Rashba effect and magnetic field in semiconductor quantum wires

Abstract

We investigate the influence of a perpendicular magnetic field on the spectral and spin properties of a ballistic quasi-one-dimensional electron system with Rashba effect. The magnetic field strongly alters the spin-orbit induced modification to the subband structure when the magnetic length becomes comparable to the lateral confinement. A new subband-dependent energy splitting at k = 0 is found which can be much larger than the Zeeman splitting. This is due to the breaking of a combined spin orbital-parity symmetry.

Spectral properties and local density of states of disordered quantum Hall systems with Rashba spin-orbit coupling

“…We have checked that the obtained energy spin splitting between paired parabolas is quantitatively consistent in high magnetic fields with the full numerical study of the quantum wire model performed in Ref. 27. The analytical solution (70) is closely related to the energy spectrum derived in Ref.…”

“…(ω)|ν 2 is the kernel of the free Green's operator [here, we have used the semiorthogonality property (27) of the SO vortex states]. In the clean case, the Green's function is therefore diagonal both in the level index n and the SO quantum number, and presents the typical coherent states nonzero overlap for the vortex position dependence.…”

“…The one-dimensional (1D) parabolic model for confinement is also not fully analytically tractable in the presence of an external magnetic field and both Rashba and Zeeman interactions. This toy model for the edge states in the regime of the integer quantum Hall effect has been studied using numerical techniques 27 or analytically but with-out properly controlled approximation schemes 28 . Twodimensional quadratic confining potentials have also been investigated, only numerically, as models for semiconductor quantum dots 11,[29][30][31][32] .…”

Spin edge states: An exact solution and oscillations of the spin current

“…Therefore, the SOI effect is significant in weak magnetic fields unless temperature fluctuations smear magnetic-quantization effects. In such fields the Zeeman effect is small 21 and we do not consider it here. We carry out the actual calculations for B 0 corresponding to the cyclotron splitting about 5 K. In GaAs with the electron effective mass m ‫ء‬ = 0.067m 0 such a cyclotron splitting is achieved for B 0 Ϸ 0.25 T and taking the Rashba coupling ␣ R Ϸ 4.72 meV Å, we have ␥ = 0.03.…”

“…17-21͒ and along magnetic interfaces. 22,23 All these works, however, find unlikely an exact analytical solution of the edge state problem and adopt different numerical approaches, [18][19][20]22,23 use a parabolic confining potential, 21 which has no flat domain, or give an analytical approximation in the limit of strong magnetic fields 17 where the effective SOI coupling is small.…”