, Allan H. MacDonald, B. Andrei Bernevig, Ali Yazdani.

Authors: Stevan Nadj-Perge1, Ilya K. Drozdov1, Jian Li1, Hua Chen2, Sangjun Jeon1, Jungpil Seo1, Allan H. MacDonald2, B. Andrei Bernevig1, Ali Yazdani1.

1Joseph Henry Laboratories and Dept of Physics, Princeton University, USA.
2Department of Physics, University of Texas at Austin, USA.

Link to Yazdani Lab >>
Link to Allan H. MacDonald's Group >>

In 1937 Italian scientist Ettore Majorana, one of the most promising theoretical physicists at that time, proposed a hypothetical fermionic excitation, now called Majorana fermion, which has a property that it is its own anti-particle [1]. Ever since significant efforts were invested in finding an elementary particle described by Majorana. While present for many years in particle physics community, it was only in 2001 that Alexei Kitaev suggested an intriguing possibility that a type of a quasi-particle, a condensed matter analog of the Majorana fermion could exist [2]. Such quasi-particle would emerge as a zero energy excitation localized at the boundary of a one dimensional topological superconductor. Following his seminal work various systems were proposed as a potential platform for realization of Majorana quasi-particles. Apart from fundamental scientific interest, the motivation for investigating Majorana bound states partly relies on their potential for use for quantum computing [3,4].

Past 2Physics article by Ali Yazdani :
August 25, 2013: "Visualizing Nodal Heavy Fermion Superconductivity"
by Brian Zhou, Shashank Misra, and Ali Yazdani.

Previous to our experiments, the most promising experimental route to realize these elusive bound states was based on semiconductor-superconductor interfaces in which Majorana fermions would appear as conductance peaks at zero energy [5,6]. Indeed experiments in 2012 reported zero energy conductance peaks suggesting presence of Majorana modes in these type of systems [7,8], however, alternative explanations related to disorder and Kondo phenomena proposed latter could not be fully ruled out. It is worth noting that in these interfaces spatial information about localized excitations is very hard to obtain.

Fig. 1: (A) Schematic of the proposal for realization and detection of Majorana states: A ferromagnetic atomic chain is placed on the surface of strongly spin-orbit–coupled superconductor and studied using STM. (B) Band structure of a linear suspended Fe chain before introducing spin-orbit coupling or superconductivity. The majority spin-up (red) and minority spin-down (blue) d-bands labeled by azimuthal angular momentum m are split by the exchange interaction J (degeneracy of each band is noted by the number of arrows). a, interatomic distance. (C) Regimes for trivial and topological superconducting phases are identified for the band structure shown in (B) as a function of exchange interaction in presence of SO coupling. The value J for Fe chains based on density functional calculations is noted. μ is the chemical potential.

Building upon previous proposal to realize Majorana modes in an array of magnetic nanoparticles [9], we proposed to use a chain of magnetic atoms coupled to a superconductor [10]. The key advantage of this platform is that the experimentally properties of this system can easily be studied using standard scanning tunneling microscopy (STM) technique. While ours and other follow-up initial proposals [11-16] consider specific orientation of the magnetic moments, the approach works also for ferromagnetic atomic chains as long as it is coupled to a superconductor with strong spin-orbit coupling (Fig. 1A) [17]. In this case, the large exchange interaction results in a band structure of the chains such that majority spin band is fully occupied while the Fermi level is in the minority spin bands. For example the electronic structure of a linear Iron (Fe) ferromagnetic atomic chain is shown in Fig. 1B. Considering only d-orbitals which are spin-polarized it is easy to show that many of the bandstructure degeneracies are lifted and that for large range of parameters, chemical potential and the exchange energy, such chains are in topologically non-trivial regime characterized by the odd number of crossing at the Fermi level (Fig 1C). When placed on the superconducting substrate with strong-spin orbit coupling the resulting superconductivity on the chain will necessarily be topological in nature resulting in zero energy Majorana bound states located at the chain ends.
Fig. 2: (A) Topograph of the Pb(110) surface after growth of Fe, showing Fe islands and chains indicated by white arrows and atomically clean terraces of Pb (regions with the same color) with size exceeding 1000 Å. (Lower-right inset) Anisotropic atomic structure of the Pb(110) surface (Upper-left insets) images of several atomic Fe chains and the islands from which they grow (scale bars, 50 Å). (B) Topography of the chain colorized by the conductance at H= ±1 T from low (dark blue) to high conductance (dark red). (C) Difference between conductance on and off the chain showing hysteresis behavior. (D and E) Atomic structure of the zigzag chain, as calculated using density functional theory. The Fe chain structure that has the lowest energy in the calculations matches the structural features in the STM measurements, aB is the Bohr radius.

