Topological insulators and superconductors -a curved space a prroach

TL;DR

This paper introduces a space-dependent basis approach to analyze topological phases in insulators and superconductors, emphasizing the role of geometry, topology, and gauge choices in electronic band classification and physical properties.

Contribution

It develops a novel method using space-dependent basis to classify topological phases and analyze electronic properties in curved crystal geometries.

Findings

Topological invariants classify electronic bands.

Connection and curvature relate to physical properties.

Application to topological insulators and superconductors.

Abstract

The method of the space dependent basis is applied to study electronic spinors in a crystal. The crystal in the momentum space is described by the Brillouine zone which might contains obstructions or degeneracies for which requires different gauges for different regions. The electronic bands are classified according to their topology. The connection and curvature determines the physical properties which are clasified according to the topological invariants. We apply this method to the Topological Insulators, Topological Superconductors, Persistent Currents in coupled rings and photoemission for a curved crystal-face boundary