Energy Levels of Bloch Electrons in Magnetic Fields

Abstract

From the calculation of the energy levels of conduction electrons in a simple model of a metal in a magnetic field three interesting results emerge. (a) Quantum corrections to Onsager's semiclassical quantization formula are found to be sufficiently small that the usual interpretation of the de Haas-van Alphen effect should provide an accurate measure of Fermi-surface cross sections in potassium. (b) The undetermined constant appearing in Onsager's formula is found to be $\frac{3}{4}$ for effects due to "lens" orbits in hexagonal metals when the magnetic field lies in the basal plane. (c) The quantization of energy levels in a variety of periodic open orbits is predicted to be observable in principle through cyclotron-resonance experiments in a suitable geometry in the intermediate magnetic-breakdown regime.