Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session W10: Topological Insulators: Optical and Other Properties (Theory) |
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Sponsoring Units: DCMP Chair: Bitan Roy, University of Maryland Room: 007A |
Thursday, March 5, 2015 2:30PM - 2:42PM |
W10.00001: Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures Kristofer Bj\"{o}rnson, Annica Black-Schaffer Topological superconductors are of interest because they are predicted to host Majorana fermions. One example are two-dimensional ferromagnetic semiconductor-superconductor heterostructures, where Majorana fermions are predicted to appear in vortices. The system has previously been classified using a Chern number, but we show that the Chern number is related to a Skyrmion spin texture in the band structure. The Skyrmion spin texture has the advantage of enabling direct experimental measurements of the topological invariant through for example spin-polarized ARPES. The Skyrmion spin texture is also of interest from a conceptual point of view, as it provides a more intuitively accessible topological invariant than the otherwise rather abstract Chern number. [Preview Abstract] |
Thursday, March 5, 2015 2:42PM - 2:54PM |
W10.00002: Compressibility as a probe of topological quantum phase transitions in 1D systems David Nozadze, Nandini Trivedi We investigate the behavior of the compressibility $\kappa$ in the Kitaev chain using the Bogoliubov-de Gennes approach. For a closed chain, we show that the topological phase transition is signaled by the divergence of $\kappa$ at the quantum critical point tuned by the chemical potential. We also explore the effect of disorder on the local compressibility $\kappa(x)$. In the presence of disorder the compressibility across the transition becomes finite and the height of the peak becomes smaller with increasing disorder strength. Our results provide a direct method, the local compressibility, for detecting the quantum phase transition in a Kitaev chain that can be realized in superconductor- semiconducting nanowire hybrid structures with strong spin-orbit coupling. [Preview Abstract] |
Thursday, March 5, 2015 2:54PM - 3:06PM |
W10.00003: Quantized Electromagnetic Response of Three Dimensional Chiral Topological Insulators Sheng-Tao Wang, Dong-Ling Deng, Joel Moore, Kai Sun, Luming Duan Protected by the chiral symmetry, three dimensional chiral topological insulators are characterized by an integer-valued topological invariant. How this invariant could emerge in physical observables is an important question. Here we show that the magneto-electric polarization can identify the integer-valued invariant if we gap the system without a quantum Hall layer on the surface. The quantized response is demonstrated to be robust against weak perturbations. We also study the topological properties by adiabatically coupling two nontrivial phases, and find that gapless states appear and are localized at the boundary region. Finally, an experimental scheme is proposed to realize the Hamiltonian and measure the quantized response with ultracold atoms in optical lattices. [Preview Abstract] |
Thursday, March 5, 2015 3:06PM - 3:18PM |
W10.00004: Charged skyrmions on the surface of a 3D topological insulator Hilary Hurst, Dmitry Efimkin, Victor Galitski We consider the interplay between magnetic skyrmions in an insulating thin film and the Dirac surface states of a 3D topological insulator (TI), coupled by proximity effect. The nontrivial magnetic texture of skyrmions can lead to confinement of Dirac states at the skyrmion radius, where out of plane magnetization vanishes. This confinement results in charging of the skyrmion texture. We find that the bound states are robust in an external magnetic field, which is needed to stabilize skyrmions. It is expected that for reasonable experimental parameters skyrmions will have a small number of bound states that can be tuned using an external magnetic field. We argue that these charged skyrmions can be manipulated directly by an electric field, with skyrmion mobility proportional to the number of bound states at the skyrmion radius. Coupling skyrmionic thin films to a TI surface can provide a more direct and efficient way of controlling skyrmion motion in insulating materials. [Preview Abstract] |
Thursday, March 5, 2015 3:18PM - 3:30PM |
W10.00005: Braiding statistics of loop excitations in three dimensions Chenjie Wang, Michael Levin While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two loop-like excitations, we argue that a more fundamental quantity is the statistical phase associated with braiding one loop $\alpha$ around another loop $\beta$, while both are linked to a third loop $\gamma$. We study this three-loop braiding in the context of $(Z_N)^K$ gauge theories which are obtained by gauging a gapped, short-range entangled lattice boson model with $(Z_N)^K$ symmetry. We find that different short-range entangled bosonic states with the same $(Z_N)^K$ symmetry (i.e. different symmetry-protected topological phases) can be distinguished by their three-loop braiding statistics. [Preview Abstract] |
