Transparent Graphene-Superconductor Interfaces: Quantum Hall and Zero Field Regimes

TL;DR

This paper investigates graphene/superconductor interfaces in quantum Hall and zero field regimes, revealing strong Andreev reflection and electron-hole hybridization that are robust across various parameters, with implications for quantum transport.

Contribution

It demonstrates that graphene's unique electronic properties enable strong Andreev reflection and electron-hole hybridization at superconductor interfaces without fine-tuning, even in quantum Hall regimes.

Findings

Strong Andreev reflection exceeds that in semiconductor 2DEG interfaces.

Electron-hole hybridization is independent of graphene filling.

Valley degeneracy and antisymmetric dispersion of chiral Andreev edge modes.

Abstract

We study clean, edge-contacted graphene/superconductor interfaces in both the quantum Hall (QH) and zero field regimes. We find that Andreev reflection is substantially stronger than at an interface with a semiconductor two-dimensional electron gas: the large velocity at graphene's conical Dirac points makes the requirement of current continuity to a metal much less restrictive. In both our tight-binding and continuum models, we find a wide range of parameters for which Andreev reflection is strong. For a transparent interface, we demonstrate the following for graphene in the lowest Landau level QH state: (i) Excellent electron-hole hybridization occurs: the electron and hole components in graphene are simply related by an exchange of sublattice. The spatial profile for the electron component is predominantly gaussian on one sublattice and peaked at the interface, and so very different from the QH edge state of a terminated lattice. (ii) The degree of hybridization is independent of the graphene filling: no fine-tuning is needed. (iii) The spectrum is valley degenerate: the dispersion of each chiral Andreev edge mode (CAEM) self-aligns to be antisymmetric about the center of each valley, independent of filling. Achieving a transparent interface requires the absence of any barrier as well as a superconductor that is suitably matched to graphene; we argue that the latter condition is not very stringent. We further consider the effect of reduced transparency and Zeeman splitting on both the wavefunctions of the CAEM and their dispersion.