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Topological classification of crystalline insulators through band structure combinatorics
- Source :
- Phys. Rev. X 7, 041069 (2017)
- Publication Year :
- 2016
-
Abstract
- We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral symmetries in any dimension. The presented results match the mathematical structure underlying the topological classification of these crystals in terms of K-theory, and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify the allowed topological phases in any possible two-dimensional crystal in class A. We also show how the same procedure can be used to classify the allowed phases for any three-dimensional space group. Employing these classifications, we study transitions between topological phases within class A that are driven by band inversions at high symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure, and identify whether or not they give rise to intermediate Weyl semimetallic phases.<br />Comment: 24 pages, 9 figures
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. X 7, 041069 (2017)
- Publication Type :
- Report
- Accession number :
- edsarx.1612.02007
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevX.7.041069