On the theory of quantum oscillation phenomena in cylindrical conductors

The quantum energy levels and density of states for conduction electrons with a quadratic anisotropic dispersion law are obtained in a cylindrical conductor in an arbitrary magnetic field H. It is shown that the anisotropy of the Fermi surface causes localization of electron states with respect to the angle φ (in the cross section plane of the conductor). For not too low temperatures the data on the states govern quantum size oscillations of the electronic characteristics of the conductors. An analysis of the quantum oscillations of thermodynamic quantities is executed in weak magnetic fields. Oscillation frequencies equidistant in H are calculated for electrons in thin cylindrical bismuth single crystals.

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