Interacting and Coherent Time-Dependent Transport in Semiconductor Heterostructures

Abstract

The hallmark of mesoscopic phenomena is the phase coherence of the charge carriers, which is maintained over a significant part of the transport process. The interference effects resulting from this phase coherence are reflected in a number of experimentally measurable properties. For example, phase coherence is central to the Aharonov-Bohm effect, Universal conductance fluctuations, (for a series of review articles, see Altshuler et al., 1991) and weak localization (reviewed by, e.g, Lee and Ramakrishnan, 1985), and can be affected by external controls such as temperature or magnetic field. The study of stationary mesoscopic physics is now a mature field, and in these notes we describe recent developments in a rapidly growing research area, where one uses an alternative way of affecting the phase coherence: external time-dependent perturbations. The interplay of external time-dependence and phase coherence can be phenomenologically understood as follows. If the single-particle energies acquire a time dependence, then the wave functions have an extra phase factor, $\Psi \infty \exp \left[ { - i\smallint ^t dt'\varepsilon \left( {t'} \right)} \right]$ . For a uniform system such an overall phase factor is of no consequence. However, if the external time dependence is different in different parts of the system, and the particles can move between these regions (without being ‘dephased’ by inelastic collisions), the phase difference becomes important.