Crystal structure effects upon the mass of an exciton

Abstract

The Mattis-Gallinar effect predicts that the scalar mass of an exciton depends upon its internal kinetic energy, and that the exciton mass may be larger than the sum of the masses of the electron and the hole. The author generalizes this effect to the tensorial case of a crystal structure which is not necessarily cubic. By assuming that the electron and hole share the same band structure, it is found that Mij-1=-(1/4) Sigma RRiRjKR where KR represents an internal excitonic kinetic energy associated to the vector R of the crystal lattice, and Mij-1 is the ijth component of the inverse mass tensor of the exciton. Thus, if the exciton becomes localized in the sense that KR to 0, the mass tensor M may become arbitrarily large.