Rashba spin–orbit coupling in a two-dimensional quantum ring superlattice

•Rashba effect on band structure of quantum ring superlattice has been investigated.•Splitting of the dispersion surfaces are obtained.•The spin–orbit interaction brings an asymmetry to the Bloch amplitudes.

The effect of the Rashba spin–orbit coupling on electronic states in GaAs/Ga1-xAlxGaAs/Ga1-xAlxAs two-dimensional quantum ring superlattice is investigated. The conduction band structure and the Bloch amplitudes of the superlattice are obtained by the exact diagonalization procedure using the Fourier transformation to the momentum space. The splitting of the mini-bands as well as the crossing of the dispersion surfaces at the high symmetry points in the Brillouin zone are obtained. It is shown that spin–orbit interaction brings an asymmetry to the Bloch amplitudes of the conduction mini-band.