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Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

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arxiv cond-mat/0503172 v2 pith:NMNU35ZW submitted 2005-03-08 cond-mat.mes-hall hep-lat

Takahiro Fukui , Yasuhiro Hatsugai , Hiroshi Suzuki This is my paper · ORCID
classification cond-mat.mes-hallhep-lat
keywords brillouinconductancesdiscretizedhallzoneberrycherncomputing
verification ladder T0 review T1 audit T2 compute T3 formal
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We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.

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Cited by 2 Pith papers

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