Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

Current-phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case that the junction length is finite and magnetic impurity exists. The similarity and difference with conventional Josephson junction is discussed. The current is calculated in the semiconductor picture. Both the $2\pi$- and $4\pi$-period current-phase relations ($I_{2\pi}(\phi), I_{4\pi}(\phi)$) are studied. There is a sharp jump at $\phi=\pi$ and $\phi=2\pi$ for $I_{2\pi}$ and $I_{4\pi}$ respectively in the clean junction. For $I_{2\pi}$, the sharp jump is robust against impurity strength and distribution. However for $I_{4\pi}$, the impurity makes the jump at $\phi=2\pi$ smooth. The critical (maximum) current of $I_{2\pi}$ is given and we find it will be increased by asymmetrical distribution of impurity.Comment: 7 pages, 5 figure

Bipolaronic blockade effect in quantum dots with negative charging energy

We investigate single-electron transport through quantum dots with negative charging energy induced by a polaronic energy shift. For weak dot-lead tunnel couplings, we demonstrate a bipolaronic blockade effect at low biases which suppresses the oscillating linear conductance, while the conductance resonances under large biases are enhanced. Novel conductance plateau develops when the coupling asymmetry is introduced, with its height and width tuned by the coupling strength and external magnetic field. It is further shown that the amplitude ratio of magnetic-split conductance peaks changes from 3 to 1for increasing coupling asymmetry. Though we demonstrate all these transport phenomena in the low-order single-electron tunneling regime, they are already strikingly different from the usual Coulomb blockade physics and are easy to observe experimentally.Comment: 6 pages, 5 figure

Disorder effect of resonant spin Hall effect in a tilted magnetic field

We study the disorder effect of resonant spin Hall effect in a two-dimension electron system with Rashba coupling in the presence of a tilted magnetic field. The competition between the Rashba coupling and the Zeeman coupling leads to the energy crossing of the Landau levels, which gives rise to the resonant spin Hall effect. Utilizing the Streda's formula within the self-consistent Born approximation, we find that the impurity scattering broadens the energy levels, and the resonant spin Hall conductance exhibits a double peak around the resonant point, which is recovered in an applied titled magnetic field.Comment: 6 pages, 4 figure