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

Takahiro Fukui·Yasuhiro Hatsugai·Hiroshi Suzuki
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Abstract

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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Takahiro Fukui, Yasuhiro Hatsugai, Hiroshi Suzuki. 2005-04-06. Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances. https://doi.org/10.1143/jpsj.74.1674

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