W annier90 is an open-source computer program for calculating maximally-localised
Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used …

The intense theoretical and experimental interest in topological insulators and semimetals
has established band structure topology as a fundamental material property. Consequently …

While the classification of noninteracting crystalline topological insulator phases by
equivariant K-theory has become widely accepted, its generalization to anyonic interacting …

We provide a constructive proof of exponentially localized Wannier functions and related
Bloch frames in 1-and 2-dimensional time-reversal symmetric (TRS) topological insulators …

Bloch oscillations originate from the translational symmetry of crystals. These oscillations
occur with a fundamental period that a semiclassical wave packet takes to traverse a …

We investigate the localization properties of independent electrons in a periodic
background, possibly including a periodic magnetic field, as eg in Chern insulators and in …

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or
odd) type, ie the time-reversal operator squares to-1-1. We investigate the existence of …

We give a constructive proof for the existence of a Bloch basis of rank NN which is both
smooth (real analytic) and periodic with respect to its d d-dimensional quasi-momenta, when …

We propose an algorithm to determine maximally localized Wannier functions (MLWFs). This
algorithm, based on recent theoretical developments, does not require any physical input …

We describe some applications of group-and bundle-theoretic methods in solid state
physics, showing how symmetries lead to a proof of the localization of electrons in gapped …