We have developed a way to grow iron atomic chains on the surface of lead (Pb) which, due to heavy atomic mass, is expected to have strong spin-orbit coupling. For this purpose we used Pb(110) crystallographic surface orientation which has characteristic anisotropy (Fig. 2(A) lower left inset). When a sub-monolayer of Fe is evaporated and slight annealing, the anisotropy of the substrate could trigger growth of one-dimensional atomic chains. We investigated the resulting structures by using STM at cryogenic temperatures (temperature was 1.4K in the experiment). On relatively large atomically ordered regions of the Pb(110) surface we observed self-assembled islands as well as single atom wide chains of Fe. Depending on growth conditions, we find Fe chains as long as 500 Å with ordered regions approaching 200 Å. In order to confirm ferromagnetic order on the chain we have performed spin-polarized measurements using bulk antiferromagnetic Chromium STM tips. Tunneling conductance (dI/dV) at a low bias voltage as a function of the out-of-plane magnetic field shows contrast for opposite fields (Fig. 2B) and a hysteresis behavior (Fig. 2C, note that no hysteresis is observed on the Pb substrate). The observed hysteresis loop corresponds to the tunneling of electrons between two magnets with the field switching only one of them at around 0.25 T.

We also observed the variation of the spin-polarized STM signal along the chain which is likely due to its electronic and structural properties. Indeed, both topographic features and periodicity of signal variation could be very well explained by our theory collaborators who performed density functional theory modeling. Their calculations suggested that our chains have zig-zag structure which explains both topographic information obtained using STM and matches well with our spin-polarized measurements (Fig. 2D and 2E).
Fig. 3: (A) STM spectra measured on the atomic chain at locations corresponding to those indicated in (B) and (C). For clarity, the spectra are offset by 100 nS. The red spectrum shows the zero-bias peak at one end of the chain. The gray trace measured on the Pb substrate can be fitted using thermally broadened BCS superconducting density of states (dashed gray line, fit parameters Δs = 1.36 meV, T = 1.45 K). (B and C) Zoom-in topography of the upper (B) and lower end (C) of the chain and corresponding locations for spectra marked (1 to 7). Scale bars, 25 Å. (D and E) Spectra measured at marked locations, as in (B) and (C). (F) Spatial and energy-resolved conductance maps of another atomic chain close to its end, which shows similar features in point spectra as in (A). The conductance map at zero bias (middle panel) shows increased conductance close to the end of the chain. Scale bar, 10 Å.

After establishing basic properties of our chains we investigated low-energy excitations using spatial spectroscopic mapping, see Fig 3. While on the surface of bare Pb(110), there is clear structure of the superconducting gap on the Fe atomic chain, the presence of the in-gap states is predominant (Fig. 3A). Most notably a peak close to zero bias voltage is observed near the chain end together with asymmetric less-developed gap-like structure in the middle of the chain (Fig. 3D and Fig. 3E). Both spatially resolved spectra and the spectroscopic maps at low bias voltage show signatures expected from Majorana bound states (Fig. 3F). The ability to correlate the location of the zero bias conductance peak with the end of the atomic chains is one of the main experimental results of our work. This is one of the basic requirements for interpreting that this feature is associated with the predicted Majorana bound state of a topological superconductor. In addition to robust observation of the zero bias peaks in many chains, we have performed several control experiments to eliminate other potential effects which may give similar looking signatures. For example, when superconductivity is suppressed by applying small magnetic field, the spectrum on the chain becomes featureless in contrast to what would be expected for Kondo effect. Also for very short chains zero biased peaks were not observed, ruling out trivial effects related to the chain ends. Furthermore, in order to increase experimental resolution we took measurements with superconducting tip which also confirm the over picture consistent with Majorana bound states in this system.

The observed spectroscopic signatures are consistent with the existence of Majorana bound states in our system. An obvious extension of our experiments is to create two dimensional islands and search for propagating Majorana modes or, for example, investigate other systems with both even and odd number of band crossing at Fermi level in order to further test the concept behind our study. Ultimately the future experiments will focus on manipulation of Majorana bound states in this system [18].

[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] A. Yu. Kitaev, "Fault-tolerant quantum computation by anyons". Annals of Physics. 303, 2 (2003). Abstract.
[4] Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen, Matthew P. A. Fisher, "Non-Abelian statistics and topological quantum information processing in 1D wire networks". Nature Physics, 7, 412 (2011). 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] Roman M. Lutchyn, Jay D. Sau, S. Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures". Physical Review Letters, 105, 077001 (2010). Abstract.
[7] 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.
[8] Anindya Das, Yuval Ronen, Yonatan Most, Yuval Oreg, Moty Heiblum, Hadas Shtrikman, "Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions". Nature Physics, 8, 887 (2012). Abstract. 2Physics Article.
[9] T. P. Choy, J. M. Edge, A. R. Akhmerov, C. W. J. Beenakker, "Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling". Physical Review B, 84, 195442 (2011). Abstract.
[10] S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig, Ali Yazdani, "Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor". Physical Review B, 88, 020407 (2013). Abstract.
[11] Falko Pientka, Leonid I. Glazman, Felix von Oppen, "Topological superconducting phase in helical Shiba chains". Physical Review B, 88, 155420 (2013). Abstract.
[12] Jelena Klinovaja, Peter Stano, Ali Yazdani, Daniel Loss, "Topological Superconductivity and Majorana Fermions in RKKY Systems". Physical Review Letters, 111, 186805 (2013). Abstract.
[13] Bernd Braunecker, Pascal Simon, "Interplay between Classical Magnetic Moments and Superconductivity in Quantum One-Dimensional Conductors: Toward a Self-Sustained Topological Majorana Phase". Physical Review Letters, 111, 147202 (2013). Abstract.
[14] M. M. Vazifeh, M. Franz, "Self-Organized Topological State with Majorana Fermions". Physical Review Letters, 111, 206802 (2013). Abstract.
[15] Sho Nakosai, Yukio Tanaka, Naoto Nagaosa, "Two-dimensional superconducting states with magnetic moments on a conventional superconductor". Physical Review B, 88, 180503 (2013). Abstract.
[16] Younghyun Kim, Meng Cheng, Bela Bauer, Roman M. Lutchyn, S. Das Sarma, "Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states". Physical Review B, 90, 060401 (2014). Abstract.
[17] Stevan Nadj-Perge, Ilya K. Drozdov, Jian Li, Hua Chen, Sangjun Jeon, Jungpil Seo, Allan H. MacDonald, B. Andrei Bernevig, Ali Yazdani, "Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor". Science 346, 602-607 (2014). Abstract.
[18] Jian Li, Titus Neupert, B. Andrei Bernevig, Ali Yazdani, "Majorana zero modes on a necklace". arXiv:1404.4058 [cond-mat] (2014).

