An updated version of wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions

wannier90 is a program for calculating maximally-localised Wannier func-tions (MLWFs) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimis-ing the total spread of the MLWFs in real space. This 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. Therefore, it may be in-terfaced straightforwardly to any electronic structure code. The locality of MLWFs can be exploited to compute band-structure, density of states and Fermi surfaces at modest computational cost. Furthermore, wannier90 is able to output MLWFs for visualisation and other post-processing purposes. Wannier functions 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 ∗Corresponding author