Cross-over from retro to specular Andreev reflections in bilayer graphene

TL;DR

This paper theoretically investigates the transition from retro to specular Andreev reflections in bilayer graphene/superconductor interfaces, revealing conductance signatures of this crossover influenced by interface potential steps.

Contribution

It provides analytical expressions for differential conductance during the crossover from intra-band to inter-band Andreev reflections in bilayer graphene.

Findings

Conductance dips occur when excitation energy is below the superconducting gap.

The sharpness of conductance features depends on the interface potential step.

A characteristic signature of the retro to specular transition is identified.

Abstract

Ongoing experimental progress in the preparation of ultra-clean graphene/superconductor (SC) interfaces enabled the recent observation of specular interband Andreev reflections (AR) at bilayer graphene (BLG)/NbSe$_{2}$ van der Waals interfaces [Nature Physics 12, (2016)]. Motivated by this experiment we theoretically study the differential conductance across a BLG/SC interface at the continuous transition from high to ultra-low Fermi energies $E_{F}$ in BLG. Using the Bogoliubov-deGennes equations and the Blonder-Tinkham-Klapwijk formalism we derive analytical expressions for the differential conductance across the BLG/SC interface. We find a characteristic signature of the cross-over from intra-band retro- (high $E_{F}$) to inter-band specular (low $E_{F}$) ARs, that manifests itself in a strongly suppressed interfacial conductance when the excitation energy $|\varepsilon |=|E_{F}|<\Delta $ (the SC gap). The sharpness of these conductance dips is strongly dependent on the size of the potential step at the BLG/SC interface $U_{0}$.