Orbital magnetization and Chern number in a supercell framework: Single k-point formula
Abstract
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 -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.
Cite
@article{arxiv.0705.3771,
title = {Orbital magnetization and Chern number in a supercell framework: Single k-point formula},
author = {D. Ceresoli and R. Resta},
journal= {arXiv preprint arXiv:0705.3771},
year = {2007}
}