PIRSA:18030072

Video URL

https://pirsa.org/18030072

Topology in crystalline lattices

van Wezel, J. (2018). Topology in crystalline lattices. Perimeter Institute for Theoretical Physics. https://pirsa.org/18030072

van Wezel, Jasper. Topology in crystalline lattices. Perimeter Institute for Theoretical Physics, Mar. 20, 2018, https://pirsa.org/18030072 

          @misc{ scivideos_PIRSA:18030072,
            doi = {10.48660/18030072},
            url = {https://pirsa.org/18030072},
            author = {van Wezel, Jasper},
            keywords = {Quantum Matter},
            language = {en},
            title = {Topology in crystalline lattices},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2018},
            month = {mar},
            note = {PIRSA:18030072 see, \url{https://scivideos.org/index.php/pirsa/18030072}}
          }

Jasper van Wezel Universiteit van Amsterdam

Talk numberPIRSA:18030072
DOI10.48660/18030072
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Topology has in the past decades become an organizing principle in the classification and characterization of phases of matter.  While all possible topological phases of free fermions in the presence of external symmetries have been fully worked out, the inclusion of lattice symmetries relevant to any real-life material provides for an active research area.

 

In this seminar, I will present a classification of all possible gapped topological phases of non-interacting insulators with lattice symmetries, both in the absence and presence of time-reversal symmetry. This is done using a very simple counting scheme based on the electronic band structure of the materials. Despite the simplicity of the procedure, it is based on (and matches all known predictions of) the far more involved mathematical framework known as K-theory, which establishes the correctness and completeness of the counting scheme. The same straightforward counting can also be used to study transitions between crystalline topological phases. This allows us to list all possible types of such transitions for any given crystal structure, and accordingly stipulate whether or not they give rise to intermediate Weyl semimetallic phases. The presented procedure is ideally suited for the analysis of real, known materials, as well as the prediction of new, experimentally relevant, topological materials.

 

References:

http://doi.org/10.1103/PhysRevX.7.041069

http://arxiv.org/pdf/1711.04769