Graphene based superconducting quantum point contacts

TL;DR

This paper studies the Josephson effect in graphene nanoribbons, revealing unique behaviors in supercurrent quantization and dependence on edge types and carrier concentration, differing from ordinary superconducting quantum point contacts.

Contribution

It provides a detailed analysis of supercurrent behavior in graphene nanoribbons with various edge types, highlighting novel quantization and dependence on geometric and electronic parameters.

Findings

Supercurrent $I_c$ is not quantized in smooth and armchair edges.

$I_c$ decreases with $W/L$ at low carrier concentration, approaching a minimum.

Zigzag nanoribbons exhibit half-integer quantization of $I_c$.

Abstract

We investigate the Josephson effect in the graphene nanoribbons of length $L$ smaller than the superconducting coherence length and an arbitrary width $W$. We find that in contrast to an ordinary superconducting quantum point contact (SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers $I_c$ decreases monotonically with lowering $W/L$ and tends to a constant minimum for a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the smooth edges but $e\Delta_{0}/\hbar$ for the armchair edges. At higher concentrations of the carriers this monotonic variation acquires a series of peaks. Further analysis of the current-phase relation and the Josephson coupling strength $I_cR_N$ in terms of $W/L$ and the concentration of carriers revels significant differences with those of an ordinary SQPC. On the other hand for a zigzag nanoribbon we find that, similar to an ordinary SQPC, $I_c$ is quantized but to the half-integer values $(n+1/2)4e\Delta_{0}/\hbar$.