Inhomogeneous dynamical mean field theory of the small polaron problem

TL;DR

This paper introduces an inhomogeneous dynamical mean field theory (I-DMFT) for studying electron-lattice interactions in inhomogeneous systems, successfully capturing local effects and defects, with applications demonstrated on surface defects and STM relevance.

Contribution

The paper develops a new I-DMFT approach that handles inhomogeneous electron-lattice systems with local self-energy assumptions, extending the applicability of DMFT to non-translationally invariant problems.

Findings

Maps of local density of states show Friedel oscillations influenced by polaron mass.

The method accurately recovers non-interacting and translationally invariant limits.

Application to surface defects demonstrates the method's capability in real-space problems.

Abstract

We present an inhomogeneous dynamical mean field theory (I-DMFT) that is suitable to investigate electron-lattice interactions in non-translationally invariant and/or inhomogeneous systems. The presented approach, whose only assumption is that of a local, site-dependent self-energy, recovers both the exact solution of an electron in a generic external potential in the non-interacting limit and the DMFT solution for the small polaron problem in translationally invariant systems. To illustrate its full capabilities, we use I-DMFT to study the effects of defects embedded on a two-dimensional surface. The computed maps of the local density of states reveal Friedel oscillations, whose periodicity is determined by the polaron mass. This can be of direct relevance for the interpretation of scanning-tunneling microscopy (STM) experiments on systems with sizable electron-lattice interactions. Overall, the easy numerical implementation of the method, yet full self-consistency, allows one to study problems in real-space that were previously difficult to access.