Influence of phonon scattering on coherent transmission of electrons through an Aharonov-Bohm ring

We investigate the influence of electron-phonon (EP) scattering on interference of electron in an Aharonov-Bohm (AB) ring's structure by solving Schrödinger equation for coupled EP states. At zero temperature the amplitude of AB oscillations exhibits a periodic variation by increasing the strength of the EP coupling, implying the interference of different EP channels. The decoherence is deduced by introducing the multi-phonon processes. We calculate average phonon numbers in different modes which are stimulated by electrons during the tunneling. It is found that the phonon number is not sensitive to the EP interaction strength and is decreased by increasing the frequency of the phonon mode. We also investigate the influence of thermal fluctuations by calculating the conductance in various temperatures. The obtained results may shed light on the effects of inelastic scattering on quantum interference in mesoscopic structures.