Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session D35: Topological Insulators: Theory II |
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Sponsoring Units: DCMP Chair: David Vanderbilt, Rutgers University Room: C140 |
Monday, March 21, 2011 2:30PM - 2:42PM |
D35.00001: Antiferromagnetic topological insulators Roger S.K. Mong, Andrew M. Essin, Joel E. Moore We consider antiferromagnets breaking both time-reversal ($\Theta$) and a primitive lattice translational symmetry ($T_{1/2}$) of a crystal but preserving the combination $S = \Theta T_{1/2}$. The $S$ symmetry leads to a $Z_2$ topological classification of insulators, separating the ordinary insulator phase from the ``antiferromagnetic topological insulator'' (AFTI) phase. This state is similar to the ``strong'' topological insulator with time-reversal symmetry, and shares with it such properties as a quantized magnetoelectric effect. However, for certain surfaces the surface states are intrinsically gapped with a half-quantum Hall effect [$\sigma_{xy} = e^2 / (2 h)$], which may aid experimental confirmation of $\theta = \pi$ quantized magnetoelectric coupling. Step edges on such a surface support gapless, chiral quantum wires. In closing we discuss GdBiPt as a possible example of this topological class. [Preview Abstract] |
Monday, March 21, 2011 2:42PM - 2:54PM |
D35.00002: Strong topological insulator phase in cold-atom systems Peter P. Orth, Stephan Rachel, Karyn Le Hur With the recent technological advance of creating (electromagnetic) gauge fields for ultracold atoms, the fascinating prospect of realizing novel topological phases in these systems arises. Specifically, we consider spin-1/2 fermions on a square lattice under the influence of various experimentally feasible gauge fields. In two dimensions and if particles with different spin are exposed to magnetic fields in time-reversed directions, the system displays a quantum spin Hall ground state. We then study the influence of hopping into the third direction (2D-3D crossover), and in the three-dimensional system, we are able to identify a strong topological insulator phase. We further elaborate on the influence of the external trapping potential as well as the unambiguous detection of the topological phases. [Preview Abstract] |
Monday, March 21, 2011 2:54PM - 3:06PM |
D35.00003: Quantum Hall Viscosity and the Torsional Response of Topological Insulators Robert Leigh, Taylor Hughes, Eduardo Fradkin In this talk I will discuss a dissipationless viscosity that has recently appeared in connection with the quantum Hall effect. I will show that this can be connected to the response of time-reversal breaking 2+1-d topological insulators under a mechanical torque. The torque is represented by a coupling of the electronic degrees of freedom to external torsion fields and gives rise to a Chern-Simons-like term commonly seen in gravitational theories in the presence of spacetime torsion. I will discuss possible thought experiments which illustrate the effects and will briefly cover the extension to 3+1-d topological insulators. [Preview Abstract] |
Monday, March 21, 2011 3:06PM - 3:18PM |
D35.00004: Topological $BF$ field theory description of topological insulators Joel E. Moore, Gil Young Cho Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian $BF$ theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The $BF$ description can be motivated from the local excitations produced when a $\pi$ flux is threaded through this state. For the three-dimensional topological insulator, the $BF$ description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields ``axion electrodynamics'', i.e., an electromagnetic $E \cdot B$ term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, $BF$ theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects. Preprint available at http://arxiv.org/abs/1011.3485. [Preview Abstract] |
Monday, March 21, 2011 3:18PM - 3:30PM |
D35.00005: Detecting 3d Non-Abelian Anyons via Adiabatic Cooling Seiji Yamamoto, Michael Freedman, Kun Yang Majorana fermions lie at the heart of a number of recent developments in condensed matter physics. One important application is the realization of non-abelian statistics and consequently a foundation for topological quantum computation. Theoretical propositions for Majorana systems abound, but experimental detection has proven challenging. Most attempts involve interferometry, but the degeneracy of the anyon state can be leveraged to produce a cooling effect, as previously shown in 2d. We apply this method of anyon detection to the 3d anyon model of Teo and Kane. Like the Fu-Kane model, this involves a hybrid system of topological insulator (TI) and superconductor (SC). The Majorana modes are localized to anisotropic hedgehogs in the order parameter which appear at the TI-SC interface. The effective model bears some resemblance to the non-Abelian Higgs model with scalar coupling as studied, for example, by Jackiw and Rebbi. In order to make concrete estimates relevant to experiments, we use parameters appropriate to Ca doped Bi$_2$Se$_3$ as the topological insulator and Cu doped Bi$_2$Se$_3$ as the superconductor. We find a temperature window in the milli-Kelvin regime where the presence of 3d non-abelian anyons will lead to an observable cooling effect. [Preview Abstract] |
