Quantum Critical Fluids at the Edge: Disorder, Interactions ad Topological Protection
| Date/Time: | Monday, 26 Mar 2018 from 4:10 pm to 5:00 pm |
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| Location: | Phys 0003 |
| Phone: | 515-294-5441 |
| Channel: | College of Liberal Arts and Sciences |
| Actions: | Download iCal/vCal | Email Reminder |
Abstract: Topology has played an integral role in condensed matter physics since the discovery of the quantum Hall effect. The key aspect of the latter is that a "quantum knot" of the bulk translates directly into an easily measured experimental observable, the precisely quantized Hall conductance. The current is carried by one-dimensional edge states that flow in only one direction; robust quantization is simply due to the fact that disorder (impurities, always present in real materials) cannot impede the unidirectional flow.
In the last 10 years, we have seen an explosion in theoretical and experimental developments concerning topological matter without magnetic fields, i.e., that preserve time-reversal symmetry. In this talk, I will discuss predictions of robustly quantized transport in 1D-edge channels of 2D topological insulators, and of 2D surface states of 3D topological superconductors. In both cases, it is a remarkable fact that the edge or surface theories had been studied a decade before the discovery of 2D topological insulators and 3D topological superconductors [1,2,3,4]! The early studies concerned the behavior of these edge and surface states in the presence of quenched disorder, with the key unusual aspect that these low-dimensional systems robustly avoid Anderson localization. This is now understood (if only indirectly) as a consequence of "topological protection." However, while quantized transport was previously predicted for noninteracting models of edge and surface states, the effects of interactions have only been considered recently. The full interplay of disorder and interactions has come to the fore with respect to experimental results on 1D-edge states of 2D topological insulators, which do not seem to show the anticipated protection. Nevertheless, I will show how a theory of generic 1D-edge states incorporating disorder, Rashba spin-orbit coupling, and interactions does predict quantized conductance, suggesting that the source of the experimental discrepancy is due to time-reversal symmetry breaking or the absence of true topological edge states. The exact solution involves a mapping to a single qubit evolving in a time-dependent field, and shows how the topology engineers a perfect adiabatic control protocol [5]. Second, I will discuss the surface states of 3D topological superconductors, and explain why we predict universal surface thermal and (if conserved) spin conductivities in the presence of both disorder and interactions [6,7].
Refs:
[1] M. R. Zirnbauer, PRL 69, 1584 (1992)
[2] Y. Takane, J. Phys. Soc. Japan 73, 1430 (2004)
[3] A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, G. Grinstein, PRB 50, 7526 (1994)
[4] A. A. Nersesyan, A. M. Tsvelik, F. Wenger, PRL 72, 2628 (1994)
[5] H.-Y. Xie, H. Li, Y.-Z. Chou, M. S. Foster, PRL 116, 086603 (2016)
[6] H.-Y. Xie, Y.-Z. Chou, M. S. Foster, PRB 91, 024203 (2015)
[7] M. S. Foster, H.-Y. Xie, Y.-Z. Chou, PRB 89, 155140 (2014)
Bio: Matthew S. Foster is an assistant professor in the Physics & Astronomy Department at Rice University. He is a condensed matter theorist. Matthew obtained his PhD at the University of California, Santa Barbara, working with Andreas Ludwig. He later worked as a post-doc at Columbia and Rutgers Universities, with Igor Aleiner and Emil Yuzbashyan. Matthew focuses on transport in disordered, interacting systems, metal-insulator transitions, Anderson delocalization and its interplay with topology, and hydrodynamic thermoelectric transport. He also works on far-from-equilibrium quantum dynamics in systems ranging from THz light-pumped superconductors to quantum quenches in integrable models that could be realized using ultracold atoms.