Labels: , , , ,

posted by Quark @ 9:17 AM      links to this post

Sunday, December 07, 2014

Collisions of Matter-Wave Solitons

[Left to right] De Luo, Jason Nguyen, and Randy Hulet

Jason H.V. Nguyen1, Paul Dyke2, De Luo1, Boris A. Malomed3, Randall G. Hulet1

1Department of Physics and Astronomy, Rice University, Houston, Texas, USA
2Centre of Quantum and Optical Science, Swinburne University of Technology, Melbourne, Australia
3Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Israel

Link to Hulet Atom Cooling Group >>

Solitons are localized wave disturbances that propagate without changing shape or spreading out. This remarkable effect depends on a self-attraction created by the medium the solitons propagate in. If the self-attraction increases with the size of the wave amplitude, solitons with larger amplitude are “squeezed” harder to keep them from spreading out, while smaller amplitude, broader solitons require a gentler squeeze. Solitons have been observed in a variety of wave phenomena, including pulses of light traveling in optical fibers, ocean waves, and in many other diverse phenomena, perhaps even in the collective oscillations of protein and DNA molecules. The largest known soliton-like object is the Great Red Spot on Jupiter.

We study matter-wave solitons, which are much rarer. Quantum mechanics tells us that matter can exhibit wave-like or particle-like behavior, depending on the circumstances. Perhaps the most exotic are collective matter waves known as Bose-Einstein condensates consisting of millions of atoms cooled to near absolute zero temperature, where the atoms act in unison and behave as if they had a common purpose. These Bose-Einstein condensates are matter-wave solitons when the interactions between atoms in the condensate are attractive, and when they are confined in a one-dimensional guide.

Early experiments studying matter-wave solitons examined properties of single solitons [1] and soliton trains [2]. In our experiment, originally published in Nature Physics [3], we create two nearly identical matter-wave solitons consisting of approximately 28000 lithium atoms per soliton. They are separated by 26 micrometers using a cylindrically focused laser beam, which acts as a barrier, and are held at opposite sides of a one-dimensional guide formed by an infrared laser beam. The guide is curved along its axis, forming a bowl-shaped potential, so that when we turn the barrier off, the solitons fall inward and collide multiple times as they oscillate back and forth.

A defining property of ideal solitons is that they pass through one another without changing their shape, amplitude, or velocity [4,5,6]. Yet, when we did the experiment, we observed violent collisions that produced interference minima and maxima in the collision region. We found the character of the collision and the interference depended on a property of a wave known as its “phase”, in agreement with the general theory of solitons. In the case that the solitons were nearly in-phase, they appear to merge during the collision and then pass through one another. When solitons were nearly out-of-phase, however, we were faced with the contradiction that solitons appeared to closely approach each other, but then to bounce off each other.
Figure 1: (a) Time evolution showing a full period of oscillation (τ=32 ms) for the case when the solitons are nearly in-phase. At the 1/4 and 3/4 points the solitons appear to merge and afterwards pass through one another. (b) Similar to (a) except for the case when the solitons are nearly out-of-phase. At the 1/4 and 3/4 points the solitons appear to be separated by a small gap, after which they appear to bounce off each other.

Since all solitons are expected to pass through one another, not just the ones with the “correct” phase, we did an experiment with “tagged” solitons: one soliton was made smaller to distinguish it from the other. Upon repeating the experiment, we discovered that even the out-of-phase solitons passed through one another. The interference at the point of collision had created a node, or empty space between solitons that only created the appearance of reflection.

Figure 2: Time evolution showing a full period of oscillation (τ=32 ms) with tagged solitons that are nearly out of phase. At the 1/4 and 3/4 points the solitons maintain a minimum gap between them during the collision, however afterwards we observe that the solitons pass through one another as they did in the nearly in-phase case.

