Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session A2: Topological Insulators and Topological Superfluids |
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Sponsoring Units: DCMP Chair: Shinsei Ryu, University of California, Berkeley Room: Oregon Ballroom 202 |
Monday, March 15, 2010 8:00AM - 8:36AM |
A2.00001: Majorana Fermions and Topological Insulators Invited Speaker: Zero energy Majorana fermion bound states offer a topologically protected method for storing and manipulating quantum information. Structures composed of topological insulators and superconductors offer a promising route to engineering these exotic states. In this talk we will discuss the theoretical foundation for the existence of Majorana fermions and describe a number of specific architectures involving topological insulators which allow various aspects of the Majorana fermions to be probed experimentally. Majorana bound states are associated with point like topological defects in a {\it three dimensional} Bogoliubov de Gennes theory. We will argue that they exhibit non-Abelian exchange statistics, despite the triviality of braids in three dimensions. A new feature of 3D non-Abelian statistics is the existence of ``braidless'' operations in which it is possible to manipulate the quantum information stored in the defects without moving or measuring them. [Preview Abstract] |
Monday, March 15, 2010 8:36AM - 9:12AM |
A2.00002: Topological insulators in applied fields: magnetoelectric effects and exciton condensation Invited Speaker: ``Topological insulators'' are insulating in bulk but have protected metallic surface states as a result of topological properties of the electron wavefunctions. Several examples of three-dimensional topological insulators have been discovered recently in ARPES experiments that directly probe the surface state, including its spin structure. One way to characterize the topological insulator is through its magnetoelectric response in a weak applied field: it generates an electrical polarization in response to an applied magnetic field, and a magnetization in response to an applied electrical field. This talk first reviews the origin of this response and its generalization to other insulators and topological states. A strong applied electrical field can combine with Coulomb interactions to generate an unusual ``exciton condensate'' involving both surfaces of a thin film of topological insulator. This exciton condensate has several topological features that distinguish it from an ordinary superfluid; the most significant is that vortices support midgap localized states (``zero modes'' in the particle-hole symmetric case) with effective fractional charge $\pm e/2$. [Preview Abstract] |
Monday, March 15, 2010 9:12AM - 9:48AM |
A2.00003: Topological superfluids and insulators with time reversal symmetry Invited Speaker: Topological insulators and superfluids with time reversal symmetry are new phases which have non trivial values of a topological invariant. Quite likely, the full physical significance of the topological invariant is yet to be understood. What is known is that these topological phases have robust edge/surface states. They can also support various interesting fractionalized defects. The different formulations of the invariant offer different perspectives on the physical significance. I report on recent progress in these areas. [Preview Abstract] |
Monday, March 15, 2010 9:48AM - 10:24AM |
A2.00004: Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with Quadratic Band Crossings Invited Speaker: In the light of recent progress in the search for topologically nontrival states of matter, discovering and/or understanding new mechanisms which could stabilize these exotic states has become increasingly important. We have investigated two-dimensional semi-metallic fermionic systems with a quadratic band-crossing point in the single-particle energy spectrum. At the noninteracting level, this quadratic band-crossing point is found to be topologically stable for a Berry flux $2\pi$ if the point symmetry group has either fourfold or sixfold rotational symmetry. However, this putative topologically stable free-fermion quadratic band-crossing point is marginally unstable in the presence of arbitrarily weak short-range repulsive interactions. For spinless fermions in the weak-coupling limit, an insulating quantum anomalous Hall phase is stabilized with a nontrivial Chern number. For relatively stronger coupling, a semi-metallic nematic phase with spontaneous rotational symmetry breaking occurs. For spin-$1/2$ fermions, two additional phases, the Z$_2$ quantum-spin-Hall phase and the nematic-spin-nematic phase, are found. [Preview Abstract] |
Monday, March 15, 2010 10:24AM - 11:00AM |
A2.00005: Entanglement entropy of quantum Hall systems in torus and spherical geometry Invited Speaker: Entanglement entropy of two-dimensional (2D) electron systems in magnetic field is studied by the density matrix renormalization group (DMRG) method. Many body interacting systems on torus and spherical geometries are mapped onto 1D models by using guiding center $X$, and angular momentum $m$, respectively. The DMRG method is then applied to these 1D models and the entanglement entropy $S$ of topologically ordered states is calculated at fractional fillings $1/m$ of the Landau level. We also study bilayer systems, whose degrees of freedom are described by charges and pseudospins. The entanglement entropy $S$ and the coefficient $c$ in area law $S=cL-\gamma+O(1/L)+...$ are analyzed for various sizes of the system in torus and spherical geometries. [Preview Abstract] |
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