Josephson effect in mesoscopic graphene strips with finite width

TL;DR

This paper investigates how the Josephson supercurrent in ballistic graphene strips varies with width and edge type, revealing distinct behaviors for smooth, armchair, and zigzag edges, including quantization effects.

Contribution

It provides a detailed analysis of the dependence of critical supercurrent on edge type and width in mesoscopic graphene, highlighting novel quantization phenomena and edge-specific behaviors.

Findings

Supercurrent decreases monotonically with width for smooth and armchair edges.

Zigzag edges exhibit half-integer quantization of supercurrent.

Critical current shows peaks at higher carrier concentrations depending on width.

Abstract

We study Josephson effect in a ballistic graphene strip of length $L$ smaller than the superconducting coherence length and arbitrary width $W$. We find that the dependence of the critical supercurrent $I_{c}$ on $W$ is drastically different for different types of the edges. For \textit{smooth} and \textit{armchair} edges at low concentration of the carriers $I_{c}$ decreases monotonically with decreasing $W/L$ and tends to a constant minimum for a narrow strip $W/L\lesssim1$. The minimum supercurrent is zero for smooth edges but has a finite value $e\Delta_{0}/\hbar$ for the armchair edges. At higher concentration of the carriers, in addition to this overall monotonic variation, the critical current undergoes a series of peaks with varying $W$. On the other hand in a strip with \textit{zigzag} edges the supercurrent is half-integer quantized to $(n+1/2)4e\Delta_{0}/\hbar$, showing a step-wise variation with $W$.