Electronic structure calculations in a uniform magnetic field using periodic supercells

We have recently presented a method that allows one to use periodic supercells in ab initio electronic structure calculations in the presence of a finite magnetic field [Phys. Rev. Lett. 92 (2004) 186402]. This method retains the simplicity and efficiency of plane-wave basis sets and Fourier transforms. The original formulation was developed for cubic cell and for the k = (0, 0, 0) point of the supercell Brillouin zone, and here we extend the formalism to arbitrarily tilted supercells and to the case of non-zero k-points. Implementation details are discussed, together with numerical benchmarks. Finally, first principles calculations of magnetic band structures are presented.