Time-dependent quantum-well and finite-superlattice tunneling

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Abstract
Theoretical considerations which pertain to electric currents through quantum-well structures or finite superlattices in the presence of periodic time-dependent applied potentials are presented. The paper includes (1) a time-dependent generalization of the time-independent, noninteracting electron, one-dimensional potential model of Tsu and Esaki, (2) a derivation of generalized unitarity identities which relate all of the elastic and inelastic transitions which a particle can undergo when it interacts with a periodic time-dependent, one-dimensional, arbitrarily shaped potential barrier, and (3) an analysis of many-body effects which reveals additional non-Tsu-Esaki current terms which disappear when the time-dependent part of the applied potential is turned off. All of the results are expressed in terms of one-particle scattering matrices which can be computed from the ordinary single-particle, time-dependent Schrödinger equation. This work may have high-frequency device applications.