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

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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, Phys. Rev. Lett. 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.