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Semiclassical Analysis and the Magnetization of the Hofstadter Model O. Gat and J. E. Avron

Summary: Semiclassical Analysis and the Magnetization of the Hofstadter Model
O. Gat and J. E. Avron
Department of Physics, Technion 32000, Haifa, Israel
(Received 12 June 2003; published 29 October 2003)
The magnetization and the de Haas­van Alphen oscillations of Bloch electrons are calculated near
commensurate magnetic fluxes. Two phases that appear in the quantization of mixed systems--the
Berry phase and a phase first discovered by Wilkinson--play a key role in the theory.
DOI: 10.1103/PhysRevLett.91.186801 PACS numbers: 73.43.­f, 75.20.­g, 75.70.­i
The magnetization of a free electron gas was calculated
by Landau in 1930 in the early days of quantum mechan-
ics [1]. Considerable efforts have since been devoted to
extending these results to Bloch electrons. Most of the
progress made was in the region of weak magnetic fields
[2,3] where the flux through a unit cell is small. This is
adequate for most solid state applications. There is, how-
ever, also considerable interest in a better understanding
of phenomena that have to do with commensuration in
condensed matter physics [4­8]. This is the case when
is close to a rational number. The magnetization of Bloch
electrons near rational fluxes, other than 0, re-


Source: Avron, Joseph - Physics Department, Technion, Israel Institute of Technology


Collections: Physics