Rashba effect in cylindrical quantum well wire with finite confining potential

Abstract: The effect of the Rashba spin-orbit interaction has been investigated in an infinite cylindrical quantum well wire (QWW) with finite confining potential. The effect has been considered in the absence and presence of an axial magnetic field. The solution of the radial Schrödinger equation has been obtained in the wire and in the barrier, in the absence of the Rashba spin-orbit interactions. The general solution in the presence of these interactions has then been expanded in terms of the obtained two solutions and in terms of the step function. The study should, however, be performed in two dimensions. For this reason, the wave vector along the axis of the wire has been chosen to be zero. The orthogonality of the elements of the resulting basis has been proved. The dependence of the Rashba coupling coefficient on the electron effective mass has also been taken into consideration. The results have been applied to the case of GaAs- GaAlAs cylindrical quantum wire. Graphical Abstract: [Figure not available: see fulltext.] The energy levels (E, E) and (E, E) in the absence and presence of the Rashba effect against the radius (R) of the QWW. The magnetic field B = 10 T, the confining potential V = 25 R and two different values for the Rashba coupling coefficient have been used in the wire and barrier.