Excitonic Bound State in the Extended Anderson Model with c-f Coulomb Interaction

TL;DR

This paper investigates the formation of excitonic bound states in the semiconducting phase of the extended Anderson model with c-f Coulomb interaction, revealing bound states within the gap through analytical and numerical methods.

Contribution

It introduces a vertex correction approach to extend the non-crossing approximation, capturing the excitonic bound state in the model.

Findings

Bound state localized at the local electron site.

Excitonic bound state appears inside the semiconducting gap.

Discontinuity observed at the gap edge for magnetic excitations.

Abstract

The Anderson model with the Coulomb interaction between the local and conduction electrons is studied in the semiconducting phase. Based on a perturbation theory from the atomic limit, leading contributions for the c-f Coulomb interaction are incorporated as a vertex correction to hybridization. An analytical solution shows that the effective attraction in the intermediate states leads to a bound state localized at the local electron site. Self-consistent equations are constructed as an extension of the non-crossing approximation (NCA) to include the vertex part yielding the bound state. A numerical calculation demonstrates the excitonic bound state inside the semiconducting gap for single-particle excitations, and a discontinuity at the gap edge for magnetic excitations.