Ubiquity of conical points in topological insulators

2020/04/15 by Alexis Drouot, Drouot, Alexis · 1 citation
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Topology (math.GN) #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #math-ph #math.DG #math.GN #math.GT #math.MP

paper · pdf · doi:10.48550/arxiv.2004.07068

25 pages

arxiv created 2020/04/15 · arxiv updated 2020/04/16

Abstract

We show that generically, the degeneracies of a family of Hermitian matrices depending on three parameters have a conical structure. Our result applies to the study of topological phases of matter. It implies that adiabatic deformations of two-dimensional topological insulators come generically with Dirac-like propagating currents, whose total conductivity equals the chiral number of conical points.

Cited by

• Edge states in square lattice media and their deformations

Related

• Long Range Topological Order, the Chiral Condensate, and the Berry Connection in QCD
• Topological Anderson Insulators by homogenization theory
• New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic
• Topological insulators and superconductors -a curved space a prroach
• Topological Insulators, Topological Crystalline Insulators, Topological Semimetals and Topological Kondo Insulators