Spin-orbit effects on the Larmor dispersion relation in GaAs quantum wells

Abstract

We have studied the relevance of spin-orbit coupling to the dispersion relation of the Larmor resonance observed in inelastic light scattering and electron-spin resonance experiments on GaAs quantum wells. We show that the spin-orbit interaction, here described by a sum of Dresselhaus and Bychkov-Rashba terms, couples Zeeman and spin-density excitations. We have evaluated its contribution to the spin splitting as a function of the magnetic field B, and have found that in the small B limit, the spin-orbit interaction does not contribute to the spin splitting, whereas at high magnetic fields it yields a B independent contribution to the spin splitting given by 2͑ R 2 − D 2 ͒, with R,D being the intensity of the Bychkov-Rashba and Dresselhaus spin-orbit terms.

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

“…This SO correction has been worked out for the n = 0 level in Ref. 22 using the equationof-motion method. It is known that the experimental results 24 for n = 1 and 2 can be reproduced if g * depends on n and B, as already shown in that reference.…”

“…Such interplay has been also discussed in Ref. 22, in relation with the violation of the Larmor theorem due to the SO couplings, and in Ref. 33, where the Zeeman and SO interplay is discussed using the unitarily transformed Hamiltonian technique.…”

“…( 9) and (13), respectively, and the corresponding a i and b i coefficients, valid up to order λ R,D , can be extracted from Eqs. (22) and (25). These Eqs.…”

“…22 The spin splitting has been observed in electron-spin resonance 23,24 and in inelastic light-scattering experiments. 25,26 In this work we extend our previous results 21,22 by obtaining an approximate, yet very accurate, analytical solution of the quantum-well SO Hamiltonian that contains both Dresselhaus and Bychkov-Rashba interactions. In the limit of high magnetic field, this solution coincides with the results of second-order perturbation theory, and allows us to study the SO corrections to the Landau levels in a simple way, and to study the transitions induced by an external electromagnetic field acting upon the system.…”

“…21 A less clear example is the change in the Larmor frequency -spin splitting. 22 The spin splitting has been observed in electron-spin resonance 23,24 and in inelastic light scattering experiments. 25,26 In this work we extend our previous results 21,22 by obtaining an approximate, yet very accurate, analytical solution of the quantum well SO Hamiltonian that contains both Dresselhaus and Bychkov-Rashba interactions.…”