Monday, March 21, 2011 3:30PM - 3:42PM |
D35.00006: Topological invariants of adiabatic cycles of Bloch Hamiltonians Rahul Roy Invariants are constructed for various adiabatic cycles of Bloch Hamiltonians and discuss their physical implications. Many of these cycles lead to a pumping of fermions, but in other cases, the physical implications are more subtle. I also discuss the construction of these invariants for insulators in the various symmetry classes and periodicities in the table of these invariants. [Preview Abstract] |
Monday, March 21, 2011 3:42PM - 3:54PM |
D35.00007: On the stability of surface states in topological insulators Young Hoon Moon, Leonid Isaev, Gerardo Ortiz The existence of robust surface/edge states is arguably a fingerprint of topological insulators. These states are protected against scattering by time-reversal invariant perturbations, and lead to dissipationless transport even at high temperatures. This characteristic behavior is believed to be quite insensitive to the properties of the surface of a particular sample. We investigate the above conjecture by considering the stability of edge states with respect to the {\it time-reversal invariant} surface perturbations in several models of topological insulators. We demonstrate that in certain regimes the surface spectrum is modified quite dramatically. In particular, the number of edge states, which cross the Fermi level inside the bulk band gap, is very sensitive to the properties of the surface. Our results can be of great importance for future transport measurements in topological insulators. [Preview Abstract] |
Monday, March 21, 2011 3:54PM - 4:06PM |
D35.00008: Topological quantization in units of the fine structure constant Joseph Maciejko, Xiao-Liang Qi, H. Dennis Drew, Shou-Cheng Zhang Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant $\alpha=e^2/\hbar c$. In this Letter, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other. [Preview Abstract] |
Monday, March 21, 2011 4:06PM - 4:18PM |
D35.00009: Refraction and interference of electrons on the topological insulator surface Ryuji Takahashi, Shuichi Murakami We theoretically study electron transport on the topological insulator surface, in analogy with optics. The surface states are represented by spinors, unlike optics, and therefore different behaviors from those in optics are expected. First, we consider the refraction phenomena at the boundary between the surfaces of two different topological insulators, where the velocities of the surface states are different. We compare its transmission and refraction coefficients with optics. Furthermore, we discuss the case when the velocities of the surface states of the two topological insulators have opposite signs. Second, we study interference phenomena on the surface states. The result shows that if the detector is very far from the scatterer or the slit, the interference is asymptotically similar to ordinary two-dimensional scattering problems. We also study the spin directions of scattered wave due to the surface interference phenomena. [Preview Abstract] |
Monday, March 21, 2011 4:18PM - 4:30PM |
D35.00010: Gauge field fluctuations in three-dimensional topological Mott insulators William Witczak-Krempa, Ting Pong Choy, Yong Baek Kim We discuss the low-energy properties of 3D topological Mott insulators that can be viewed as strong topological insulators of spinons interacting with a 3D gauge field. The low-energy behavior of such systems is dominated by gapless surface spinons (Dirac fermions) coupled to bulk gauge bosons. We find that a dimensional crossover from 3D to 2D in the gauge field fluctuations may occur as the system's thickness and/or temperature is varied. In the thin sample limit, the gauge field fluctuations effectively become 2D and the problem becomes analogous to the standard 2D spinon-gauge field theory. In the 3D limit, the bulk gauge field fluctuations lead to a novel low-energy theory for the coupled system that is more controlled than in the 2D regime. We discuss various experimental signatures such as the heat capacity scaling as T ln(1/T) as well as modified RKKY interactions on the surface. [Preview Abstract] |
Monday, March 21, 2011 4:30PM - 4:42PM |
