Quantum Spin Hall Effect in a Three-orbital Tight-binding Hamiltonian

TL;DR

This paper investigates the quantum spin Hall effect within a three-orbital tight-binding model influenced by loop current order, revealing topological properties and connections to nonabelian gauge theories.

Contribution

It introduces a novel three-orbital model exhibiting quantum spin Hall states with nontrivial topological invariants linked to loop current order.

Findings

The model has nontrivial Chern parity.

Wave-function singularities depend on gauge choices.

Berry phase maps to Nonabelian instanton.

Abstract

We consider the quantum spin hall state in a three orbital model due to certain loop current order induced by spin-dependent interactions. This type of order is motivated by the loop current model which is proposed to describe the pseudogap phase of cuprates. It is shown that this model has nontrivial Chern parity by directly counting the zeros of the Pfaffian of time reversal operator. By connecting to the second order Chern number, we explicitly show the singularities of wave-functions and how they depend on gauge choices. In this case, it is shown that the Berry phase can be mapped to Nonabelian instanton.