Exact solution of the magnetic breakdown problem in quasi-one-dimensional geometry

TL;DR

This paper provides an exact analytical solution for the electronic wave functions in a quasi-one-dimensional system with a band gap under magnetic field, relevant to Bechgaard salts, revealing new spectral properties and solutions.

Contribution

It introduces an exact solution to the magnetic breakdown problem in quasi-one-dimensional systems, including cases with complex dimerization effects, extending previous approximate methods.

Findings

Exact wave functions for quasi-1D electrons in magnetic fields

Identification of conditions for tunneling and classical behavior

Discovery of new spectral properties with transverse dimerization

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)2ClO4 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.