Topology

This module calculates the topological invariants of a hopping Hamiltonian.

Chern Number

[Kohmoto][Kohmoto85] Haldane [Fukui, Hatsugai, and Suzuki][Fukui05]

Z₂ Topological Index of a Time-Reversal-Invariant System

[Fu and Kane][Fu06]. [Fukui and Hatsugai][Fukui07].

Issue with Superconductors

References

• Mahito Kohmoto, Topological invariant and the quantization of the Hall conductance, Ann. Phys. 160, 343 (1985). Kohmoto85
• Takahiro Fukui, Yasuhiro Hatsugai, and Hiroshi Suzuki, Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances, J. Phys. Soc. Jpn. 74, 1674 (2005). Fukui05
• Liang Fu and C. L. Kane, Time reversal polarization and a ${Z}_{2}$ adiabatic spin pump, Phys. Rev. B 74, 195312 (2006). Fu06
• Takahiro Fukui and Yasuhiro Hatsugai, Quantum Spin Hall Effect in Three Dimensional Materials: Lattice Computation of Z2 Topological Invariants and Its Application to Bi and Sb, J. Phys. Soc. Jpn. 76, 053702 (2007). Fukui07