The surface states of topological insulators - Dirac fermion in curved two dimensional spaces

TL;DR

This paper explores the behavior of surface states in topological insulators modeled as Dirac fermions on curved surfaces, revealing chiral states and quantized Hall effects under magnetic fields.

Contribution

It introduces a framework for describing topological insulator surface states as Dirac fermions in curved 2D spaces, including effects of magnetic fields and resulting chiral and Hall phenomena.

Findings

Chiral states exist on the side faces of slab-like samples.

Quantized charge Hall effect coexists with spin Hall effect in strong magnetic fields.

Surface states are effectively described by Dirac Hamiltonian in curved geometries.

Abstract

The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields the quantized charge Hall effect ($\s_{xy}=(2n+1)e^2/h$) will coexist with spin Hall effect.