Stark effect upon the effective mass and radius in a tight-binding exciton model

TL;DR

This paper investigates how a Stark electric field influences the effective mass and radius of excitons in a one-dimensional tight-binding model, revealing oscillatory behaviors and spectrum features through Green's function analysis.

Contribution

It introduces a Green's function approach to analyze the Stark effect on exciton properties in a tight-binding model, highlighting oscillations in effective mass and radius.

Findings

Effective mass oscillates with inverse electric field.

Exciton radius shows field-dependent oscillations.

Eigenvalue spectrum forms a Wannier-Stark ladder with avoided crossings.

Abstract

With a Green's function formalism we obtain the eigenvalue spectrum of a tight-binding one-dimensional exciton model characterized by a contact interaction, a Coulombic electron and hole attraction, the Heller-Marcus exciton-hopping energy and an external constant and homogeneous electric field. The resulting eigenvalue spectrum, in the form of an unevenly spaced Wannier-Stark ladder with envelope profiles, is used to obtain the effective mass of the exciton by the application of the Mattis-Gallinar effective mass formula [D. C. Mattis and J.-P. Gallinar, {\it Phys. Rev. Lett.} {\bf{53}}, 1391 (1984)]. We obtain positive and negative effective masses for the exciton. The inverse effective mass may oscillate periodically as a function of the inverse of the electric field, with the frequency of oscillation linearly dependent upon the tight-binding hopping matrix element. The exciton radius is also obtained with the Green's function formalism, and it too exhibits Keldysh-like field dependent oscillations, as well as abrupt variations associated to strongly avoided crossings in the eigenvalue spectrum. Finally, some comments are made about the experimental relevance of our results.