Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
Mesoscale and Nanoscale Physics
2014-11-20 v2 High Energy Physics - Lattice
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.
Cite
@article{arxiv.cond-mat/0503172,
title = {Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances},
author = {Takahiro Fukui and Yasuhiro Hatsugai and Hiroshi Suzuki},
journal= {arXiv preprint arXiv:cond-mat/0503172},
year = {2014}
}
Comments
4 pages, 3 figures, to appear in JPSJ