Boltzmann approach to the spin Hall effect revisited and electric field modified collision integrals

Abstract

The intrinsic contribution to the spin Hall effect in a 2DEG with non-magnetic impurities is studied in a quantum Boltzmann approach. It is shown that if the steady state response is perturbative in the spin-orbit coupling parameter $\lambda$, then the precession term--vital for Dyakonov-Perel relaxation and the key to the spin Hall effect in previous similar Boltzmann studies--must be left out to first order in spin-orbit coupling. In such a case one would have that to lowest order in the parameters electric field, spin-orbit coupling, impurity strength and impurity concentration there is no intrinsic contribution to the spin Hall effect, not only for a Rashba coupling but for a general spin-orbit coupling. To cover all possible lowest order terms we consider also electric field induced corrections to the collision integral in the Keldysh formalism. However, these corrections turn out to be of second order in $\lambda$. For comparison we derive some familiar results in the case when the response is not assumed to be perturbative in $\lambda$. We also include a detailed discussion of why a relaxation time approximation of the collision integral fails. Finally we make a comment on pseudospin currents in bilayer graphene.

arXiv comment15 pages, 1 table. The second version was extended with a summarizing table, a section on the relaxation time approximation and a comment on pseudospin currents in bilayer graphene

References in corpus (24)

• Spin Hall effect
• Universal Intrinsic Spin-Hall Effect
• Dissipationless Quantum Spin Current at Room Temperature
• Direct electronic measurement of the spin Hall effect
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Room Temperature Reversible Spin Hall Effect
• Spin current and polarization in impure 2D electron systems with spin-orbit coupling
• Suppression of the Persistent Spin Hall Current by Defect Scattering
• On A Proper Definition of Spin Current
• Semiclassical theories of the anomalous Hall effect
• Giant Spin Relaxation Anisotropy in Zinc-Blende Heterostructures
• Diffuse transport and spin accumulation in a Rashba two-dimensional electron gas
• Spin-Hall effect in a disordered 2D electron-system
• Spin-Hall conductivity due to Rashba spin-orbit interaction in disordered systems
• Quasiclassical approach to the spin-Hall effect in the two-dimensional electron gas
• Spin Hall Effect
• Generalized kinetic equations for charge carriers in graphene
• Small-angle impurity scattering and the spin Hall conductivity in 2D systems
• Kinetic equation for strongly interacting dense Fermi systems
• Spin Hall effect of conserved current: Conditions for a nonzero spin Hall current
• Dependence of the intrinsic spin Hall effect on spin-orbit interaction character
• Non-vanishing spin Hall currents in disordered spin-orbit coupling systems
• On the nature of steady states of spin distributions in the presence of spin-orbit interactions
• Hybrid skew scattering regime of the anomalous Hall effect in Rashba systems: unifying Keldysh, Boltzmann, and Kubo formalisms

Cited by in corpus (3)

• Spin Relaxation, Diffusion and Edelstein Effect in Chiral Metal Surface
• Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: I. Kinetic equation and anomalous Hall and spin-Hall effects
• Quantum corrections in the Boltzmann conductivity of graphene and their sensitivity to the choice of formalism