Energy spectrum of the Kronig-Penney model in the presence of the strong spin-orbit coupling

Rui Li

Published 2017-09-15Version 1

The Kronig-Penney model, an exactly solvable one-dimensional model of crystal in solid physics, shows how the allowed and forbidden bands are formed in solids. In this paper, we study this model in the presence of both the strong spin-orbit coupling and the Zeeman field. We analytically obtain four transcendental equations, each defined in the corresponding energy regime. Solving these four transcendental equations, we obtain the total band structure of the Kronig-Penney model exactly. Our results give a clear physical picture of the combined effects of the strong spin-orbit coupling and the periodic potential. Especially, the energy anticrossing can give rise to a large bad gap in this model.