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

By T. Fukui, Y. Hatsugai, Hiroshi Suzuki. 2005

982 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5fbfa9920f0eaae60661207f10ed1cc932c1c818

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. S. Nakatsuji
2. Ji Feng
3. Ryotaro Arita
4. Q. Niu
5. P. Goswami
6. Takashi Koretsune
7. Di Xiao

In Materials Chemistry

1. S. Nakatsuji
2. Ji Feng
3. J. Qi
4. Xiao Li
5. Q. Niu
6. P. Goswami
7. Takashi Koretsune
8. Di Xiao

Citations in the corpus

• Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal (2018, methodology): “S4) and find that the pertinent bands in the numerical calculations produce Weyl points around E0 ≈ +20 meV above EF[11] (Fig.”
• Giant and tunable valley degeneracy splitting in MoTe2 (2015, methodology): “vature [26], Ω (units Å 2 ), of the valence bands occupied up to the MoTe2 gap of the heterostructure when EuO substrate is magnetized upward (band structure in Fig.”