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

The key formula for computing the orbital magnetization of a crystalline system has been recently found [D. Ceresoli , Phys. Rev. B 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 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 two dimensions) can be evaluated using a single Hamiltonian diagonalization.