Dimensional crossover in cylindrical quantum-box structures formed by penetrable barriers

Abstract

We study the density of states (DOS) in a cylindrical quantum box formed by a cylindrical penetrable barrier and a planer penetrable double barrier perpendicular to the cylinder. The control of the cylindrical barrier thickness or height is found to cause the dimensional transitions from a three-dimensional (3D) DOS to a quasi-one-dimensional (Q1D) DOS and from a quasi-two-dimensional (Q2D) DOS to a quasi-zero-dimensional (Q0D) DOS, if the strength of the planer double barrier is zero and infinity, respectively. In between the 3D and the Q1D (Q2D and Q0D) limiting regimes, we found the presence of a Q2D (Q1D) like crossover regime.