Thursday, March 5, 2015 3:30PM - 3:42PM |
W10.00006: Vortex-line condensation in three dimensions: A physical mechanism of bosonic topological insulators Peng Ye, Zheng-Cheng Gu 3d bosonic topological insulators (BTI) are symmetry protected topological(SPT) phases with U(1) and Z$^T_2$ (time-reversal symmetry with $T^2$=1). BTI were first proposed based on the group cohomology theory which suggests two distinct root states. Soon after, surface anomalous topological orders were proposed to identify different root phases and also leads to a new root state beyond group cohomology. Nevertheless, it is still unclear what is the universal physical mechanism for BTI phases. In this work, we answer the question by proposing an universal physical mechanism via vortex-line condensation in a superfluid, e.g., helium-4 or cold atoms in optical lattices. Using such a simple physical picture, we find three root phases, of which two of them are classified by group cohomology theory while the other is beyond group cohomology classification. The physical picture also leads to a ``natural'' bulk dynamic topological quantum field theory (TQFT) description for BTI and gives rise to a physical pathway of practical realization. Finally, we generalize the vortex-line condensation picture to other symmetries and find that in three dimensions, even for a unitary $Z_2$ symmetry, there is a nontrivial $Z_2$ SPT phase beyond the group cohomology classification. [Preview Abstract] |
Thursday, March 5, 2015 3:42PM - 3:54PM |
W10.00007: Topological BF theory of the quantum hydrodynamics of incompressible polar fluids Apoorv Tiwari, Xiao Chen, Titus Neupert, Luiz Santos, Shinsei Ryu, Claudio Chamon, Christopher Mudry We analyze a hydrodynamical model of a polar fluid in (3+1)-dimensional spacetime. We explore a spacetime symmetry -- volume preserving diffeomorphisms -- to construct an effective description of this fluid in terms of a topological BF theory. The two degrees of freedom of the BF theory are associated to the mass (charge) flows of the fluid and its polarization vorticities. We discuss the quantization of this hydrodynamic theory, which generically allows for fractionalized excitations. We propose an extension of the Girvin-MacDonald-Platzman algebra to (3+1)-dimensional spacetime by the inclusion of the vortex-density operator in addition to the usual charge density operator and show that the same algebra is obeyed by massive Dirac fermions that represent the bulk of $Z_{2}$ topological insulators in three-dimensional space. [Preview Abstract] |
Thursday, March 5, 2015 3:54PM - 4:06PM |
W10.00008: Berry phase and Rashba fields in realistic semiconductor quantum rings under tilted magnetic field Vivaldo Lopes-Oliveira, Victor Lopez-Richard, Sergio Eduardo Ulloa The geometric Berry phase has been experimentally measured and manipulated in InGaAs-based mesoscopic rings, as seen from magnetotransport data [1]. Motivated by these experiments, we present here an analysis of the influence of the magnetic field orientation and intensity on the Berry phase experienced by electrons in a realistic quantum ring structure (similar model has been used in ref. [2]). We use the k.p formalism and fully incorporate the effects of confinement asymmetry, as well as the resulting Rashba spin-orbit-coupling (SOC) fields within the same framework. We obtain spin maps for angle and magnetic field intensities for different levels. At the anticrossing regions, with strong level mixing produced by varying flux dependence, we observe pronounced asymmetry effects in the shape and character of excited states. The asymmetry plays an important role in determining the Berry phase of the different states. We also find that effects of varying magnetic field tilt and intensity, as well as SOC, are more pronounced in the ground state. The substantial phase modulation observed in the lower energy level manifold can be monitored and exploited in transport experiments. [1] F.Nagasawa et al. Nat. Comm. 4, 2526 (2013); [2] V.Lopes-Oliveira et al. PRB 90, 125315 (2014). [Preview Abstract] |
Thursday, March 5, 2015 4:06PM - 4:18PM |
W10.00009: Uhlmann Measure in Topological Insulators and Superconductors at Finite Temperature Oscar Viyuela, Angel Rivas, Miguel Angel Martin-Delgado I will introduce the Uhlmann geometric phase as a tool to characterise density matrices of 1D and 2D topological insulators and superconductors. We achieve this goal by constructing new topological invariants called Topological Uhlmann numbers. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. New effects appear such as the existence of critical temperatures, novel thermal-topological transitions in models with high Chern numbers, breakdown of the usual bulk-edge correspondence, etc. Moreover, as the Uhlmann phase is an observable itself, we analyse potential measurement schemes that could be applicable to current experimental setups like cold atoms in optical lattices. \\[4pt] [1] 2D Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers, O. Viyuela, A. Rivas, M.A. Mart\'in-Delgado, Phys. Rev. Lett 113, 076408 (2014).\\[0pt] [2] Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems, O. Viyuela, A. Rivas, M.A. Mart\'in-Delgado, Phys. Rev. Lett 112, 130401 (2014). [Preview Abstract] |