Since solitons depend on self-attraction, they can collapse into high density compact objects when their density becomes too large. By controlling the strength of the interaction, we observed that in-phase soliton collisions can result in collapse, as the increasing density during collision causes their self-attraction to be overwhelming. In addition to the two solitons annihilating each other in this way, we also observed that a pair of solitons may merge into a single, smaller soliton.

Although independent solitons have been well-understood for some time, their interaction has brought new insights. In the future, we will explore how solitons can be made into an interferometer, much like a matter-wave version of a laser gyro. To do this, we will use a sheet of light as a beam-splitter for solitons, where solitons have a quantum mechanical probability to be reflected or transmitted, each taking separate paths around a closed loop.

[1] L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, “Formation of a matter-wave bright soliton”, Science, 296, 1290-1293 (2002). Abstract.
[2] Kevin E. Strecker, Guthrie B. Partridge, Andrew G. Truscott, Randall G. Hulet, “Formation and propagation of matter-wave soliton trains”, Nature, 417, 150-153 (2002). Abstract.
[3] Jason H. V. Nguyen, Paul Dyke, De Luo, Boris A. Malomed, Randall G. Hulet, “Collisions of matter-wave solitons”, Nature Physics, 10, 918-922 (2014). Abstract.
[4] N.J. Zabusky & M.D. Kruskal. “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states”, Physical Review Letters, 15, 240 (1965). Abstract.
[5] V.E. Zakharov, A.B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media”, Soviet Physics JETP, 34, 62 (1972). Full Article.
[6] G.L. Lamb, “Elements of soliton theory”, New York, Wiley (1980).

Labels: , ,

posted by Quark @ 8:17 AM      links to this post

Sunday, November 30, 2014

Enhancement of Long-Range Correlations in a 2D Vortex Lattice by an Incommensurate 1D Disorder Potential

(Left to Right) Top Row: Isabel Guillamón, Rosa Córdoba; Middle Row: Javier Sesé, José María De Teresa, M. Ricardo Ibarra; Bottom Row: Sebastián Vieira, Hermann Suderow.

Isabel Guillamón1,2, Rosa Córdoba3,*, Javier Sesé3, José María De Teresa3,4, M. Ricardo Ibarra3, Sebastián Vieira1, Hermann Suderow1

1Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales Nicolás Cabrera, Condensed Matter Physics Center, Unidad Asociada de Bajas Temperaturas y Altos Campos Magnéticos, Universidad Autónoma de Madrid, Spain
2H.H. Wills Physics Laboratory, University of Bristol, UK
3Laboratorio de Microscopías Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, Spain
4Instituto de Ciencia de Materiales de Aragón (ICMA), CSIC-Universidad de Zaragoza, Spain
*Present address: Department of Applied Physics, Eindhoven University of Technology, The Netherlands.

Recently we studied the effect of random disorder in a particularly simple two dimensional system and found a new recipe to enhance order. We used a thin superconductor under magnetic fields[1]. The Cooper pairs in the superconductor turn and form quantum vortices. Each one is like a small tornado, but they are all very tiny and, what is most important, they all look exactly the same and repel each other. As a result, they form a perfect hexagonal lattice, which can be imaged with a surprising accuracy.

Past 2Physics article by this group:
March 10, 2013: "Nanostructuring Improves Vortex Pinning in Superconductors at Elevated Temperatures and Magnetic Fields" by R. Córdoba, T. I. Baturina, J. Sesé, A. Yu. Mironov, J. M. De Teresa, M. R. Ibarra, D. A. Nasimov, A. K. Gutakovskii, A.V. Latyshev, I. Guillamón, H. Suderow, S.Vieira, M. R. Baklanov, J. J. Palacios, V.M.Vinokur.

To introduce random disorder in a controlled way, we made a one-dimensional nanostructure and showed that, under certain conditions, the hexagonal lattice floats over the nanostructure (Fig.1 right panel). The floating lattice disorders when increasing the vortex density. Random disorder appears because both lattices are incommensurate. We find that the transition into the disordered state occurs far above present expectations from random field theory. Our conclusion is that the weak one-dimensional correlations inhibit the effect of random disorder.
Figure 1: Vortices in a hexagonal lattice are shown as red points. A linear modulation acts on the vortex positions. When the vortex density is low, vortices are confined to the minima of the linear modulation, and the interaction among them is essentially confined to the lines along the potential minima, as schematically shown in the left panel. However, when the vortex density increases, one can accommodate many vortices within one modulation’s wavelength. In the right panel we schematically show this situation (for clarity, we only draw a small amount of vortices). In that case, the lattice and 1D potential modulation have incommensurate spatial periods and the orientation of the lattice no longer follows the linear modulation. The resulting vortex landscape is quasi-random. The vortex positions are slightly displaced with respect to the ordered lattice. In this work, we show that the displacement grows logarithmically with distance, a feature which demonstrates that the disorder created by this situation is scale-invariant.

