J. Phys. IV France
114
(2004)
129
DOI: 10.1051/jp4:2004114029
Exact solution of the magnetic breakdown problem
in quasi-one-dimensional geometry
D. Radic1, A. Bjelis1 and D. Zanchi2
1
Department of Physics, Faculty of Science, University of Zagreb, POB 162,
10001 Zagreb, Croatia
e-mail: bjelis@phy.hr
2
Laboratoire de Physique Théorique et Hautes Énergies, 2 place Jussieu, 75252 Paris Cedex 05, France
e-mail: drazen@lpthe.jussieu.fr
Abstract
We present exact solution of the problem of electronic
wave functions of quasi one-dimensional band with an inter-band gap at the
Fermi surface and in the presence of magnetic field. The details of the
analyzed model are appropriate to the situation in the Bechgaard salt (TMTSF)
2ClO
4 with the dimerizing anion order in the transverse
direction. Limiting the effects of dimerization to the standard dimerization
gap only, one obtains the electronic spectrum represented through solutions
of a generalized Hill system of equations with simply periodic coefficients.
The resulting wave-functions are discussed. In particular, we present the
solutions for the case when the electrons spend as much time in the
"junctions" as on their quasi-classical orbits. On the other hand, the
limit when the tunnelling approach is valid is identified and the results
are confronted with the well-known Slutskin-Kadigrobov solution.
Furthermore, taking into account also the presumably finite transverse
dimerizing displacements of chains, one encounters the qualitatively more
complex problem of a system of equations with two-periodic coefficients.
Some qualitatively new properties of electronic spectrum and corresponding
one-electron physical quantities in this case will be discussed in detail.
Key words. anion gap, magnetic breakdown
© EDP Sciences 2004