Symmetry indicators of topological superconductors by Haruki Watanabe

DISCUSSION MEETING

NOVEL PHASES OF QUANTUM MATTER

ORGANIZERS:

Adhip Agarwala, Sumilan Banerjee, Subhro Bhattacharjee, Abhishodh Prakash and Smitha Vishveshwara

DATE: 23 December 2019 to 02 January 2020

VENUE: Ramanujan Lecture Hall, ICTS Bangalore

Recent theoretical and experimental developments in the physics of quantum matter has necessitated an expanded framework to understand "quantum ordering". On the theoretical front, rapid development in the last decade or so has unveiled non-trivial patterns of quantum entanglement, fractionalization of statistics as well as symmetry charges that have been found to produce novel and exotic phases of matter. Work on classifying such phases and understanding their unique properties is an ongoing collaborative effort involving high-energy, condensed matter, and quantum information physicists as well as mathematicians. On the experimental front, the discovery of two and three dimensional topological insulators, semimetals as well as the proposal of various candidate spin-liquid materials have generated considerable excitement. More recently, the discovery of unconventional superconducting and magnetic phases in twisted bilayer graphene has opened a new platform to study strongly correlated phases.

In this light, it is pertinent to bring together theorists and experimentalists working in these areas and provide a vibrant platform to discuss results, ideas, initiate collaborations and help shape future research directions for the community and this discussion meeting aims to do that. The topics of focus are 1. Topological order in condensed matter systems 2. Symmetry protected and enriched topological phases of condensed matter and 3. Superconductivity and other correlated phases in twisted bilayer graphene. The program would consist of invited talks with ample time for discussions.

During the program, Prof. Ashvin Vishwanath, Harvard University will deliver the Infosys-ICTS Chandrashekar lecture series focusing on current developments in the study of novel phases of quantum matter.


CONTACT US: [email protected]
PROGRAM LINK: https://www.icts.res.in/discussion-me...

Table of Contents (powered by https://videoken.com)
0:00:00 Symmetry indicators of topological superconductors
0:00:59 Plan of this talk
0:02:07 Symmetry Indicators
0:04:44 Fu-Kane formula
0:06:26 Symmetry indicator for inversion & TRS with SOC in 3D
0:08:08 Thousands of exotic 'topological' materials discovered through sweeping search
0:08:42 More details on the formalism
0:08:49 Representations in band structure
0:09:39 Combinations of irreps
0:10:27 Example: 2D lattice with inversion symmetry
0:11:08 Trivial insulators
0:11:20 Atomic Insulators
0:12:45 Irrep contents of Al
0:14:12 Extracting nontrivial topology
0:14:21 Definition of trivial insulator
0:16:31 Extract nontrivial topology
0:17:28 Symmetry indicator for inversion & TRS with SOC in 3D
0:17:54 Extension to superconductors
0:18:02 BdG formalism
0:18:32 Quasiparticle spectrum
0:19:29 Inversion symmetric second-order TSC
0:21:31 Problem of this approach
0:22:55 Definition of 'trivial' SCs
0:23:52 Example1: s-wave SCs
0:24:30 Example 2: Kitaev chains
0:25:10 Two copies of Kitaev chains with inversion symmetry
0:26:36 Definition of 'trivial' SCs
0:27:48 Refined SIs for SCs
0:30:01 Summary
0:32:13 Q&A