Charge Oscillations in a Simple Model of Interacting Magnetic Orbits
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RONIC PROPERTIES OF SOLID
Charge Oscillations in a Simple Model of Interacting Magnetic Orbits Jean-Yves Fortina,b,* a
Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University, Seoul, 08826 Korea b Laboratoire de Physique et Chimie Théoriques, CNRS (UMR 7019), Université de Lorraine, BP 70239 Vandoeuvre-lès-Nancy Cedex, F-54506 France * e-mail: [email protected] Received August 23, 2019; revised December 22, 2019; accepted January 24, 2020
Abstract—Exact eigenstates for a set of two or more interacting electronic orbits in a magnetic field are studied for a class of factorized Hamiltonians with coupled Fermi surfaces. We study the condition for the existence of annihilation-creation operators that allows for the construction of eigenstates. For the case of two interacting cyclotronic orbits, we consider the oscillations of the overlap function and the transfer of charge density between the orbits as function of the inverse field. The expressions of the Fourier frequencies are given in the semiclassical regime and they depend on the geometrical structure of the electronic bands. A generalization of this construction is provided for a chain of several interacting orbits with exact eigenfunctions. DOI: 10.1134/S1063776120050143
1. INTRODUCTION The two-state problem in quantum mechanics, such as the Rosen–Zener two-level model, gives precise information on how the wavefunction propagates through a junction and has important applications in time-driven quantum systems [1–4], where resonance and phase shifts are studied in details for exact solvable cases of potentials. This general problem can be applied in the case of magnetic breakdown as well, where a quasi-particle orbits a Fermi surface which can be composed of multiple sheets connected by junctions through which the particle can tunnel. A realization of such Fermi surfaces, resembling a linear chain of coupled orbits, is presented in Fig. 1 for the organic conductor (BEDO-TTF)5[CsHg(SCN)4]2 [5] (BEDO-TTF is the abbreviation for bis-ethylenedioxi-tetrathiafulvalene molecule): an incoming wavepacket (a) on a giant orbit β is transmitted to the small cyclotronic orbit α (b) and reflected onto the same orbit β (c) within the chain. Fermi surfaces with a finite number of interacting orbits also exist and the Fourier spectrum of their magnetic oscillations have been studied in details. For example, compensated Fermi structures with only three bands, made of one hole and two electron pockets, can be found in com⋅ pound α-'pseudo-κ'-(ET)4H3O[Fe(C2O4)3] (C6H4Br2), where the α-type and 'pseudo-κ'-type are conducting and insulating layers respectively [6]. At the magnetic breakdown junction, the Hamiltonian can be linearized and the two sheets hybridized with
some energy coupling g. This simplest form of twolevel Hamiltonian was solved by Rosen and Zener in a different context [7] using this approximation around the tunneling region. The probability of tunneling is exponentially small in the ratio between a breakdow
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