Thermodynamic functions of a relativistic electron gas on a tube in a magnetic field

Abstract

On the basis of the one-particle Dirac equation, an exact solution for the problem of the energy spectrum of a relativistic electron on the surface of a tube in a magnetic field is obtained. The spectra of a relativistic rotator and a relativistic electron in a two-dimensional electron gas are obtained in limiting cases. The density of electron states and the main thermodynamic functions of a relativistic electron gas on a tube in a magnetic field are calculated. These values experience Aharonov–Bohm oscillations and oscillations of the de Haas–van Alphen type with a change of the magnetic field and parameters of the problem. The asymptotics of thermodynamic functions at low- and high-temperatures are obtained. The results can be used in studies of nanotubes of a two-dimensional electron gas and in astrophysics.