Reentrance effect in a graphene $n\text{−}p\text{−}n$ junction coupled to a superconductor

We study the interplay of Klein tunneling ($=\text{interband}$ tunneling) between $n$-doped and $p$-doped regions in graphene and Andreev reflection ($=\text{electron}$-hole conversion) at a superconducting electrode. The tunneling conductance of an $n\text{−}p\text{−}n$ junction initially increases upon lowering the temperature, while the coherence time of the electron-hole pairs is still less than their lifetime, but then drops back again when the coherence time exceeds the lifetime. This reentrance effect, known from diffusive conductors and ballistic quantum dots, provides a method to detect phase coherent Klein tunneling of electron-hole pairs.

Figure 1

Top panel: Graphene layer connected to one normal metal electrode and one superconducting electrode. A bottom and top gate control the electrostatic doping, so that the graphene regions covered by the electrodes are $n$-type and the central region is $p$-type. Bottom panel: electrostatic potential profile across the $n\text{−}p\text{−}n$ junction. The Fermi level (at $E_F=0$) lies in the conduction band in the two $n$-regions, while it lies in the valence band in the $p$-region.

Figure 2

Differential conductance normalized to its normal-state value as a function of the applied voltage, for three values of the ratio $G_{p\text{−}n}^S∕G_{p\text{−}n}^N$ (with $G_{p\text{−}n}^S$ the tunnel conductance of the $p\text{−}n$ junction closest to the superconductor and $G_{p\text{−}n}^N$ the tunnel conductance of the other interface). The normal-state conductance $G_0$ is the series conductance defined by $1∕G_0=1∕G_{p\text{−}n}^N+1∕G_{p\text{−}n}^S$.

Figure 3

Same as Fig. 2, but now for the linear response conductance as a function of temperature.