Quantum interference control of current in semiconductors: Universal scaling and polarization effects

Quantum interference control ~QUIC! of current in semiconductors is a subject of current interest dealing with the manipulation of the magnitude and the direction of a photo-current. It is an example of a class of phenomena involving quantum interference between optical transitions that have been studied in atomic media. In all cases, interference between single-photon absorption ~SPA! and twophoton absorption ~TPA! produces directional photoelectrons in the continuum of conduction band states. The directionality of the photogenerated electrons results from the fact that the two pairs of initial and final states involved in the singleand two-photon transitions are degenerate but contain different parity. Device applications based on QUIC in semiconductors have now been proposed, including the generation of short ~single cycle! bursts of terahertz frequency radiation. A calculation of the QUIC current density tensor Ji jkl in bulk semiconductors was given by Atanasov et al. for GaAs using a numerical model which uses a full band structure of GaAs within the local density approximation. Khurgin employed a simple parabolic band structure to show that QUIC and third-order optical rectification are the ‘‘real’’ and ‘‘virtual’’ manifestations of the same nonlinear process. In this paper, a three-band model will be presented that, in analytical form, describes the QUIC scaling as well as its polarization dependence. Simple theoretical models leading to analytical solutions allow for a generality that is descriptive of a large class of materials. A simple model also provides a clear physical picture that is often difficult to extract from numerical treatments. The system studied here is a zinc-blende semiconductor characterized by a conduction band and two valence bands in Kane’s theory. The two valence bands are a heavy-hole ~hh! and a light-hole ~lh! band as depicted in Fig. 1. The starting formalism is described in Refs. 11 and 12 where initial ~valence! and final ~conduction! states are taken as dressed Bloch functions where the acceleration of the electrons and holes are taken into account by considering the first order ~i.e., time-dependent! Stark shift of the energy states due to the applied fields: