Low-temperature transport through a quantum dot between two superconductor leads

By means of infinite-$U$ noncrossing approximation we investigate the transport properties of a quantum dot coupled to two BCS superconductors. The nonequilibrium density of states and differential conductance are carried out in the regime where gap energy $\Delta$ is much larger than the Kondo temperature $T_K$. In the equilibrium density of states two sharp peaks around the gap bounds are observed. Application of a finite voltage bias leads these peaks to split, leaving suppressed peaks near the edges of energy gap of each lead. Further, in the nonlinear differential conductance there are three peaks, one around zero bias, another two at biases $\pm 2\Delta$. With decreasing temperature, the differential conductances at biases $\pm 2\Delta$ anomalously increase, while the linear conductance descends.

Figure 1

The equilibrium density of states for a quantum dot coupled to two superconducting leads at several temperatures: $T=10T_K$, $5T_K$, and $4T_K$. The inset shows a blowup of the region around $\omega =-\Delta$.

Figure 2

The nonequilibrium density of states for a quantum dot between two superconducting leads. Several biases are applied, $eV∕2=0$, $\Delta ∕3$, and $\Delta$. The temperature is $T=4T_K$. The inset shows a blowup of the region around $\omega =-\Delta$.

Figure 3

The voltage dependence of differential conductance for a quantum dot connected with two superconductors. The inset shows a blowup of the region around zero bias.