Issue J. Phys. IV France Volume 114, April 2004 Page(s) 129 - 132 DOI 10.1051/jp4:2004114029

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. Zanchi<sup>2

1</sup>  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

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