Orbital magnetization and Chern number in a supercell framework: Single k-point formula

Details Orbital magnetization and Chern number in a supercell framework: Single k-point formula Orbital magnetization and Chern number in a supercell framework: Single k-point formula

2007-05-25

arxiv.org/abs/0705.3771v3

Phys. Rev. B 76, 012405 (2007)

Physics

Condensed Matter

Materials Science

4 pages, 3 figures; appendix added

Scientific paper

10.1103/PhysRevB.76.012405

The key formula for computing the orbital magnetization of a crystalline system has been recently found [D. Ceresoli, T. Thonhauser, D. Vanderbilt, R. Resta, Phys. Rev. B {\bf 74}, 024408 (2006)]: it is given in terms of a Brillouin-zone integral, which is discretized on a reciprocal-space mesh for numerical implementation. We find here the single ${\bf k}$-point limit, useful for large enough supercells, and particularly in the framework of Car-Parrinello simulations for noncrystalline systems. We validate our formula on the test case of a crystalline system, where the supercell is chosen as a large multiple of the elementary cell. We also show that--somewhat counterintuitively--even the Chern number (in 2d) can be evaluated using a single Hamiltonian diagonalization.

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