D35.00011: Symmetry aspects of localized Dirac fermions within topological defects Chi-Ken Lu, Igor Herbut We study the conditions for the existence of zero-energy bound states within topological defects in various insulating and superconducting order parameters for Dirac fermions in graphene and topological insulators. In particular, we discuss several physically relevant realizations of the ``Dirac vortex'' which include the finite chemical potential and Zeeman terms, and the orbital magnetic fields, and present some explicit solutions for the zero-modes. The crucial role in our discussion is assumed by the antilinear symmetry between the positive and negative parts of the energy spectrum. The effects of the orbital symmetry of the defect's underlying order on the zero-modes are also considered. [Preview Abstract] |
Monday, March 21, 2011 4:42PM - 4:54PM |
D35.00012: Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator Yulin Chen, Jiun-Haw Chu, James Analytis, Zhongkai Liu, Kyushiro Igarashi, Hsueh-Hui Kuo, Xiaoliang Qi, Sung-Kwan Mo, Robert Moore, Donghui Lu, Makoto Hashimoto, Takao Sasagawa, Shoucheng Zhang, Ian Fisher, Zahid Hussain, Zhi-Xun Shen Insulating massive Dirac fermion state is a novel state of topological insulators in which the massless surface Dirac fermion becomes massive due to the braking of time reversal symmetry. In this state a gap develops at the Dirac point, with the Fermi energy resides inside both the surface and bulk gaps. By introducing magnetic dopants into three dimensional topological insulator Bi$_{2}$Se$_{3}$ to break the time reversal symmetry, we successfully observed the formation of massive Dirac fermion on the surface, with the Dirac gap magnitude tunable by magnetic dopant concentration. Furthermore, by precise control of simultaneous magnetic and charge doping, we successfully position the Fermi level inside the Dirac gap, thus realizing the much sought after insulating massive Dirac fermion state. This discovery paves the way for realizing striking topological phenomena and testing profound theoretical predictions. [Preview Abstract] |
Monday, March 21, 2011 4:54PM - 5:06PM |
D35.00013: Exotic Effects of Spin-Flip Scattering on Massive Dirac Fermions Shengyuan Yang, Zhenhua Qiao, Yugui Yao, Junren Shi, Qian Niu We investigate the effects of spin-flip scattering on the Hall transport and spectral properties of massive Dirac fermions. We find that in the weak scattering regime, the Berry curvature distribution is dramatically compressed in the electronic energy spectrum, becoming singular at band edges. As a result the Hall conductivity suffers a sudden jump (or drop) of $e^2/2h$ when the Fermi energy sweeps across the band edges, and otherwise is a constant quantized in units of $e^2/2h$. In parallel, spectral properties such as the density of states and spin polarization are also greatly enhanced at band edges. Possible experimental methods to detect these effects are discussed. [Preview Abstract] |
Monday, March 21, 2011 5:06PM - 5:18PM |
D35.00014: Weak indices and dislocations in general topological band structures Ying Ran It has recently been shown that crystalline defects - dislocation lines - in three dimensional topological insulators, can host protected one dimensional modes propagating along their length. We generalize this observation to the case of topological superconductors and other insulators of the Altland Zirnbauer classification, in d=2,3 dimensions. In general, protected dislocation modes are controlled by the topological indices in (d-1) dimensions. This is shown by relating this feature to characteristic properties of surface states of these topological phases. This observation also allows us to constrain these surface states properties, which is illustrated by an addition formula for (d-1) and (d-2) indices of a topological superconductor. [Preview Abstract] |
Monday, March 21, 2011 5:18PM - 5:30PM |
D35.00015: Topological insulator in a non-Abelian lattice model and anyonic fermions in two-body color code model Mehdi Kargarian, Gregory A. Fiete We investigated topological phases in several decorated lattices such as the square- octagon and spin ruby lattices. The underlying models can be potentially simulated in optical lattices or in multi-orbital transition metal oxides. In the square-octagon lattice we apply a set of non-Abelian gauge fields to modulate the hopping between sites. Inversion symmetric fields open a gap and the model realizes topological band insulating phase. If the inversion symmetry is broken, a quantum phase transition between phases with different quantum orders takes place. These phases are characterized by number of Dirac nodes and the associated winding numbers. We also probe the topological phases in the spin ruby lattice with emerging anyonic fermions coupled to nontrivial gauge fields associated with the local symmetry of the model. And we further characterize our results by topological entanglement entropy and entanglement spectrum. M. Kargarian and G. A. Fiete, Phys. Rev. B 82, 085106 (2010). [Preview Abstract] |
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