Non-linear charge currents and the planar Hall effect in quantum wells with Rashba and Dresselhaus spin-orbit interactions.

We calculate the non-linear charge currents in a two-dimensional electron system with Rashba (α) and Dresselhaus (β) linear spin-orbit interactions (SOIs) in the presence of in-plane electricEand magneticBfields. Working in a rotated system of coordinates that introducesα±βas effective couplings on perpendicular directions, we show that the currents, quadratic in the electric field, exist for all values of the chemical potentialµ, above or below the band crossing energyE0. Our formalism uses a second order correction to the particle distribution functionδf(2)derived in a semi-classical approximation that takes into account the local change in the single-particle energy under the action of the electric field. In a quantum well, whereμ>E0, for a spin-orbit energy larger than the Zeeman splitting, the non-linear currents that flow perpendicular on the direction of the magnetic field are found to be proportional withα±βwhenE⊥Band with(α±β)2/(α∓β)whenE∥B, a result independent of the presence of any additional SOIs, such as the cubic Dresselhaus or warping.