Optimal decay of Wannier functions in Chern and Quantum Hall insulators
Weinvestigatethelocalizationpropertiesofindependentelectronsinaperi- odic background, possibly including a periodic magnetic field, as e. g. in Chern insulators and in quantum Hall systems. Since, generically, the spectrum of the Hamiltonian is absolutely continuous, localization is characterized by the decay, as |x| → ∞, of the composite (magnetic) Wannier functions associated to the Bloch bands below the Fermi energy, which is supposed to be in a spectral gap.