Electron-phonon interaction in correlated electronic systems: polarons and the formation of orbital ordering

TL;DR

This paper investigates how electron-phonon interactions influence polaron and bipolaron formation, orbital ordering, and magnetic properties in correlated electron systems, using a Jahn-Teller-Hubbard model and strong-coupling analysis.

Contribution

It introduces a comprehensive analysis of the Jahn-Teller-Hubbard model, mapping it to a spin-1/2 Heisenberg model and comparing polaronic effects at different fillings.

Findings

Jahn-Teller polarons and bipolarons can form and are stable under certain conditions.

The model maps onto a spin-1/2 Heisenberg model with phonon-dependent couplings.

Exact solutions for few-particle cases are obtained and compared with effective lattice theories.

Abstract

The properties of a dilute electron gas, coupled to the lattice degrees of freedom, are studied and compared with the properties of an electron gas at half-filling, where spinless fermions with two orbitals per lattice site are considered. The simplest model which includes both the local electron-lattice interaction of the Jahn-Teller type and the electronic correlations is the $E\otimes\beta$-Jahn-Teller-Hubbard model. We analyze the formation and stability of Jahn-Teller polarons and bipolarons, respectively. Our approach is based on a hopping expansion in the strong-coupling regime. The results are compared with recently published findings for the Hubbard-Holstein model [1,2]. The special case of the Jahn-Teller-Hubbard model at half-filling is mapped on a spin-1/2 Heisenberg model with phonon-dependent coupling constants. This has been derived within a projection formalism that provides a continued-fraction representation of the Green's function. We study the exact solution for two and three particles and compare it with the effective theory on the infinite lattice with one particle per site.