Magnetic properties of electrons confined in an anisotropic cylindrical potential

In the present paper a theoretical model, describing the effects of external electric and magnetic fields on an electron confined in an anisotropic parabolic potential, is considered. The exact wave functions are used to calculate electron current and orbital magnetic dipole momentum for the single electron. Exact expressions, giving the force and energy of the dipole–dipole interaction, are also determined. Further, the system is coupled to a heat bath, and mean values and fluctuations of the magnetic dipole momentum, utilizing the canonical ensemble are calculated. Influences of the temperature, as well as the external magnetic field, expressed via the Larmor frequency are analyzed. We also include the dependencies of the magnetic dipole momentum and its fluctuations on the effective mass of the electron, considering some experimental values for low-dimensional systems, that are extensively studied for various applications in electronics. Our results suggest that the average momentum or its fluctuations are strongly related to the effective mass of the electron. Having on mind that parabolically shaped potentials have very wide area of application in the low-dimensional systems, such as quantum dots and rings, carbon nanotubes, we believe that the proposed model and the consequent analysis is of general importance, since it offers exact analytical approach.