To see this in more detail, let us think of many identical particles that repel each other forming a single layer on a corrugated surface and at zero temperature. Let the position of the particles depend on the size of the corrugation. If the surface shows a periodic one-dimensional pattern, as the wrinkles you create on a carpet when you lay it down on your floor, you may obtain hexagonal order commensurate to the wrinkles (left panel of Fig.1, [2]). The question is, what happens if you produce a fully random pattern which looks the same at all scales and increase the size of the corrugation? To answer this question (posed in several theory papers some time ago, see e.g.Refs. [3,4]) we first need to create such a random pattern. Think of a carpet with many small (much smaller than the particle size) and stiff yarns of many different lengths. To make such a carpet, you have to prune it yarn by yarn choosing each time a completely random height. This looks difficult.

Instead, we preferred to use the one-dimensional modulation [5]. The wavelength of the modulation is incommensurate to the wavelength of the ordered particle lattice. Disorder in the particle positions appears automatically, simply because both lattices do not match.

Then, as the second step, we decrease the interaction strength among particles. This is easy for vortices in superconductors [6]. We just have to increase the magnetic field, and we effectively increase the size of the corrugation, with respect to the strength of the interaction among particles.

The experiment directly showing the disorder transition in the vortex lattice was made using a scanning tunneling microscope effectively at absolute zero in the low temperature laboratory of the Universidad Autonóma de Madrid [7]. The thin superconductor with a weak one-dimensional modulation was fabricated in the Laboratory of advanced Microscopies & Nanoscience Institute of Aragón [8]. We eliminated the effect of temperature altogether and produced a very well controlled linear nanostructure. We imaged up to several thousands of vortices in Madrid. This allowed us to characterize the critical exponents of the transition very accurately.

Transitions are often measured in macroscopic experiments, where the obtained information is the result of the average of particles’ positions and the interaction among them. Even microscopic experiments, as neutron scattering, provide an average over many particles. In our work, we were able to show the macroscopic behavior by imaging lots of vortices one by one. This allowed us to characterize precisely the transition. The order-disorder transition goes on by particle displacements producing topological defects (dislocations and disclinations) in an otherwise ordered lattice. The experiment shows how random quenched disorder progresses in the lattice when increasing the magnetic field. We find a logarithmic increase of displacements with respect to the ordered lattice at low fields and density fluctuations in the high field disordered phase. Both effects nicely agree with random field theories.

But we also find that the size of the random potential at which the transition takes places does not agree with random field theory. On rather universal arguments, theory finds that those topological defects should arise at a critical disorder strength of 1/8 [3,4]. The experiment gives a much higher critical value, of 1/2. The lattice stays ordered over a significantly larger range of magnetic fields than expected. What is favoring order? The answer lies in the correlations produced by the one-dimensional modulation. This was discussed theoretically for spin systems [9], but had not been fully addressed by experiments before. Although the one-dimensional modulation does not influence the orientation of the lattice nor directly determines the precise positions of the particles in the lattice, correlations give consistency to the two dimensional hexagonal order.
Figure 2: Image of the vortex lattice in the high field disordered phase at 5.5 T taken with our microscope. Background color represents the intensity of vortex density fluctuations. The lattice is shown by its Delaunay triangulation. Disclinations –five or seven coordinated vortices, green and orange dots, respectively– and disclination pairs –dislocations– are present over the whole surface producing a very disordered vortex lattice. The 1D thickness modulation generating the symmetry breaking disorder is also shown.

The result that you can help supporting an ordered hexagonal two-dimensional lattice in a random medium by introducing a tiny amount of symmetry breaking correlations is both useful and unexpected. It adds now a new looking-glass for vortex physics in nanostructured superconductors.

Our to-do list includes studying vortex dynamics in presence of the disorder potential. By applying a current, we want to see when vortices start moving and study the stability of superconductivity to disorder. The careful observation of vortex lattices in superconductors will be useful to understand more about the influence of disorder in macroscopic quantum coherence.

[1] I. Guillamón, R. Córdoba, J. Sesé, J. M. De Teresa, M. R. Ibarra, S. Vieira, H. Suderow, "Enhancement of long-range correlations in a 2D vortex lattice by an incommensurate 1D disorder potential". Nature Physics, 10, 851 (2014). Abstract.
[2] Piero Martinoli, "Static and dynamic interaction of superconducting vortices with a periodic pinning potential". Physical Review B, 17, 1175–1194 (1978). Abstract.
[3] Thomas Nattermann, Stefan Scheidl, Sergey E. Korshunov, Mai Suan Li, "Absence of reentrance in the two-dimensional XY-model with random phase shift". Journal of Physics I France, 5, 565–572 (1995). Abstract.
[4] David Carpentier, Pierre Le Doussal, "Melting of two dimensional solids on disordered substrates". Physical Review Letters, 81, 1881 (1998). Abstract.
[5] Laurent Sanchez-Palencia, Maciej Lewenstein, "Disordered quantum gases under control". Nature Physics, 6, 87 (2010). Abstract.
[6] Ernst Helmut Brandt, "Vortex-vortex interaction in thin superconducting films". Physical Review B, 79, 134529 (2009). Abstract.
[7] http://lbtuam.es
[8] http://ina.unizar.es/, http://www.icma.unizar-csic.es/ICMAportal/, http://www.unizar.es 
[9] J. Wehr, A. Niederberger, L. Sanchez-Palencia, M. Lewenstein, "Disorder versus the Mermin–Wagner–Hohenberg effect: From classical spin systems to ultracold atomic gases". Physical Review B, 74, 224448 (2006). Abstract.

