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

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

2005-03-08

arxiv.org/abs/cond-mat/0503172v2

J. Phys. Soc. Jpn. 74 (2005) pp. 1674-1677

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 figures, to appear in JPSJ

Scientific paper

10.1143/JPSJ.74.1382

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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