Spin Hall effect in two-dimensional $p$-type semiconductors in a magnetic field

Abstract

We calculate the spin Hall conductivity driven by Rashba spin-orbit interaction in $p$-type two-dimensional semiconductors in the presence of a perpendicular magnetic field. For a highly confined quantum well, the system is described by a $k$-cubic Rashba term for two-dimensional heavy holes. The eigenstates of the system can be described by Landau spinor states. First we consider the conventional spin Hall conductivity. The contribution of the interband transitions to the Kubo-Greenwood formula gives the density dependent intrinsic spin Hall conductivity, which approaches its universal value ${\sigma }_{xy}^z=9e/8\pi$ for weak spin-orbit coupling and low Fermi energies, in agreement with previous work. However two intraband contribution terms cancel this effect leading to zero conventional spin Hall conductivity. Adding the torque dipole contribution to the definition of spin current, we also study the {\it effective} spin conductivity. This is shown to be proportional to the total magnetization plus surface terms which exactly cancel it for small spin-orbit coupling. If in low magnetic field the intraband transitions evolve to vertex corrections, the fact that both {effective} and conventional spin Hall conductivities vanish is unexpected. This suggests that the zero magnetic field limit of the model is singular.

6 pages, 6 figures. will appear in PRB 73

References in corpus (20)

• Dissipationless Quantum Spin Current at Room Temperature
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Spin current and polarization in impure 2D electron systems with spin-orbit coupling
• On A Proper Definition of Spin Current
• Theory of Spin Hall conductivity in n-doped GaAs
• Can Non-Equilibrium Spin Hall Accumulation be Induced in Ballistic Nanostructures?
• Spin-Hall effect in a disordered 2D electron-system
• Spin Hall effect and Berry phase in two dimensional electron gas
• Intrinsic Spin Hall Effect in the Two Dimensional Hole Gas
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• Spin-Hall Effect in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling and Disorder
• Spin-Hall transport of heavy holes in III-V semiconductor quantum wells
• Absence of vertex correction for the spin Hall effect in p-type semiconductors
• Sum rules for spin-Hall conductivity cancelation
• Edge spin accumulation in semiconductor two-dimensional hole gases
• Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry
• Dependence of the intrinsic spin Hall effect on spin-orbit interaction character
• Landau level mixing by full spin-orbit interactions
• Numerical Study of the Spin Hall Conductance in the Luttinger Model
• Disorder effects on the spin-Hall current in a diffusive Rashba two-dimensional heavy-hole system

Cited by in corpus (20)

• Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems
• Generation of spin currents and spin densities in systems with reduced symmetry
• On the nature of steady states of spin distributions in the presence of spin-orbit interactions
• Wave packet dynamics and zitterbewegung of heavy holes in a quantizing magnetic field
• Sign changes and resonance of intrinsic spin Hall effect in two-dimensional hole gas
• Geometrical phase effects on the Wigner distribution of Bloch electrons
• Topological nature of the proper spin current and the spin-Hall torque
• Electrical and thermoelectric transport properties of two-dimensional fermionic systems with $k$-cubic spin-orbit coupling
• Spin Hall Conductance of the Two Dimensional Hole Gas in a Perpendicular Magnetic Field
• Magnetotransport properties of two-dimensional fermions with $k$-cubic Rashba spin-orbit interaction
• Polarization and third-order Hall effect in III-V semiconductor heterojunctions
• Wave packet dynamics in various two-dimensional systems: a unified description
• Drude weight and optical conductivity of a two-dimensional heavy-hole gas with $k$-cubic spin-orbit interactions
• Disorder effect of resonant spin Hall effect in a tilted magnetic field
• Theory of resonant spin Hall effect
• Tunable correlation effects of magnetic impurities by the cubic Rashba spin-orbit couplings
• Steady-state spin densities and currents
• Magnetotransport of a 2DEG with anisotropic Rashba interaction at the LaAlO${}_3$/SrTiO${}_3$ interface
• Oscillation of spin polarization in a two-dimensional hole gas under a perpendicular magnetic field
• Spin magnetotransport in two-dimensional hole systems