Impurity-bound excitons in one and two dimensions

TL;DR

This paper investigates the existence of impurity-bound excitons in one- and two-dimensional systems, showing that strong impurity charges prevent bound states, supported by spectral analysis and numerical computations.

Contribution

It provides a rigorous spectral analysis of three-body Schrödinger operators with impurity interactions, identifying conditions for the absence of bound states in low-dimensional systems.

Findings

Bound states do not exist when impurity charge exceeds a critical value.

Spectral results are validated through variational numerical methods.

The study models physically relevant interaction potentials from the literature.

Abstract

We study three-body Schr\"odinger operators in one and two dimensions modelling an exciton interacting with a charged impurity. We consider certain classes of multiplicative interaction potentials proposed in the physics literature. We show that if the impurity charge is larger than some critical value, then three-body bound states cannot exist. Our spectral results are confirmed by variational numerical computations based on projecting on a finite dimensional subspace generated by a Gaussian basis.