Apparent Dresselhaus coefficient in (001) GaAs quantum wells: Correlation-time renormalization in D'yakonov-Perel' spin relaxation

We study the Dresselhaus coefficient inferred from D'yakonov-Perel' spin relaxation in bulk GaAs and (001) GaAs quantum wells using nonballistic Monte Carlo simulations. In bulk GaAs, inelastic LO-phonon simulations reproduce the spin relaxation with a cubic Dresselhaus coefficient \gamma_{3D}\simeq12.4 eV{\AA}^3 and a cubic-field correlation time \tau_3^{3D}\simeq150 fs. In a projected two-dimensional quantum-well model, however, k_z^2 is replaced by the static expectation value \langle k_z^2 \rangle, converting the dominant Dresselhaus field into a term linear in the in-plane wave vector. We show that this projection changes the D'yakonov-Perel' correlation kernel from K_3^{2D} to a first- and third-order hybridized kernel K_{1+3}^{2D}, for which the correlation time \tau_{1+3}^{2D} approaches 235 fs in the strict two-dimensional limit, in contrast to the third-order correlation time \tau_3^{2D} of 130 fs. Consequently, the coefficient entering the projected two-dimensional model is not the intrinsic cubic coefficient itself but an apparent coefficient, \gamma_{2D}^{app}=\gamma_{3D} \sqrt{\tau_3^{2D}/\tau_{1+3}^{2D}}. Since \tau_{1+3}^{2D}\simeq1.8\tau_3^{2D} under LO-phonon-dominated scattering, \gamma_{2D}^{app}\simeq9.2 eV{\AA}^3, consistent with spin relaxation in (001) GaAs quantum wells. This correlation-time renormalization clarifies why Dresselhaus coefficients extracted from two-dimensional spin relaxation can differ from the cubic bulk coefficient and provides a useful framework for interpreting linear and cubic Dresselhaus parameters in quantum wells.