Genesis and fading away of persistent currents in a Corbino disk geometry

The detailed analytical and numerical analysis of the electron spectrum, persistent currents, and their densities for an annulus placed in a constant magnetic field (Corbino disk geometry) is presented. We calculate the current density profiles and study their dependence on the inner and outer radii of the annular. We study the evolution of the persistent currents and track their emergence and decay for different limiting cases of such a geometry, starting from a nanodot and ending by a macroscopic circle. Our analytical results for the currents are confirmed by the agreement between the integration of the corresponding current densities and the application of the Byers-Yang formula, when it is applicable. Among other results, we find the general expression for the persistent current in a narrow annulus, which in the one channel approximation reproduces the well-known result for quasi-one-dimensional mesoscopic metallic ring. Moreover, it allows to analyze the multichannel case of a relatively wide annulus. Our study can be used for more accurate treatment and interpretation of the experimental data with measurements of the persistent currents in different doubly connected systems.