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

Have, Jonas; Kovařík, Hynek; Pedersen, Thomas Garm; Cornean, Horia D.

doi:10.1063/1.4983921

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…Alternatively, excitons interacting with an immobile charged impurity may lead to impurity-bound excitons [6,2]. The latter can be modelled as a light electron-hole pair interacting with an infinitely heavy impurity charge κ. n two previous papers we studied in detail one-dimensional impurity-bound excitons where the interactions were modelled by contact potentials [3], as well as trions [9]. In the current manuscript, we extend the analysis to the physically more relevant case of two-dimensional atomically thin semiconductors, in which impurity-bound excitons are frequently observed.…”

Section: Introduction and Main Resultsmentioning

confidence: 93%

Impurity-bound excitons in one and two dimensions

Cornean¹,

Kovařík²,

G.³

2018

Preprint

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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.

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Section: Introduction and Main Resultsmentioning

confidence: 93%

Impurity-bound excitons in one and two dimensions

Cornean¹,

Kovařík²,

G.³

2018

Preprint

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“…-for the description of atoms in strong magnetic fields [BD06]; -in the theory of semiconductors as a model for excitons [HKPC17];…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane

Exner

Kondej

Lotoreichik

2018

Journal of Mathematical Physics

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In this paper we consider the three-dimensional Schrödinger operator with a δ-interaction of strength α > 0 supported on an unbounded surface parametrized by the mappingThe surface supporting the interaction can be viewed as a local deformation of the plane. It is known that the essential spectrum of this Schrödinger operator coincides with [− 1 4 α 2 , +∞). We prove that for all sufficiently small β > 0 its discrete spectrum is non-empty and consists of a unique simple eigenvalue. Moreover, we obtain an asymptotic expansion of this eigenvalue in the limit β → 0+. In particular, this eigenvalue tends to − 1 4 α 2 exponentially fast as β → 0+.2010 Mathematics Subject Classification. 35P15 (primary); 58J50, 81Q37 (secondary). Key words and phrases. Singular Schrödinger operator, δ-interaction on a locally deformed plane, existence of bound states, asymptotics of the bound state, small deformation limit, Birman-Schwinger principle.

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“…Another physical use of the Hamiltonian H α,Σ N can be found in the few-body quantum mechanics with zero-range interactions -see, e.g. , [BK13,BD06,CDR08,HKPC17,LL63].…”

Section: Introductionmentioning

confidence: 99%

Optimization of the lowest eigenvalue for leaky star graphs

Exner¹,

Lotoreichik²

2018

Contemporary Mathematics

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We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrödinger operator with an attractive δ-interaction of a fixed strength, the support of which is a star graph with finitely many edges of an equal length L ∈ (0, ∞]. Under the constraint of fixed number of the edges and fixed length of them, we prove that the lowest eigenvalue is maximized by the fully symmetric star graph. The proof relies on the Birman-Schwinger principle, properties of the Macdonald function, and on a geometric inequality for polygons circumscribed into the unit circle.2010 Mathematics Subject Classification. 35P15 (primary); 58J50, 81Q37 (secondary).

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

Cited by 4 publications

References 26 publications

Impurity-bound excitons in one and two dimensions

Impurity-bound excitons in one and two dimensions

Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane

Optimization of the lowest eigenvalue for leaky star graphs

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