Quasiperiodicity and a spin-dependent Kronig-Penney model

Using a transfer matrix method, the band structure is calculated for a spin-dependent generalization of the Kronig-Penney model which consists of a one-dimensional array of delta function potentials whose strengths depend on the relative orientation of the electron spin and a vector located at each delta function site, the direction of which is helically modulated. This is compared with a spin-independent Kronig-Penney model in which only the amplitude of each delta function is modulated. The period of the modulation can be incommensurate with the periodicity of the delta function array. The fractal nature of the band structure in the spin-independent case is shown to be quenched by the additional symmetry in the spin-dependent model.