Thursday, March 5, 2015 4:18PM - 4:30PM |
W10.00010: Equilibrium currents in chiral systems with nonzero Chern number Oleg Starykh, Eugene Mishchenko We describe a simple quantum-mechanical approach to calculating equilibrium particle current along the edge of a system with nontrivial band spectrum topology. The approach does not require any a priori knowledge of the band topology and, as a matter of fact, treats topological and nontopological contributions to the edge currents on the same footing. We illustrate its usefulness by demonstrating the existence of ``topologically nontrivial'' particle currents along the edges of three different physical systems: two-dimensional electron gas with spin-orbit coupling and Zeeman magnetic field, surface state of a topological insulator, and kagome antiferromagnet with Dzyaloshinskii-Moriya interaction. [Preview Abstract] |
Thursday, March 5, 2015 4:30PM - 4:42PM |
W10.00011: Surface plasmon polaritons in topological insulators Junjie Qi, Haiwen Liu, X.C. Xie We study surface plasmon polaritons on a topological insulator-vacuum interface. When the time-reversal symmetry is broken due to ferromagnetic coupling, the surface states exhibit a magneto-optical Kerr effect. This effect gives rise to a novel transverse-type surface plasmon polariton, in addition to the longitudinal type. In specific, these two types contain three different channels, corresponding to the pole of the determinant of the Fresnel reflection matrix. All three channels of the surface plasmon polaritons display tight confinement and a long lifetime and show strong light-matter coupling with a dipole emitter. [Preview Abstract] |
Thursday, March 5, 2015 4:42PM - 4:54PM |
W10.00012: Giant Faraday effect due to Pauli exclusion principle in 3D topological insulators Hari Paudel, Michael Leuenberger Experiments using ARPES, which is based on the photoelectric effect, have shown that the surface states in 3D topological insulators (TI) are gapless. Here we consider Weyl interface fermions due to band inversion in narrow-bandgap semiconductors, such as Pb\textbraceleft 1-x\textbraceright Sn\textbraceleft x\textbraceright Te. We determine the optical selection rules of electron-hole pair excitation by means of the solutions of the 3D Dirac equation. We calculate explicitly the electric dipole matrix elements by means of bandstructure calculations for Pb\textbraceleft 1-x\textbraceright Sn\textbraceleft x\textbraceright Te. Using the 3D Dirac equation and bandstructure calculations, we show that the transitions between positive and negative energy solutions, giving rise to electron--hole pairs, obey strict optical selection rules. We apply our results to calculate the Faraday effect due to the Pauli exclusion principle in a pump--probe setup using a 3D TI double interface of a PbTe/Pb\textbraceleft 0:31\textbraceright Sn\textbraceleft 0:69\textbraceright Te/PbTe heterostructure. The Faraday rotation angle exhibits oscillations as a function of probe wavelength and thickness of the heterostructure. The maxima in the Faraday rotation angle are of the order of mrds. [Preview Abstract] |
Thursday, March 5, 2015 4:54PM - 5:06PM |
W10.00013: Effect of electron-phonon interaction on the finite frequency conductivity of 3D Dirac materials Boris Pavlovic, Elisabeth J. Nicol Recently, interest has been directed toward identifying and characterizing materials with 3D Dirac energy dispersions. We present our theoretical results for the finite frequency optical conductivity of 3D Dirac materials with the inclusion of an electron-phonon (e-p) interaction. Using a Holstein e-p interaction and allowing for varying chemical potential, we show how the e-p self energy modifies the electronic density of states and the optical conductivity. The results for 3D are contrasted with their 2D analogs, as previously discussed for graphene.$^{[1]}$ $^{[1]}$ J.P. Carbotte, E.J. Nicol and S.G. Sharapov, PRB 81, 045419 (2010). $\\$ [Preview Abstract] |
Thursday, March 5, 2015 5:06PM - 5:18PM |
W10.00014: Thermoelectric Effect in Topological Insulators Yong Xu, Shou-Cheng Zhang Improving the thermoelectric figure of merit $zT$ is one of the greatest challenges in material science. The recent discovery of topological insulators (TIs) offers new promise in this prospect. In this talk, we demonstrate theoretically that $zT$ is strongly size dependent in TIs, and the size parameter can be tuned to enhance $zT$ to be significantly greater than 1. Furthermore, we show that the lifetime of the edge states in TIs is strongly energy dependent, leading to large and anomalous Seebeck effects with an opposite sign to the Hall effect. Some recent experimental progress will also be introduced. [Preview Abstract] |
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