Labels: , ,

posted by Quark @ 7:33 AM      links to this post

Sunday, November 23, 2014

Imaging Spin-Valley-Layer Locking in a Transition-Metal Dichalcogenide

Transition-metal dichalcogenides (TMDs) of the form MCh2, where M is a transition-metal and Ch a chalcogen, have received much attention in recent years. They can be stabilised as single Ch-M-Ch monolayers, which display a host of attractive materials properties including direct band gaps in the visible region and ambipolar conduction, suggesting a range of applications in electronics and optoelectronics [1]. Moreover, they host degenerate band extrema at the corners of the hexagonal Brillouin zone, which gives rise to a so-called valley degree of freedom. A combination of strong spin-orbit interactions with broken inversion symmetry in the monolayer causes this valley pseudospin to become strongly coupled to the real spin [2]. Valley-dependent optical selection rules combined with suppressed inter-valley scattering resulting from their coupled spin-valley texture has opened new possibilities for optical control of spin and valley pseudospins [3-5].

This suggests unique potential to exploit TMDs in novel schemes of electronics exploiting the spin (a.k.a. spintronics) or valley (a.k.a. valleytronics) degrees of freedom, with the ultimate potential for faster, smaller, and more energy-efficient devices. One might naturally expect this potential to be lost for their bulk counterparts, where the most common structure (the 2H polymorph) is formed by stacking single TMD monolayers together with a 180° rotation between neighbouring layers (other stacking sequences host their own interesting properties [6], but we don’t consider these here). The bulk unit cell therefore contains two such monolayers, having a centre of inversion. It is well established that such inversion symmetry, together with time-reversal symmetry, enforces all electronic states in solids to be spin-degenerate.

In our recent work published in Nature Physics [7], performed in a collaboration between my group in St Andrews (UK) and researchers at the Norwegian University of Science and Technology, the universities of Tokyo (Japan), Aarhus (Denmark), and Suranaree (Thailand), the Max-Planck Institute in Stuttgart (Germany), MAX-IV Laboratory (Sweden) and Diamond Light Source (UK), we have instead observed spin-polarised states persisting in centrosymmetric bulk WSe2.

We used angle-resolved photoemission spectroscopy (ARPES) to probe the electronic structure of bulk crystals of 2H-WSe2. Through a process of Mott scattering, we also measured the spin polarisation of the emitted photoelectrons, and discovered that the electronic states around the corners of the Brillouin zone were almost 100% spin polarised. Surely this would seem to contradict the inversion symmetry that this material possesses?

Figure 1: Valence band dispersions of WSe2 measured by angle-resolved photoemission, showing excellent agreement with theoretical calculations of the kz-dependent bulk electronic structure (coloured lines). The spin texture measured at the K and K’ points of the Brillouin zone is shown schematically by coloured arrows.

Through a combination of photon-energy dependent ARPES experiments and first-principles theoretical calculations, we observed how, for the electronic states close to the Brillouin zone corners, their wavefunctions are spatially localised within single monolayers of the bulk crystal structure where locally, inversion symmetry is not present. The combination of this inversion symmetry breaking together with strong spin-orbit coupling drives these states to develop huge spin polarisations, leading to spin-valley locking as for isolated monolayers.
Figure 2: Angle-resolved photoemission measurements of WSe2 throughout the Brillouin zone, schematically showing the intertwined layer- and momentum-dependent spin texture uncovered here.

The 180° rotation between neighbouring monolayers in the bulk crystal structure, however, imposes an additional layer-dependent sign change of the spin polarisation for a given valley, as found in previous theoretical calculation [8], and recently also suggested from polarisation-resolved optical experiments [9]. By exploiting photon energy-dependent interference between photoelectrons emitted from different crystal layers, we could tune the measured photoelectron spin-polarisation nearly to zero, effectively averaging over neighbouring layers, or could selectively probe just the top monolayer of the crystal. These measurements together provide the first direct observation of the entangling of the spin with valley and layer pseudospins in a bulk transition-metal dichalcogenide.

Moreover, our study provides an experimental observation that local, rather than global, inversion symmetry breaking is sufficient to stabilise spin-polarised states in solids [10], contrary to conventional wisdom. This is exciting because it reveals that a whole new class of materials which we previously thought must have only spin-degenerate energy bands can in fact locally host spin-polarised states. Controlling this could bring fantastic new opportunities for spin- and valleytronics, and a whole arsenal of new materials in which we can achieve this.

