Control of field-induced localization in superlattices: Coherence and relaxation

We consider a $d$-dimensional conductor (a semiconductor/optical superlattice, quantum/molecular wire) with arbitrary electron dispersion within the independent-electron one-band approach. Its nonperturbative nonstationary response to arbitrary time-periodic electric fields is studied (a) in the quantum coherent “dynamic” (or short-time) regime and (b) in the “kinetic” (or long-time) regime under the influence of weak scattering. We provide a classification and analysis of field-induced dynamic localization and response through the dc/ac current and mean square displacement of electrons. We demonstrate that the overall localization increases in passing from the periodic regime through the commensurate to the incommensurate one (governed by the relation of field period and Bloch frequency) both in the dynamic and kinetic cases. Simultaneously, exceptional localization (for some particular values of field parameters or symmetries) typically retains its order in the small relaxation rate, but on the background of increasing overall localization becomes less pronounced, both in dynamic and kinetic regimes. In the dynamic regime exceptional localization is manifested through diffusion and dc response, in the kinetic—through diffusion and ac response. In the commensurate case with long-range overlap the leading responses are formed by “resonant” neighbors only; within nearest-neighbor approximation the commensurate regime becomes qualitatively analogous to the incommensurate one. Ways of controlling localization/response by the applied field and the reasons for the similarity/difference of dynamic and kinetic regimes are discussed.