2016/12/06 by Jorrit Kruthoff, Jan de Boer, Jasper van Wezel +2 · 3 citations
Physics and Astronomy · Mathematics · #cond-mat.mes-hall #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevx.7.041069
published as Phys. Rev. X 7, 041069 (2017) · 24 pages, 9 figures
arxiv created 2016/12/06 · arxiv updated 2017/12/27
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.