Transmission through an Aharonov-Bohm ring with two quantum dots

We study the phase behavior of the oscillating conductance for a modified Aharonov-Bohm (AB) ring threaded by a magnetic flux, with a quantum dot embedded in each arm, respectively (dot-1 for studying and dot-0 for reference). Using Keldysh's nonequilibrium-Green-function the expressions for the current j and the transmission probability T(epsilon) are derived. For the AB ring with one dot, we show that the phase behavior of the AB oscillating is in agreement with the observation qualitatively. In particular, we can obtain an abrupt phase drop by pi near the centre of the two succesive resonance peaks, thus explain that the corresponding points of the succesive peaks are in phase. For the AB ring with two dots, we find that the symmetrical positions of a peak are in phase; no phase change happens as passing a single resonance peak but an abrupt phase change by pi occurs around somewhere between the peak and the valley. These phase characters can be explained in terms of the transmission probability. (C) 1998 Elsevier Science Ltd.