wannier90: A tool for obtaining maximally-localised Wannier functions

We present wannier90, a program for calculating maximally-localised Wannier func-tions (MLWF) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWF in real space. This is done in the space of unitary matrices that describe rotations of the Bloch bands at each k-point. As a result, wannier90 is independent of the basis set used in the underlying calculation to obtain the Bloch states. There-fore, it may be interfaced straightforwardly to any electronic structure code. The locality of MLWF can be exploited to compute band-structure, density of states and Fermi surfaces at modest computational cost. Furthermore, wannier90 is able to output MLWF for visualisation and other post-processing purposes. Wannier func-tions are already used in a wide variety of applications. These include analysis of chemical bonding in real space; calculation of dielectric properties via the modern theory of polarisation; and as an accurate and minimal basis set in the construc-tion of model Hamiltonians for large-scale systems, in linear-scaling quantum Monte