Dynamical mean-field study of the Mott transition in thin films

TL;DR

This study uses dynamical mean-field theory to analyze the Mott transition in thin films of the Hubbard model, revealing how surface geometry and thickness influence electronic properties and critical interaction strengths.

Contribution

It provides a detailed layer- and thickness-dependent analysis of the Mott transition in thin films, including analytical insights into the critical interaction parameters.

Findings

Finite film thickness affects the Mott transition more in open surface geometries.

Layer dependence of quasi-particle weight varies with surface orientation.

Critical interaction strengths approach bulk values as thickness increases.

Abstract

The correlation-driven transition from a paramagnetic metal to a paramagnetic Mott-Hubbard insulator is studied within the half-filled Hubbard model for a thin-film geometry. We consider simple-cubic films with different low-index surfaces and film thickness d ranging from d=1 (two-dimensional) up to d=8. Using the dynamical mean-field theory, the lattice (film) problem is self-consistently mapped onto a set of d single-impurity Anderson models which are indirectly coupled via the respective baths of conduction electrons. The impurity models are solved at zero temperature using the exact-diagonalization algorithm. We investigate the layer and thickness dependence of the electronic structure in the low-energy regime. Effects due to the finite film thickness are found to be the more pronounced the lower is the film-surface coordination number. For the comparatively open sc(111) geometry we find a strong layer dependence of the quasi-particle weight while it is much less pronounced for the sc(110) and the sc(100) film geometries. For a given geometry and thickness d there is a unique critical interaction strength Uc2(d) at which all effective masses diverge and there is a unique strength Uc1(d) where the insulating solution disappears. Uc2(d) and Uc1(d) gradually increase with increasing thickness eventually approaching their bulk values. A simple analytical argument explains the complete geometry and thickness dependence of Uc2. Uc1 is found to scale linearly with Uc2.