Weak localization magneto-conductivity in quantum wells with Rashba and Dresselhaus spin-orbit interaction - An analytic solution

We formulate an analytic solution to the problem of the weak localization (WL) corrections to the conductivity in the presence of a quantizing magnetic field that incorporates all three spin-orbit terms that are relevant to semiconductors: linear Rashba, linear and cubic Dresselhaus. Our theory produces a complete phenomenological description of the WL contributions that showcases in a direct way the interplay between the Landau level quantization of the electron states and the spin-orbit-driven spin-flip processes. The form of the solution is determined by the relative strengths of the linear couplings, α for Rashba and β for Dresselhaus. Although present throughout the calculation, the cubic Dresselhaus term becomes important only in the α ≈ β case when it acts as a spin-symmetry breaking factor. All the contributions to magnetoconductivity associated with the quantification of the electron orbits are calculated in a Landau level invariant form. The analytic expression obtained for β >> α (or α >> β) becomes an exact solution when α = 0 (or β = 0). A closed-form formula describes the α ≈ β regime, where the result depends only on the difference between the linear Rashba and Dresselhaus terms and the cubic Dresselhaus parameter.