Correlated Mott insulators in strong electric fields: Role of phonons in heat dissipation

TL;DR

This paper investigates how phonons influence heat dissipation and electrical transport in Mott insulators under strong electric fields, revealing their limited but significant role near resonances and in the metallic phase.

Contribution

It introduces a detailed non-equilibrium DMFT study of Mott insulators with phonon and fermionic bath dissipation, highlighting phonons' impact on current and charge distribution.

Findings

Phonons enhance current near half-gap field strengths.

Phonons reduce current at the Wannier-Stark resonance.

Charge accumulates in the upper Hubbard band with effective chemical potentials.

Abstract

We study the spectral and transport properties of a Mott insulator driven by a static electric field into a non-equilibrium steady state. For the dissipation, we consider two mechanisms: Wide-band fermion reservoirs and phonons included within the Migdal approximation. The electron correlations are treated via non-equilibrium dynamical mean field theory with an impurity solver suitable for strong correlations. We find that dissipation via phonons is limited to restricted ranges of field values around Wannier-Stark resonances. To cover the full range of field strengths, we allow for a small coupling with fermionic baths, which stabilizes the solution. When considering both dissipation mechanisms, we find that phonons enhance the current for field strengths close to half of the gap while lowering it at the gap resonance as compared to the purely electronic dissipation used by Murakami and Werner [arXiv:1804.08257]. Once phonons are the only dissipation mechanism, the current in the metallic phase is almost one order of magnitude smaller than the typical values obtained by coupling to a fermionic bath. In this case, the transport regime is characterized by an accumulation of charge in the upper Hubbard band described by two effective chemical potentials.