Research On Andreev Reflection In The Graphene-superconductor Junction

After graphene produced successfully in the experiment,there are more and more works on the physical characters of the 2D material.One focus of the condensed matter physics is the electronic transport properties in the graphene-superconductor junction.Using the non-equilibriun Green function method,we have calculated the coefficients of Andreev reflection at the interface between the graphene and superconductor by tight-binding model.1)We study the Andreev reflection in a Y-shaped graphene-superconductor device.Considering both the zigzag and armchair terminals,we confirm that the zigzag terminals are the better choice for detecting the Andreev reflection in absence of external field.Due to scattering from the boundaries of the finite-size centre region,the difference between Andreev retroreflection and specular reflection is hard to be distinguished.Although adjusting the size of the device makes the difference visible,to distinguish them quantitatively is still impossible through the transport conductance of a three-terminal device.The problem is circumvented when applying a perpendicular magnetic field on the centre region,which makes the incident electrons and the reflected holes propagate along the edge or the interface.In this case,the retroreflected and specular reflected holes from the different bands have opposite effective mass,therefore the moving direction of one is opposite to the other.Which external terminal the reflected holes flow into depends entirely on the kind of the Andreev reflection.Therefore,the specular Andreev reflection can be clearly distinguished from the retroreflected one in the presence of strong magnetic field,even for the device with finite size.2)Using the tight binding model and the non-equilibrium Green function method,we study Andreev reflection in graphene-superconductor junction,where graphene has two nonequal Dirac Cones split in energy and therefore time reversal symmetry is broken.Due to the anti-chiral edge states of the current graphene model,an incident electron travelling along the edges makes distinct contribution to Andreev reections.In a two-terminal device,because Andreev retro-reection is not allowed for just the anti-chiral edges,in this case the mutual scattering between edge and bulk states is necessary,which leads that the coefficient of Andreev retro-reflection is always symmetrical about the incident energy.In a four-terminal junction,however,the edges are parallel to the interface of superconductor and graphene,so at the interface an incident electron travelling along the edges can be retro-reected as a hole into bulk modes,or specularly reflected as a hole into anti-chiral edge states again.It is noted that,the coefficient of specular Andreev reection keeps symmetric as to the incident energy of electron which is consistent with the reported results before,however the coefficient of Andreev retro-reflection shows an unexpected asymmetrical behavior due to the presence of anti-chiral edge states.Our results present some new ideas to study the anti-chiral edge modes and Andreev reection for a graphene model with the broken time reversal symmetry.