Andreev Reflection in a Bilayer Graphene Junction: Role of Spatial Variation of the Charge Neutrality Point

A graphene sheet partially covered with a bulk superconductor serves as a normal conductor--superconductor (NS) junction, in which electron transport is mainly governed by Andreev reflection (AR). As excess carriers induced over the covered region penetrate into the uncovered region over a screening length, the charge neutrality point (CNP) in the uncovered region shifts only near the NS interface. We theoretically study the electron transport in a bilayer graphene junction taking account of such spatial variation of the CNP in the electron-doped case. When the Fermi level is close to the CNP away from the NS interface, the AR takes place in a specular manner owing to the diffraction of a reflected hole occurring at a $pn$ junction, which is naturally formed in the uncovered region. It is shown that the differential conductance shows an unusual asymmetric behavior as a function of bias voltage under the influence of the $pn$ junction. It is also shown that, if the Fermi level is located below the CNP, the $pn$ junction gives rise to quasi-bound states near the NS interface, leading to the appearance of resonant peaks in the differential conductance.