Topological Classification of Crystalline Insulators through Band Structure Combinatorics

By J. Kruthoff, Jan de Boer, Jasper van Wezel, C. L. Kane, Robert-Jan Slager. 2016

615 citations recorded by the source corpus.

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented 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 all allowed topological phases of spinless particles in crystals in class A. Employing this classification, 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 to identify whether or not they give rise to intermediate Weyl semimetallic phases.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/0b2669f36aac9b7d8c3ab1eb5844e40cda8fbddc

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Quantization of fractional corner charge in Cn -symmetric higher-order topological crystalline insulators (2018, background): “[56] Jorrit Kruthoff, Jan de Boer, Jasper van Wezel, Charles L.”
Symmetry and Topology in Non-Hermitian Physics (2018, background): “[217] J.”
Topological Semimetals from First Principles (2018, background): “These attempts have led to a set of recent ideas centered around the notion of symmetry indicators (162, 163, 164, 165, 140).”
Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions (2021, background): “[1] Jorrit Kruthoff, Jan de Boer, Jasper van Wezel, Charles L.”