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The spin-Hall effect in the two-dimensional electron gas (2DEG) generatessymmetric out-of-plane spin Sz accumulation about the current axis in theabsence of external magnetic field. Here we employ the real spaceLandauer-Keldysh formalism [B. K. Nikolic et al., Phys. Rev. Lett. 95, 046601(2005); Phys. Rev. B 73, 075303 (2006)] by considering a four-terminal setup toinvestigate the circumstances in which this symmetry is broken. For the absenceof Dresselhaus interaction, starting from the applied out-of-plane Bcorresponding to Zeeman splitting energy 0 - 0.5 times the Rashba hoppingenergy tR, the breaking process is clearly seen. The influence of the Rashbainteraction on the magnetization of the 2DEG is studied herein. For coexistedRashba tR and Dresselhaus tD spin-orbit couplings in the absence of B,interchanging tR and tD reverses the entire accumulation pattern.

Broken spin-Hall accumulation symmetry by magnetic field and coexisted Rashba and Dresselhaus interactions