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 …

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 investigate some foundational issues in the quantum theory of spin transport, in the
general case when the unperturbed Hamiltonian operator H_0 H 0 does not commute with …

We consider a real periodic Schrödinger operator and a physically relevant family of m ≧ 1
m≥ 1 Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the …

We present mathematical details of the construction of a topological invariant for periodically
driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps …

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 …

Topological insulators are solid state systems of independent electrons for which the Fermi
level lies in a mobility gap, but the Fermi projection is nevertheless topologically non-trivial …

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 …