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Topological aspects of the quantum Hall effect

1997; IOP Publishing; Volume: 9; Issue: 12 Linguagem: Inglês

10.1088/0953-8984/9/12/003

1361-648X

Yasuhiro Hatsugai,

Graphene research and applications

The quantum Hall effect is a typical realization of topological effects in condensed matter physics. In this article, some of the topological aspects of the quantum Hall effect are reviewed. For the lattice fermions, the Hall conductance of the system is expressed in terms of two different topological invariants. One is the famous TKNN integer which is related to the bulk state. The other is the winding number of the edge state on the complex-energy surface which is generally a high-genus Riemann surface. We will describe them in detail.