Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with a Rashba Interaction in a Perpendicular Magnetic Field

We study transport properties of a two-dimensional electron system with Rashba spin-orbit coupling in a perpendicular magnetic field. The spin-orbit coupling competes with Zeeman splitting to introduce additional degeneracies between different Landau levels at certain magnetic fields. This degeneracy, if occurring at the Fermi level, gives rise to a resonant spin Hall conductance, whose height is divergent as $1/T$ and whose weight is divergent as $-\ln T$ at low temperatures. The Hall conductance is unaffected by the Rashba coupling..

Figure 1

Illustration of the two-dimensional electron system studied in the text.

Figure 2

Landau levels of an electron as functions of $\eta =\lambda m{l}_b/{\hslash }^2$ for $g=g_{s}m/2m_e=0.1$. Arrows indicate those level crossings giving rise to resonant spin Hall conductance.

Figure 3

(a) Average spin $⟨{\sigma }_z⟩$ (unit: $\hslash /2$) per electron as a function of $1/B$. (b) Spin Hall conductance versus $B$ at $T=0$. The parameters used are $\lambda =0.9\times {10}^{-11}\mathrm{eV}\mathrm{m}$, $n_e=1.9\times {10}^{16}/{\mathrm{m}}^2$, $g_s=4$, and $m=0.05m_e$, taken for the inversion heterostructure ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}/{\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ (see Ref. 17).

Figure 4

Spin Hall conductance as a function of $B$ at various temperatures for a two level system with $n_e$ fixed, $g=0.1$, and $\nu =0.5$ at the resonant field $B_0$. $b=(B-B_0)/B_0$; $t=kT/\hslash \omega (B_0)$.