Magnetic flux effects in an Aharonov-Bohm ring with an inserted quantum dot

The magnetic-flux effects in an Aharonov-Bohm ring with an inserted quantum dot (QD) are investigated in detail. In the present model studied the flux is attached to the coupling between the QD and the ring. Two important subjects are addressed; one the persistent current (PC), and the other the transmission phase shift. It is found that the magnetic flux plays an important role in both the enhancement of the PC and the evolution of the transmission phase shift. At zero temperature one finds that (i) the position of the Kondo resonance (KR) is not sensitive to the flux, and (ii) the width of the KR is, instead, dependent on the flux. The new mechanism for the KR channel is found: when the Fermi level goes across the KR, the PC is strongly enhanced; otherwise, the PC is suppressed. This mechanism provides deep insight into the enhancement and suppression of the PC. On the other hand, both the magnetic flux and the temperature are important features governing the phase evolution through the quantum dot. At high temperature, the phase evolution is dominated by the temperature and acquires $\pi$ as passing through each of the Coulomb blockade peaks, while the magnetic flux $\Phi$ plays a minor role. On the contrary, at zero or low temperature, the phase evolution is dominated by the magnetic flux; it acquires $\pi$ as $\Phi$ is about $\pm {\Phi }_0/2\mathrm{}$ $({\Phi }_0$ is flux quantum) and acquires $\pi /2\mathrm{}$ as $\Phi$ is about zero. Our results are consistent with the experimental observations and other theoretical calculations.