Nonmonotonic Behavior of Resistance in a Superconductor–Luttinger Liquid Junction

Transport through a superconductor–Luttinger liquid junction is considered. When the interaction in the Luttinger liquid is repulsive, the resistance of the junction with a sufficiently clean interface shows nonmonotonic temperature or voltage dependence due to the competition between the superconductivity and the repulsive interaction. The result is discussed in connection with recent experiments on single-wall carbon nanotubes in contact with superconducting leads.

Figure 1

A schematic diagram of the resistance $R$ as a function of the temperature $T$. Curve $A$ shows $R(T)$ for an ideal interface ($U_0=0$). Curves $B$, $C$, and $D$ describe progressively less ideal interfaces, and curve $E$ shows $R(T)$ for large $U_0$. In curves $B$ and $C$, $R(T)$ below $T_c$ is nonmonotonic due to the competition between the superconductivity and the repulsive interaction. The black squares in curves $B$ and $C$ denote the crossover temperature $T_{\mathrm{c}\mathrm{r}}$. Inset: Monte Carlo result for the action (7) with $K_{\mathrm{c}}=0.25$, $U_0=0$.

Figure 2

A schematic drawing of the $dV/dI–V$ characteristic for an almost ideal interface. Curve 10 is for $T\approx T_{\mathrm{c}}$, curves 9, 8, . . ., 1 for progressively lower $T$, and curve 0 for $T=0$. Curves are vertically shifted for clarity. Without the shift, all curves should almost collapse over each other near $eV=\Delta$. When $T$ is below the crossover temperature $T_{\mathrm{c}\mathrm{r}}$ (temperature for curve 5), $dV/dI$ becomes nonmonotonic in $V$ due to the competition between the superconductivity and the repulsive interaction. The black squares in curves 0–5 denote the crossover voltage $V_{\mathrm{c}\mathrm{r}}(T)$.