[1] Qing Hua Wang, Kourosh Kalantar-Zadeh, Andras Kis, Jonathan N. Coleman, Michael S. Strano, "Electronics and optoelectronics of two-dimensional transition metal dichalcogenides". Nature Nanotechnology, 7, 699 (2012). Abstract.
[2] Di Xiao, Gui-Bin Liu, Wanxiang Feng, Xiaodong Xu, Wang Yao, "Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides". Physical Review Letters, 108, 196802 (2012). Abstract.
[3] Hualing Zeng, Junfeng Dai, Wang Yao, Di Xiao, Xiaodong Cui, "Valley polarization in MoS2 monolayers by optical pumping". Nature Nanotechnology, 7, 490 (2012). Abstract.
[4] Kin Fai Mak, Keliang He, Jie Shan, Tony F. Heinz, "Control of valley polarization in monolayer MoS2 by optical helicity". Nature Nanotechnology, 7, 494 (2012). Abstract.
[5] Xiaodong Xu, Wang Yao, Di Xiao, Tony F. Heinz, "Spin and pseudospins in layered transition metal dichalcogenides". Nature Physics, 10, 343 (2014). Abstract.
[6] R. Suzuki, M. Sakano, Y. J. Zhang, R. Akashi, D. Morikawa, A. Harasawa, K. Yaji, K. Kuroda, K. Miyamoto, T. Okuda, K. Ishizaka, R. Arita, Y. Iwasa, "Valley-dependent spin polarization in bulk MoS2 with broken inversion symmetry". Nature Nanotechnology, 9, 611 (2014). Abstract.
[7] J.M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerød, M. Leandersson, T. Balasubramanian, M. Hoesch, T.K. Kim, H. Takagi, W. Meevasana, Ph. Hofmann, M.S. Bahramy, J.W. Wells, P. D. C. King, "Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor". Nature Physics, 10, 835 (2014). Abstract.
[8] Zhirui Gong, Gui-Bin Liu, Hongyi Yu, Di Xiao, Xiaodong Cui, Xiaodong Xu, Wang Yao, "Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers". Nature Communications, 4, 2053 (2013). Abstract.
[9] Aaron M. Jones, Hongyi Yu, Jason S. Ross, Philip Klement, Nirmal J. Ghimire, Jiaqiang Yan, David G. Mandrus, Wang Yao, Xiaodong Xu, "Spin–layer locking effects in optical orientation of exciton spin in bilayer WSe2". Nature Physics, 10, 130 (2014). Abstract.
[10] Xiuwen Zhang, Qihang Liu, Jun-Wei Luo, Arthur J. Freeman, Alex Zunger, "Hidden spin polarization in inversion-symmetric bulk crystals". Nature Physics, 10, 387 (2014). Abstract.

Labels: ,

posted by Quark @ 8:09 AM      links to this post

Sunday, November 16, 2014

The Plasmoelectric Effect: A New Strategy for Converting Optical Energy into Electricity

Matthew Sheldon

Author: Matthew Sheldon

Affiliation: Department of Chemistry, Texas A&M University, USA.

Link to Sheldon Research Group >>

A plasmon resonance is a remarkable optical phenomenon that occurs in metallic nanostructures and other nanoscale materials that have high electrical conductivity. As reported in 'Science' on October 30 [1], we have demonstrated a new way to use plasmon resonances to generate electrical potentials during optical excitation. Our work could lead to new ways of converting optical energy into electrical energy, and may guide new opportunities in the very active research areas of plasmonics and nanophotonics.

A plasmon resonance results from the oscillations of electrons (or other electrical carriers) lining up with the oscillating electric field of incident radiation. This resonance causes significant concentration of light energy within the small sub-wavelength volume defined by the nanostructure. Because the resonant frequency can be tailored by controlling the nanoscale geometry, plasmonic materials have been the subject of considerable scientific activity for a host of applications that benefit from the ability to tune and concentrate radiation, such as Raman spectroscopy, cell labeling, sub-wavelength optical communication, or enhanced light trapping in solar cells, to list a few examples [2]. However, much of the confined optical energy is quickly absorbed by the metal and converted to heat. This heating is generally regarded as a limitation for optical applications.

Despite this loss of optical energy as heat, we questioned whether the strong plasmonic concentration of energy could still be utilized to perform electrical work. Electrical work can be understood as the movement of electrons through a circuit load, so it seemed natural to wonder if the plasmon resonance, which fundamentally results from the coupling of light to the motion of electrons, could also move electrons through a circuit. As reported in Science on October 30th [1], we discovered a mechanism by which optical absorption in plasmonic resonances indeed produces an electrical potential, a necessary first step towards performing useful electrical work. We have labeled this phenomenon the ‘plasmoelectric effect’. In conjunction with a thermodynamic model we developed, our analysis shows how a plasmonic resonance can act as a heat engine that uses thermal energy from the absorption of light to move electrons and produce static electric potentials.

Currently, the photovoltaic effect is the primary mechanism used in technology for the production of electrical potentials from the absorption of light, i.e. photo-voltages. The photovoltaic effect is the generation of excess electrical carriers in semiconductors during optical excitation with energy greater than the band gap energy. Our discovery, the plasmoelectric effect, is a fundamentally different mechanism for generating an electrical potential, and instead results from the dependence of the plasmon resonance frequency on electron density in conductors.

