Quantum transport of charge carriers with small velocities

It is usually assumed that charge carriers in crystals have a ballistic propagation between scattering events. Yet this standard semi-classical model breaks down if the charge carriers velocity is small and their mean free path becomes smaller than a typical extension of their wavefunction. In that case, as we show, an insulating like regime can occur. This phenomenon gives the first coherent explanation of the unconventional transport properties of an important class of metallic alloys including quasicrystals. Many examples of charge carriers with a small velocity regime can be found in particular among correlated phases such as heavy fermions or polaronic systems.