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arXiv · 1701.04302

On the existence of impurity bound excitons in one-dimensional systems with zero range interactions

Jonas Have·Hynek Kovarik·Thomas G. Pedersen·Horia D. Cornean
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Abstract

We consider a three-body one-dimensional Schr\"odinger operator with zero range potentials, which models a positive impurity with charge $\kappa > 0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$ there exists a unique bound state whose binding energy behaves like $\kappa^4$, and we explicitly compute its leading coefficient. On the other hand, if $\kappa$ is larger than some critical value then the system has no bound states.

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Jonas Have, Hynek Kovarik, Thomas G. Pedersen, Horia D. Cornean. 2017-01-16. On the existence of impurity bound excitons in one-dimensional systems with zero range interactions. https://doi.org/10.1063/1.4983921

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