Spin splitting of surface states in HgTe quantum wells

We report on beating appearance in Shubnikov–de Haas oscillations in conduction band of 18–22 nm HgTe quantum wells under applied top-gate voltage. Analysis of the beatings reveals two electron concentrations at the Fermi level arising due to Rashba-like spin splitting of the first conduction subband H₁. The difference ΔN_s in two concentrations as a function of the gate voltage is qualitatively explained by a proposed toy electrostatic model involving the surface states localized at quantum well interfaces. Experimental values of ΔN_s are also in a good quantitative agreement with self-consistent calculations of Poisson and Schrödinger equations with eight-band k p Hamiltonian. Our results clearly demonstrate that the large spin splitting of the first conduction subband is caused by surface nature of H₁ states hybridized with the heavy-hole band.