We present a microscopic derivation of the generalized Boltzmann and Eilenberger equations in the presence of non-Abelian gauges for the case of a nonrelativistic disordered Fermi gas. A unified and symmetric treatment of the charge ͓U͑1͔͒ and spin ͓SU͑2͔͒ degrees of freedom is achieved. Within this framework, just as the U͑1͒ Lorentz force generates the Hall effect, so does its SU͑2͒ counterpart gives rise to the spin Hall effect. Considering elastic and spin-independent disorder we obtain diffusion equations for charge and spin densities and show how the interplay between an in-plane magnetic field and a time-dependent Rashba term generates in-plane charge currents.
Dedicated to Ulrich Eckern on the occasion of his 60th birthday.Spin-orbit interaction is usefully classified as extrinsic or intrinsic, depending on its origin: the potential due to random impurities (extrinsic), or the crystalline potential associated with the band or device structure (intrinsic). In this paper we will show how, by using a SU (2) formulation, the two sources may be described in an elegant and unified way. As a result we obtain a simple description of the interplay of the two types of spin-orbit interaction, and a physically transparent explanation of the vanishing of the d.c. spin Hall conductivity in a Rashba two-dimensional electron gas when spin relaxation is neglected, as well as its reinstatement when spin relaxation is allowed. Furthermore, we obtain an explicit formula for the transverse spin polarization created by an electric current, which generalizes the standard formula obtained by Edelstein, and Aronov and Lyanda-Geller by including extrinsic spin-orbit interaction and spin relaxation.
A systematic theory of the conductance measurements of noninvasive (weak probe) scanning gate microscopy is presented that provides an interpretation of what precisely is being measured. A scattering approach is used to derive explicit expressions for the first-and second-order conductance changes due to the perturbation by the tip potential in terms of the scattering states of the unperturbed structure. In the case of a quantum point contact, the first-order correction dominates at the conductance steps and vanishes on the plateaux where the second-order term dominates. Both corrections are nonlocal for a generic structure. Only in special cases, such as that of a centrally symmetric quantum point contact in the conductance quantization regime, can the second-order correction be unambiguously related with the local current density. In the case of an abrupt quantum point contact, we are able to obtain analytic expressions for the scattering eigenfunctions and thus evaluate the resulting conductance corrections.
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