Josephson Effect through an isotropic magnetic molecule

We investigate the Josephson effect through a molecular quantum dot magnet connected to superconducting leads. The molecule contains a magnetic atom, whose spin is assumed to be isotropic. It is coupled to the electron spin on the dot via exchange coupling. Using the numerical renormalization group method we calculate the Andreev levels and the supercurrent and examine intertwined effect of the exchange coupling, Kondo correlation, and superconductivity on the current. Exchange coupling typically suppresses the Kondo correlation so that the system undergoes a phase transition from 0 to $\pi$ state as the modulus of exchange coupling increases. Antiferromagnetic coupling is found to drive exotic transitions: the reentrance to the $\pi$ state for a small superconducting gap and the restoration of 0 state for large antiferromagnetic exchange coupling. We suggest that the asymmetric dependence of supercurrent on the exchange coupling could be used as to detect its sign in experiments

Nanomechanical effects in an Andreev quantum dot

We consider a quantum dot with mechanical degrees of freedom which is coupled to superconducting electrodes. A Josephson current is generated by applying a phase difference. In the absence of coupling to vibrations, this setup was previously proposed as a detector of magnetic flux and we wish here to address the effect of the phonon coupling to this detection scheme. We compute the charge on the quantum dot and determine its dependence on the phase difference in the presence of phonon coupling and Coulomb interaction. This allows to identify regions in parameter space with the highest charge to phase sensitivity, which are relevant for flux detection. Further insight about the interplay of such couplings and subsequent entanglement properties between electron and phonon degrees of freedom are gained by computing the von Neuman entropy.Comment: 9 pages, 7 figures; minor corretion

Quantum phase transition of dynamical resistance in a mesoscopic capacitor

We study theoretically dynamic response of a mesoscopic capacitor, which consists of a quantum dot connected to an electron reservoir via a point contact and capacitively coupled to a gate voltage. A quantum Hall edge state with a filling factor nu is realized in a strong magnetic field applied perpendicular to the two-dimensional electron gas. We discuss a noise-driven quantum phase transition of the transport property of the edge state by taking into account an ohmic bath connected to the gate voltage. Without the noise, the charge relaxation for nu>1/2 is universally quantized at R_q=h/(2e^2), while for nu<1/2, the system undergoes the Kosterlitz-Thouless transtion, which drastically changes the nature of the dynamical resistance. The phase transition is facilitated by the noisy gate voltage, and we see that it can occur even for an integer quantum Hall edge at nu=1. When the dissipation by the noise is sufficiently small, the quantized value of R_q is shifted by the bath impedance.Comment: 5 pages, 2 figures, proceeding of the 19th International Conference on the Application of High Magnetic Fields in Semiconductor Physics and Nanotechnology (HMF-19

Andreev quantum dot with several conducting channels

We study an Andreev quantum dot, that is a quantum dot inserted in a superconducting ring, with several levels or conducting channels. We analyze the degeneracy of the ground state as a function of the phase difference and of the gate voltage and find its dependence on the Coulomb interaction within and between channels. We compute a (non integer) charge of the dot region and Josephson current. The charge-to-phase and current-to-gate voltage sensitivities are studied. We find that, even in the presence of Coulomb interaction between the channels, the sensitivity increases with the number of channels, although it does not scale linearly as in the case with no interactions. The Andreev quantum dot may therefore be used as a sensitive detector of magnetic flux or as a Josephson transistor.Comment: 13 pages, 10 figures, minor correction