Dynamical mean-field theory of the small polaron

TL;DR

This paper develops a dynamical mean-field theory for small polarons, revealing how spectral properties change with electron-phonon coupling and phonon frequency, including the formation of quasiparticle subbands and spectral gaps.

Contribution

It introduces a DMFT approach to the small polaron problem, providing detailed spectral analysis and identifying a critical coupling for gap formation.

Findings

Spectral gaps open at low phonon frequencies beyond a critical coupling.

Coexistence of narrow quasiparticle subbands with broad incoherent structures.

Finite temperature causes damping and broadening of polaron subbands.

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.