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

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 ⊗ β-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. The ModelThe Hamiltonian for fermions with spin σ and pseudospin γ = θ, ǫ, coupled to phonons, is given by H = H t + H 0 , where H t is a nearest neighbor tunneling term for the fermionsand H 0 is local, containing a (Hubbard) interaction and a term for dispersionless phonons of energy ω 0 with H 0 = j H 0j andwhere the plus (minus) sign refers to Holstein (E ⊗ β Jahn-Teller) electron-phonon coupling [3]. H 0j is diagonalized by a Lang-Firsov transformation [4] and has energiesif there are n j (≥ 0) phonons and n jγσ (= 0, 1) electrons with (pseudo)spin σ (γ) at site j. Each electron has an energy gain E p = g 2 /ω 0 . The regime U < 2E p has an attractive interaction, leading to an on-site bipolaron.

Jahn-Teller effect in the augmented Hubbard model

“…This last conclusion was also found from studies of the bipolaron problem of the model. 21 In other words, changing the orbital configuration reduces the energy gain. The different contributions from the hopping processes yield a symmetry breaking in the orbital sector and SU͑2͒ orb cannot be restored by a special choice of parameters.…”