J. Phys. Soc. Jpn. 74, pp. 1674-1677 (2005) [4 Pages]
LETTERS
Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
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Received March 8, 2005; Accepted March 14, 2005
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.
©2005 The Physical Society of Japan
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