Theoretical approach to the excitonic response of GaAs nanomembranes in the averaged-strain approximation

GaAs nanomembranes are thin crystalline GaAs semiconductor structures that can be bent or otherwise elastically deformed from their natural shape. We present a microscopic theory of the linear optical response of such deformed structures. Our approach combines conventional structural analysis (based on the theory of elasticity), the valence band Hamiltonians (Luttinger and Pikus-Bir) for III-V semiconductors, and the semiconductor Hamiltonian including Coulomb interaction. We formulate the general equation of motion for the interband polarization for thin elastically deformed nanomembranes. A simple limiting case results from the single-subband approximation and the averaged-strain approximation. Within this approximation scheme, we present numerical results for excitonic spectra for a cylindrically deformed membrane.