Topological edge states and quantum Hall effect in the Haldane model

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.

5 pages, 6 figures

References in corpus (5)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• The insulator/Chern-insulator transition in the Haldane model

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