J. Phys. IV France
Exact solution of the magnetic breakdown problem
in quasi-one-dimensional geometry
D. Radic1, A. Bjelis1 and D. Zanchi2
Department of Physics, Faculty of Science, University of Zagreb, POB 162,
10001 Zagreb, Croatia
Laboratoire de Physique Théorique et Hautes Énergies, 2 place Jussieu, 75252 Paris Cedex 05, France
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)
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.
anion gap, magnetic breakdown
© EDP Sciences 2004