Effects of Electron(Hole)–SO-Phonon Coupling on the Ground Exciton State in Quantum Wires

Taking account of electron(hole)–SO-phonon coupling, the ground exciton state in free-standing quantum-well wires with circular cross-section is studied in detail. Two unitary transformations are carried out, the SO-phonon-induced potential in ϱ-direction and the SO-phonon-induced interaction between an electron and a hole in z-direction as well as the effective Hamiltonian of the exciton–SO-phonon systems are obtained. The ground exciton state binding energy is calculated from a trial wave function separable in spatial coordinates. An unexpected result is obtained: although the electron (hole)–SO-phonon coupling is very strong in quantum wires, its influence on the exciton binding energy is not so notable as that in 3D or 2D exciton-phonon systems.