Magnetic Breakdown: Effective Hamiltonian and de Haas-van Alphen Effect

Publisher Website
Google Scholar
Abstract
The influence of magnetic breakdown on the usual effective-Hamiltonian theory for Bloch electrons in a magnetic field is discussed using a simple two-dimensional rectangular model. The theory is based upon an expansion of the wave function in Wannier functions, but these have to be replaced by generalized Wannier functions (suggested by Blount) to handle breakdown. It is shown how to construct a linear network essentially equivalent to the network derived previously by the author for a nearly-free-electron model. The de Haas-van Alphen effect is discussed by expressing the energy density of states in terms of a time-independent Green's function on the network. It is shown how to construct a wave function lying on a two-dimensional network as used by Pippard.

This publication has 17 references indexed in Scilit: