Dynamical mean-field theory of the small polaron

Abstract

A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion (CFE), both at zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground state properties such as the effective polaron mass, which have a smooth behaviour, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more and more open in the density of states at low energy, while the high energy part of the spectrum is broad and can be explained by a strong coupling adiabatic approximation. As a consequence narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum has always a multipeaked structure.Comment: 21 Pages Latex, 19 PostScript figure

Spectral properties and isotope effect in strongly interacting systems: Mott-Hubbard insulator versus polaronic semiconductor

“…The present theory is valid in the opposite limit, D ≫ ω 0 , which is more often realized in solids [36,37,38]. Due to the large transfer integrals between molecular units, the discrete shakeoff spectrum characteristic of isolated molecules is converted here into a continuous gaussian spectral density [16], and a sizeable high-energy dispersion is recovered.…”

“…Bottom: in a polaronic system (U = 0) with the same electron-boson parameters. The green dashed curve here is the noninteracting band, the black solid line is the exact DMFT result [16], and the blue dotted curve is the approximate result based on equation (13). Vertical lines mark the reference energy of incoming particles.…”

“…For the problem of a single electron coupled to a dispersionless boson, a complete characterization of the excitation spectrum has been given in references [16,34], based on the Dynamical Mean Field Theory. In the adiabatic regime, the spectra are composed of one (or several, depending on the coupling strength) narrow features at low energy, equally spaced by ω 0 , coexisting with a continuous high energy background centered around the polaron binding energy E P .…”

“…In the former case, the validity of our approach relies on the separation of electronic and bosonic energy scales, which is achieved due to a strong electronelectron repulsion. In the latter case, the present CPA results are controlled by direct comparison with an exact solution obtained by Dynamical Mean Field Theory (DMFT) [16].…”

Polaron features for long-range electron–phonon interaction

“…In this regime, as shown by several numerical studies [7][8][9][10][11] and variational approaches, [12][13][14] the system undergoes a crossover from a weakly dressed electron to a massive localized polaronic quasiparticle, the small Holstein polaron (SHP ), with increasing the strength of interaction. All the ground state properties of the Holstein moldel can be described with great accuracy by a variational approach 13 Recently a quite general el − ph lattice Hamiltonian with a "density-displacement" type interaction has been introduced in order to understand the role of long-range (LR) coupling on the polaron formation.…”