Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session G13: Topological Insulators: Theory II |
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Sponsoring Units: DCMP Chair: Roman Lutchyn, Microsoft Station Q Room: 315 |
Tuesday, March 19, 2013 11:15AM - 11:27AM |
G13.00001: The strong index classification of reflection symmetric topological insulators and superconductors Ching-kai Chiu, Hong Yao, Shinsei Ryu We discuss the topological invariants of topological insulators and superconductors protected by spatial reflection symmetry in any spatial dimensions. In the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer classification and reflection symmetry, we introduce two new topological invariants: a mirror integral number and a binary integral number, which is determined by the larger one of the $Z$ number and mirror integral number. We claim that the topological states are characterized by one of `$0$', $Z_2$, $Z$, and the two new topological invariants. Furthermore, those topological invariants are also determined by commutation or anticommutation relations between the discrete non-spatial symmetry operators and the reflection symmetry operator. By using the construction of bulk Dirac Hamiltonians, we provide the complete classification, which still has the same dimensional periodicities with the original Altland-Zirnbauer classification. When a boundary is introduced, which is reflected into itself, these non-trivial topological insulators and superconductors support gapless modes localized at the boundary. [Preview Abstract] |
Tuesday, March 19, 2013 11:27AM - 11:39AM |
G13.00002: Symmetry protected topological phases from decorated domain walls Xie Chen, Yuan-Ming Lu, Ashvin Vishwanath Symmetry protected topological phases are gapped quantum phases with gapless edge excitations protected by certain symmetries of the system. While SPT phases in lower dimensions (especially 1D) are relatively well understood, less is known about higher dimensional (2D and 3D) SPT phases including what their edge excitations are like and how to detect them. In this work, we present a construciton of $d$ dimensional SPT phases with $Z_2\times G$ symmetry by decorating the $Z_2$ domain walls in the $d$ dimensional bulk with $d-1$ dimensional SPT phases with $G$ symmetry. Such a construction not only provides a simple understanding of higher dimensional SPT phases starting from lower dimensional ones, but also reveals a special topological feature of such SPT phases. That is, on the boundary of the system, the domain wall end points/loops carry gapless edge states of the $d-1$ dimensional SPT phase with $G$ symmetry. We discuss in detail a 2D SPT phase with $Z_2 \times Z_2^T$ symmetry and a 3D SPT phase with $Z_2\times Z_2$ symmetry, which illustrate a more general hierarchical structure of SPT phases related to the cup product of group cohomology. [Preview Abstract] |
Tuesday, March 19, 2013 11:39AM - 11:51AM |
G13.00003: Lattice model for the surface states of a topological insulator Marcel Franz, Dominic Marchand A surface of a strong topological insulator (STI) is characterized by an odd number of linearly dispersing gapless electronic surface states. It is well known that such a surface cannot be described by an effective two-dimensional lattice model (without breaking the time-reversal symmetry), which often hampers theoretical efforts to quantitatively understand some of the properties of such surfaces, including the effect of strong disorder, interactions and various symmetry-breaking instabilities. Here we describe a lattice model that can be used to describe a pair of STI surfaces and has an odd number of Dirac fermion states with wavefunctions localized on each surface. The Hamiltonian consists of two planar tight-binding models with spin-orbit coupling, representing the two surfaces, weakly coupled to each other by terms that remove the redundant Dirac points from the low-energy spectrum. The utility of this model is illustrated by studying the magnetic and exciton instabilities of the STI surface state driven by short-range repulsive interactions. [Preview Abstract] |
Tuesday, March 19, 2013 11:51AM - 12:03PM |
G13.00004: 3D Dirac Electrons on a Cubic Lattice with Noncoplanar Multiple-$Q$ Order Satoru Hayami, Takahiro Misawa, Youhei Yamaji, Yukitoshi Motome Noncoplanar multiple-$Q$ orders often lead to new low-energy excitations and/or topologically nontrivial states. In particular, triple-$Q$ orders have attracted much interest due to the emergence of topological (Chern) insulators and associated anomalous quantum Hall effects. In the present study, we explore the possibility of such multiple-$Q$ orderings on a simple cubic lattice and their influence on the electronic structure. We find that a four-sublattice triple-$Q$ magnetic order significantly affects the low-energy single-particle spectrum which is described by the three-dimensional massless Dirac electrons. In order to clarify the stability of such noncoplanar magnetic order in microscopic models, we investigate the ground-state phase diagram of an extended periodic Anderson model on a cubic lattice by mean-field approximation. As a result, we find that the triple-$Q$ phase appears in a wide range of parameters at 3/2 filling. The 3D Dirac nature gives rise to a characteristic gapless surface state. We discuss the bulk and surface electronic states in details. We also discuss a possible realization of a topological insulating phase by opening an energy gap in the triple-$Q$ phase. [Preview Abstract] |
