Stark effect upon the effective mass and radius in a tight-binding   exciton model
  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. 
Jean El-khoury, Jean-Pierre Gallinar