Impurity-bound excitons in one and two dimensions

  • Horia Cornean

    Aalborg University, Denmark
  • Hynek Kovařík

    Università degli Studi di Brescia, Italy
  • Thomas G. Pedersen

    Aalborg University, Denmark
Impurity-bound excitons in one and two dimensions cover
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Abstract

We study three-body Schrödinger 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.

Cite this article

Horia Cornean, Hynek Kovařík, Thomas G. Pedersen, Impurity-bound excitons in one and two dimensions. J. Spectr. Theory 10 (2020), no. 3, pp. 1103–1138

DOI 10.4171/JST/322