Tuesday, March 19, 2013 12:03PM - 12:15PM |
G13.00005: Fermi loop in interface states and surface flat bands in diamond lattice models Ryuji Takahashi, Shuichi Murakami Previously we have shown the gapless interface states between two topological insulators with different chiralities by means of the mirror Chern number [1]. In this presentation we use the Fu-Kane-Mele tight-binding model on diamond lattice {\it with} the spin-orbit interaction, and calculate their gapless interface states. We find that when the particle-hole symmetry is imposed in the whole system the Fermi surface of the gapless states becomes a loop in the interface Brillouin zone. We show how to characterize the existence of such Fermi loop in terms of topology. Next we report flat band states in the surface of the diamond lattice model with anisotropic hopping integrals {\it without} the spin-orbit interaction. When anisotropy is not so strong, the surface flat band exits in some part of the Brillouin zone. Moreover when the anisotropy becomes sufficiently strong, the surface flat bands cover the whole surface Brillouin zone. [1] R. Takahashi, S. Murakami, Phys. Rev. Lett. 107,166805 (2011). [Preview Abstract] |
Tuesday, March 19, 2013 12:15PM - 12:27PM |
G13.00006: Effect of electron-phonon interaction on the velocity renormalization of the surface state of 3D topological insulator Qiuzi Li, Sankar Das Sarma Explicitly taking into account of electron-phonon interaction, we consider the velocity renormalization of the surface state of 3D topological insulator. The velocity renormalization is shown to be strongly dependent on the carrier density of the system. We compare our theoretical calculation to recent experimental data. We further consider the correction to the compressibility arising from electron-phonon coupling, and discuss its implication in experiments. [Preview Abstract] |
Tuesday, March 19, 2013 12:27PM - 12:39PM |
G13.00007: ABSTRACT WITHDRAWN |
Tuesday, March 19, 2013 12:39PM - 12:51PM |
G13.00008: 2D compressibility of surface states on 3D topological insulators David Abergel, Sankar Das Sarma We develop a theory for the compressibility of the surface states of 3D topological insulators and propose that surface probes of the compressibility via scanning single electron transistor microscopy will be a straightforward way to access the topological states without interference from the bulk states. We describe the single-particle nature of the surface states taking into account an accurate Hamiltonian for the bands and then include the contribution from electron-electron interactions and discuss the implications of the ultra-violet cutoff, including the universality of the exchange contribution when expressed in dimensionless units. We also compare the theory with experimentally obtained $\frac{d\mu}{dn}$ as extracted from angle-resolved photoemission spectroscopy measurements. Finally, we point out that interaction-driven renormalization of the Fermi velocity may be discernible via this technique. [Preview Abstract] |
Tuesday, March 19, 2013 12:51PM - 1:03PM |
G13.00009: Dislocations in topological phases of matter and their topological terms Akihiro Tanaka, Toru Kikuchi When dislocations are present in topological insulators/superconductors and their variants, they are known to endow subgap boundstates. We revisit their physics from the viewpoint of topological field theories, discussing sevral issues among which are 1) the interplay of the Nieh-Yan torsional invariant with other topological terms, 2) possibile appearance of Nieh-Yan-like terms in nonlinear sigma models of competing orders, 3) the subtle controversy on the absence/existence of Callan-Harvey-like anomaly-inflow in the dual formulation. [Preview Abstract] |
Tuesday, March 19, 2013 1:03PM - 1:15PM |
G13.00010: Massless Axions: the Callan-Harvey effect revisited Toru Kikuchi, Akihiro Tanaka Axion-like degrees of freedom appear in the low energy physics of various condensed matter systems, which range from quantum spin systems and superconductors to topological insulators and their variants. When topological defects such as domain walls and vortices are formed by the axion fields, their responses to external fields are dominated by the current inflow from the surrounding bulk (Callan-Harvey effect). However, a dual reformulation due to Izquierdo-Townsend is known to present a controversy regarding the existence of this inflow in the case when axions are massless, and can have important consequences. We revisit this problem and discuss its possible relevance to condensed matters. [Preview Abstract] |
Tuesday, March 19, 2013 1:15PM - 1:27PM |
