Transmission of electron through an Aharonov－Bohm interferometer with a quantum dot in Coulomb blockade regime

We calculate conductance of an Aharonov－Bohm (AB) interferometer for which a single-level quantum dot in the Coulomb blockade regime is embedded in one of its arms. Using the Schr?dinger equations and taking into account the Coulomb interaction on the dot, we calculate conductance G as a function of flux φ threaded through the ring and as a function of gate voltage V applied to the dot. It is found that the AB oscillations of G(φ) depend on the particle occupation on the dot, controlled by V. If the system is closed, there is no loss of particles, G(φ) is periodic and G(φ)=G(-φ), satisfying the Onsager relation. In this case G(φ) can reach its maximum value, 2e^2/h, at the resonance. When the system is open, one has G(φ)≠G(-φ), G(φ) yields a phase shift which depends on the loss rate of electrons in this open system.