Bychkov-Rashba spin splitting and its dependence on magnetic field inInSb/In0.91Al0.09Sbasymmetric quantum wells

Abstract

Spin splitting of conduction subbands due to structure inversion asymmetry (called Bychkov-Rashba splitting) in ${\mathrm{I}\mathrm{n}\mathrm{S}\mathrm{b}/\mathrm{I}\mathrm{n}}_{0.91}{\mathrm{Al}}_{0.09}\mathrm{Sb}$ quantum wells and its dependence on a magnetic field is investigated theoretically and compared with existing spin resonance data. The $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory for nonparabolic bands is used taking into account modifications of the band parameters due to strain. An influence of spin-dependent boundary conditions for the wave functions on the splitting is discussed. It is shown that the total spin splitting, composed in a nontrival way of the Bychkov-Rashba (BR) splitting and the Zeeman splitting, does not change sign as a function of the field. An alternative way of expressing the BR splitting as a function of the Landau number is shown to give instructive results. Assuming residual depletion densities in the range of $2.4\ifmmode\times\else\texttimes\fi{}{10}^{11}$ to $4.4\ifmmode\times\else\texttimes\fi{}{10}^{11}{\mathrm{cm}}^{\ensuremath{-}2}$ we successfully describe the observed spin splittings in four ${\mathrm{I}\mathrm{n}\mathrm{S}\mathrm{b}/\mathrm{I}\mathrm{n}}_{0.91}{\mathrm{Al}}_{0.09}\mathrm{Sb}$ samples.