Umklapp-Assisted Electron Transport Oscillations in Metal Superlattices

We consider a superlattice of parallel metal tunnel junctions with a spatially non-homogeneous probability for electrons to tunnel. In such structures tunneling can be accompanied by electron scattering that conserves energy but not momentum. In the special case of a tunneling probability that varies periodically with period $a$ in the longitudinal direction, i.e., perpendicular to the junctions, electron tunneling is accompanied by “umklapp” scattering, where the longitudinal momentum changes by a multiple of $h\mathrm{/}a$. We predict that as a result a sequence of metal-insulator transitions can be induced by an external electric- or magnetic field as the field strength is increased.