G13.00011: Semi-metal-insulator transition at the surface of a topological insulator with in-plane magnetization Flavio Nogueira, Ilya Eremin We discuss the role of quantum fluctuations when the surface of a topological insulator (TI) is used as a substrate for a layered ferromagnetic (FM) material. As is well known, an out-of-plane magnetization gaps the surface states and modifies the Landau-Lifshitz-Gilbert equation in an essential way, due to the topological magnetoelectric effect. On the other hand, for the case of in-plane magnetization the surface states are gapless. We show that quantum fluctuations may modify this picture if the exchange interaction between the TI and the FM is sufficiently large. Indeed, we will show that a gap is dynamically generated in this case, turning in this way the semi-metallic state into an insulating one. Another situation of interest where a similar mechanism applies involves the Coulomb interaction between the fermions at the interface between the TI and the FM. The interplay between the magnetization dynamics and the Coulomb interaction is discussed in detail. [Preview Abstract] |
Tuesday, March 19, 2013 1:27PM - 1:39PM |
G13.00012: Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids Hiroki Isobe, Naoto Nagaosa We study theoretically the quantum critical phenomenon of the phase transition between the trivial insulator and the topological insulator in (3+1) dimensions, which is described by a Dirac fermion coupled to the electromagnetic field. The intriguing result is the recovery of the Lorentz invariance in the infrared limit, and the electrons in solids obey the conventional QED. In detail, the renormalization group (RG) equations for the running coupling constant $\alpha$, the speed of light $c$, and electron $v$ are derived by using perturbative RG method to one-loop level. The almost exact analytic solutions to these RG equations are obtained to reveal that (i) $c$ and $v$ approach to the common value with combination $c^2v$ being almost unrenormalized, (ii) the RG flow of $\alpha$ is the same as that of usual QED with $c^3$ being replaced by $c^2v$, and (iii) there are two crossover momentum/energy scales separating three regions of different scaling behaviors. The dielectric and magnetic susceptibilities, angle-resolved photoemission spectroscopy (ARPES), and the behavior of the gap are discussed from this viewpoint. Reference: H. Isobe and N. Nagaosa, Phys. Rev. B {\bf 86}, 165127 (2012). [Preview Abstract] |
Tuesday, March 19, 2013 1:39PM - 1:51PM |
G13.00013: Nonequilibrium Transport Through a Gate-Controlled Barrier on the Quantum Spin Hall Edge Roni Ilan, Jerome Cayssol, Jens Bardarson, Joel Moore The quantum spin Hall insulator is characterized by the presence of gapless helical edge states where the spin of the charge carriers is locked to their direction of motion. In order to probe the properties of the edge modes, we propose a design of a tunable quantum impurity realized by a local gate under an external magnetic field. Using the integrability of the impurity model, the conductance is computed for arbitrary interactions, temperatures and voltages, including the effect of Fermi liquid leads. The result can be used to infer the strength of interactions from transport experiments. [Preview Abstract] |
Tuesday, March 19, 2013 1:51PM - 2:03PM |
G13.00014: Magnetic translation algebra with or without magnetic field Christopher Mudry, Claudio Chamon The magnetic translation algebra plays an important role in the quantum Hall effect. Murthy and Shankar have shown how to realize this algebra using fermionic bilinears defined on a two-dimensional square lattice. We show that, in any dimension d, it is always possible to close the magnetic translation algebra using fermionic bilinears, be it in the continuum or on the lattice. We also show that these generators are complete in even, but not odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions that conserves particle number can be represented in terms of the generators of this algebra, whether or not time-reversal symmetry is broken. As an example, we reproduce the f-sum rule of interacting electrons at vanishing magnetic field using this representation. We also show that interactions can significantly change the bare band width of lattice Hamiltonians when represented in terms of the generators of the magnetic translation algebra. [Preview Abstract] |
Tuesday, March 19, 2013 2:03PM - 2:15PM |
G13.00015: Spin-orbital Texture in Topological Insulators Chaoxing Liu, Haijun Zhang, Shou-Cheng Zhang Relativistic spin-orbit coupling plays an essential role in the field of topological insulators and quantum spintronics. It gives rise to the topological non-trivial band structure and enables electric manipulation of the spin degree of freedom. Because of the spin-orbit coupling, rich spin-orbital coupled textures can exist both in momentum and in real space. For three dimensional topological insulators in the Bi2Se3 family, topological surface states with pz orbitals have a left-handed spin texture for the upper Dirac cone and a right-handed spin texture for the lower Dirac cone. In this work, we predict a new form of the spin-orbital texture associated with the px and the py orbitals. For the upper Dirac cone, a left-handed (right-handed) spin texture is coupled to the ``radial'' (``tangential'') orbital textures, whereas for the lower Dirac cone, the coupling of spin and orbital textures is the exact opposite. A spin-resolved and photon polarized angle-resolved photoemission spectroscopy experiment is proposed to observe this novel spin-orbital texture. [Preview Abstract] |
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