Electron structure of the Falicov-Kimball model with a magnetic field

TL;DR

This paper studies how electron correlations and magnetic fields influence the electron structure in the Falicov-Kimball model, revealing the interplay between metal-insulator transitions and the Hofstadter butterfly pattern.

Contribution

It introduces a dynamical mean-field theory analysis of the Falicov-Kimball model under magnetic fields, showing how correlations affect the Hofstadter butterfly's structure.

Findings

Electron correlations smear out the Hofstadter butterfly during metal-insulator transition.

In long-range ordered phases, the correlation-induced gap preserves the butterfly's fine structure.

The Hofstadter butterfly splits into two wings in the ordered phase due to the gap.

Abstract

The two-dimensional Falicov-Kimball model in the presence of a perpendicular magnetic field is investigated by the dynamical mean-field theory. Within the model the interplay between electron correlations and the fine electron structure due to the magnetic field is essentially emerged. Without electron correlations the magnetic field induces the electron structure to the so-called Hofstadter butterfly. It is found that when electron correlations drives the metal-insulator transition, they simultaneously smear out the fine structure of the Hofstadter butterfly. In a long-range ordered phase, the electron correlation induced gap preserves the fine structure, but it separates the Hofstadter butterfly into two wings.