Magneto-acoustic phonon antiresonances in Wannier-Stark superlattices

We have measured the hopping current of electrons magnetically confined in a 1D superlattice. We find that phonon assisted hopping between Wannier-Stark states vanishes at hopping energies where the momentum of an LA phonon mode satisfies the condition of Bragg reflection in the superlattice. This effect proves that, even in the presence of an external electric field, the electron states of a crystal conserve their periodicity in k-space. This periodicity reveals a fundamental property of Wannier's effective Hamiltonian.