Topological edge states and quantum Hall effect in the Haldane model

TL;DR

This paper investigates the topological edge states and quantum Hall effect in the Haldane model, revealing how edge states relate to topological invariants and conductance quantization.

Contribution

It derives the Harper equation for edge states and links their winding numbers to the quantized Hall conductance in the Haldane model.

Findings

Two edge states exist in the bulk energy gap.

Edge state energy loops encircle the Riemann surface hole.

Quantized Hall conductance is expressed by winding numbers.

Abstract

We study the topological edge states of the Haldane's graphene model with zigzag/armchair lattice edges. The Harper equation for solving the energies of the edge states is derived. The results show that there are two edge states in the bulk energy gap, corresponding to the two zero points of the Bloch function on the complex-energy Riemann surface. The edge-state energy loops move around the hole of the Riemann surface in appropriate system parameter regimes. The quantized Hall conductance can be expressed by the winding numbers of the edge states, which reflects the topological feature of the Haldane model.