Dimensional crossover of the effective Dresselhaus coefficient in GaAs spin relaxation

In noncentrosymmetric semiconductors, the Dresselhaus coefficient γ determines the strength of the momentum-dependent spin–orbit field and is often applied without distinction to bulk and quantum-confined systems. Here, we show that the effective coefficient inferred from D'yakonov–Perel' spin relaxation exhibits a dimensional crossover governed by the correlation time of the fluctuating spin–orbit field. Monte Carlo simulations reproduce the carrier-density dependence of spin relaxation in bulk GaAs with γ3D=11.6 and 12.4 eVÅ3 for elastic and inelastic-scattering models, respectively, and yield a third-harmonic correlation time τ3 of approximately 150 fs. In 001GaAs quantum wells, the correlation time τ1+3 of the total projected Dresselhaus field approaches 320-340 fs in the two-dimensional limit and continuously decreases toward τ3 with increasing well width. Defining apparent Dresselhaus coefficient γ2Dapp=γ3Dτ3/τ1+3, γ2Dapp exhibits 8 eVÅ3 in narrow wells and recovers the bulk coefficient in wide wells. The resulting inelastic calculations agree with experiment and with an independently calibrated elastic model using γ≃γ2Dapp(11.6/12.4). These results identify the correlation-time crossover as the origin of the reduced Dresselhaus coefficient inferred from quantum-well spin relaxation. This correlation-time framework provides a quantitative basis for predicting and engineering spin relaxation times in quantum-well-based spintronic devices.