Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure

TL;DR

This paper introduces the principles of dynamical mean-field theory (DMFT) for understanding strongly correlated electron systems, emphasizing its applications to Mott transitions and electronic structure in complex materials.

Contribution

It provides an overview of DMFT, its formal analogies, and recent advances in combining it with electronic structure methods for complex materials.

Findings

DMFT effectively describes Mott transitions.

Spectroscopy and transport experiments support DMFT predictions.

Combining DMFT with electronic structure methods advances material understanding.

Abstract

These are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean-field theory (DMFT) are then briefly reviewed. I emphasize the formal analogies with classical mean-field theory and density functional theory, through the construction of free-energy functionals of a local observable. I review the application of DMFT to the Mott transition, and compare to recent spectroscopy and transport experiments. The key role of the quasiparticle coherence scale, and of transfers of spectral weight between low- and intermediate or high energies is emphasized. Above this scale, correlated metals enter an incoherent regime with unusual transport properties. The recent combinations of DMFT with electronic structure methods are also discussed, and illustrated by some applications to transition metal oxides and f-electron materials.