Berry phases and zero-modes in toroidal topological insulator

TL;DR

This paper derives an effective Hamiltonian for surface states of a toroidal topological insulator, revealing bound states, zero-modes, and Berry phases induced by the surface's curvature and topology.

Contribution

It introduces a novel effective Hamiltonian capturing curvature effects and predicts the existence of zero-modes and Berry phases specific to the toroidal topology.

Findings

Support for bound states and zero-modes on the torus surface

Identification of two distinct Berry phases due to topology

Wave-functions oscillate harmonically around the surface

Abstract

An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential, which ultimately yields the zero-modes whose wave-functions harmonically oscillate around the toroidal surface. In addition, two distinct Berry phases are predicted to take place by the virtue of the toroidal topology.