Extension of the Semiconductor Bloch Equations for Spin Dynnamics

Abstract

The dynamics of the spin of carriers has attracted a lot of attention in the last few years especially with respect to spintronics and quantum computation. Spin dephasing and relaxation times are usually studied using time-resolved spectroscopy with circularly polarized light [1]. Carrier dynamics in semiconductors and semiconductor heterostructures under excitation with light are usually described within the concept of the Semiconductor Bloch Equations (SBE), which was originally designed for a two-level system and a scalar electric field [2]. It includes electron-electron interaction but does not account for the degrees of freedom of the carrier spin and the polarization of the light field. In order to overcome these limitations, we use an extension of the SBE to a four-level system, including spin-split levels for holes and electrons and the vector character of the light field [3]. Scattering processes due to carrier-carrier and carrier-phonon interaction are taken into account, which in combination with spin-orbit interaction become spin-sensitive. By evaluating the Liouville equation we obtain a set of equations of motion (EOM) of the density matrix, which due to spin-dependent many-particle interactions exhibits a hierarchical structure and needs to be properly truncated for further treatment. In contrast to the Hartree-Fock truncation, which leads to coherent SBE, we include incoherent processes in lowest order in the entries of the density matrix. For the diagonal entries these first order corrections of the EOM can be rewritten as Boltzmann-like scattering contributions. In conclusion, by extending the SBE to a four-level system and by including energy dissipating processes we have found an access to describe spin relaxation and spin dephasing on a microscopical level.