The Quantum Transport Properties Of AB Interferometer With Electron-phonon Interaction

With the rapid development of microfabrication techniques it is feasible to manufacture ultrasmall electronic devices in order to miniaturize integrated circuits. Thus, the quantum conherence become very important in electronic devices.In order to investigate the electron wave phase coherence, AB effect is successfully applied to the quantum device named AB interferometer. AB interferometer can let us observe famous Fano effect induced by electronic phase coherence. Electron-phonon interactions have more effects on the conherece and easily make it disappeared.In this paper, considering Coulomb interaction and electron-phonon interaction meanwhile, we study the transport properties of the AB interferometer by the nonequilibrium Green's function approach. We first recall some important conceptions in the mesoscopic physics, such as the quantum dot, Fano effect, AB effect and so on. Then, we gives the related research background and development of the electron-phonon effect in theorical and experimental aspects. And The approachs of dealing the electron-phonon interaction are also introduced including the canonical transformation method,the nonequilibrium Green's function etc. Finally, we study the influence that the electron-phonon (e-ph) interaction and the Coulomb interaction have on the Fano resonance and the Breit-Wigner resonance of the transport through the AB interferometer.Using the non-equilibrium Green function,we obtain the expressions of the current and find the negative differential conductance when the e-ph interaction have more effect than the Coulomb interaction in the Fano resonance due to the interference;The positive and effective Coulomb interaction makes the width of main peak narrower, the negative one makes the the width of main peak wider. When the e-ph interaction have more effect than the Coulomb interaction in the Breit-Wigner resonance, the negative differential conductance no longer appear.