Recent works from other researchers studying plasmonic systems [3-5] have demonstrated that it is possible to tune the plasmon resonance frequency of a nanostructure by modulating electron density. Specifically, these researchers applied a static electric potential to inject or remove electrons from resonant structures, and they observed a shift to higher or lower frequency, respectively, of the plasmonic absorption resonance. In essence, the electrical state of the conductor, whether it is charged positively, negatively, or neutral, is coupled with the frequency of the plasmonic absorption. This behavior is analogous to how the resonant pitch of a musical instrument, such as a flute, would change if you modify the density of the air in the acoustic cavity.

Inspired by these experiments, we considered the extent to which the optical absorption, the plasmon resonance frequency, and the charge state are linked in this way, and if the reverse of this behavior would also occur. That is, can optical excitation with off-resonant light cause a change in the electron density of a plasmonic structure that shifts the plasmonic absorption into resonance with the illumination, and thereby induce an electrical potential? Considering the acoustic analogy above, this would be like the chamber of a flute adopting a slightly modified air density in order to become resonant with a loud pitch playing nearby that would otherwise be slightly out of tune.

To probe this possibility experimentally, we monitored the electric potential of a conductive surface coated with plasmonic Au nanoparticles using Kelvin probe force microscopy (KPFM). For KPFM a conductive atomic force microscope (AFM) tip is maintained a few nanometers above a sample surface, and the electrical potential between the tip and sample is measured. During KPFM experiments we also illuminated the nanoparticles with a tunable laser, varying the output from higher frequency to lower frequency through the plasmon resonance. We observed that higher frequency light caused negative surface potentials and that lower frequency light caused positive surface potentials, but there was no potential measured when the incident light was the same frequency as the plasmon resonance. This is the exact behavior expected if the nanoparticles are adjusting charge density so that the plasmon resonance is better matched with the frequency of the optical excitation.

Our report also details a thermodynamic model that anticipates this behavior for plasmonic materials. We show how the condition of minimum free energy, the preferred thermodynamic state of a system, corresponds to a configuration of charge density that modulates the plasmon resonance frequency in order to maximize the amount of heat produced via optical absorption. However, the energy required to electrically charge the structure moderates how much the plasmon resonance can shift. Therefore, for a given optical intensity, single frequency light induces a specific charge state that balances these counteracting effects. In general, during illumination a plasmonic structure will only remain neutral if incident light is the same frequency as the plasmon resonance of the neutral structure.

To show that the behavior is general to plasmonic systems, we also measured the optical response of periodic arrays of nanoscale holes in thin gold films that have strong, tunable plasmonic resonances across the visible spectrum based on the hole pitch. These fabricated hole arrays also displayed electrical potential trends consistent with our description of the plasmoelectric effect, as summarized in Fig. 1.
Figure 1: Plasmoelectric effect (a) Schematic of a metal nanoparticle that becomes electrically charged by illumination. (b) Electron microscopy image of the metal nanocircuit, composed of an array of nanoscale holes in a 20-nm-thin gold film. The scale bar is 500 nanometer. (c) Measured optical absorption spectra for metal nanocircuits with different spacings between the holes (175, 225, 250, and 300 nm). (d) Electrical potential of the nanocircuits in (c) as a function of wavelength of the incident light. The measured potentials range from -100 mV to +100 mV as the wavelength of the incident light is tuned from high frequency blue light to low frequency red light.

We believe our results are exciting for two fundamental reasons: First, we have demonstrated a new way to generate an electrical potential by the absorption of radiation. There is general interest in materials that can convert light to electrical potentials for sensing and for optical power conversion, for example, and our report lays the groundwork for these possible applications. Second, we believe our analysis provides more insight into the basic thermodynamic behavior of plasmonic materials. Given the very active research in this area by scientists from many different disciplines, these insights may open new opportunities in plasmonics research.

[1] Matthew T. Sheldon, Jorik van de Groep, Ana M. Brown, Albert Polman, Harry A. Atwater, "Plasmoelectric potentials in metal nanostructures". Science, 346, 828–831 (2014). Abstract.
[2] Albert Polman, "Plasmonics Applied". Science, 322, 868–869 (2008). Abstract.
[3] Carolina Novo, Alison M. Funston, Ann K. Gooding, Paul Mulvaney, "Electrochemical Charging of Single Gold Nanorods". Journal of the American Chemical Society, 131, 14664–14666 (2009). Abstract.
[4] S. K. Dondapati, M. Ludemann, R. Müller, S. Schwieger, A. Schwemer, B. Händel, D. Kwiatkowski, M. Djiango, E. Runge, T. A. Klar, "Voltage-Induced Adsorbate Damping of Single Gold Nanorod Plasmons in Aqueous Solution". Nano Letters, 12, 1247–1252 (2012). Abstract.
[5] Guillermo Garcia, Raffaella Buonsanti, Evan L. Runnerstrom, Rueben J. Mendelsberg, Anna Llordes, Andre Anders, Thomas J. Richardson, Delia J. Milliron, "Dynamically Modulating the Surface Plasmon Resonance of Doped Semiconductor Nanocrystals". Nano Letters, 11(10), 4415–4420 (2011). Abstract.

Labels: ,

posted by Quark @ 6:40 AM      links to this post