Effect of Virtual Andreev Reflection on Tunneling in Normal/Superconductor Graphene Junction

Abstract

The Andreev reflection (AR) process and the tunneling conductance in graphene-based normal metal/superconductor junction are studied, where both massless and massive fermions are considered. As a result, the evanescent type of AR or the virtual Andreev reflection (VAR), is found to take place at the interface above the critical angle or in case where AR decays due to massive energy gap. Significantly, current of the junction is found to exist in the evanescent AR regime. In this work, we modify tunneling conductance formalism by including the current induced by the evanescent type of AR process (or VAR), which has not been taken into account in previous studies. In contrast to the previous work, our formula leads to a new result due to the influence of the VAR when the energy of the quasiparticles greater than the superconducting gap.

Tunneling conductance of the s-wave and d-wave pairing superconductive graphene–normal graphene junction

“…and FS v the dependence of conductivity on the excitation energy of quasiparticles in the above energy range 0 S E < < ∆ takes place. This result is qualitatively different from that obtained in papers [13][14][15][16][17][18][19][20][21][22][23] and it shows that the value of the conductivity of the system under investigation depends on energy E throughout its whole range.…”

“…As follows from references [2,3,[5][6][7][8][9][10] the magnitude of the Fermi velocity may vary approximately up to 4 in relation to this value in the pristine graphene. Curve 1 shows that the calculations of our work are in agreement with the results of the previous studies [13][14][15][16][17][18][19][20][21][22][23] according to which conductivity * G is not dependent on energy E in the range where it does not exceed the size of the superconducting gap. However, we see that in the case of different values of the Fermi velocity…”

“…(The analogous to (1)- (5) formulae have been widely used in literature, e.g., in the papers [13][14][15][16][17][18][19][20][21][22][23]). The coefficients in (3), (4) can be found by applying the following appropriate boundary conditions on the eigenfunctions…”

“…At the same time the pristine graphene can also be induced by the external forces to become the superconducting material, for example, super-conductivity can be induced in a graphene layer in the presence of a superconducting electrode near it due to the proximity effect. That's why a lot of works were devoted to exploring of the properties of such structures as the superconductive graphene, graphene-superconductive graphene, graphene-insulator-superconductive graphene, graphenebased Josephson junctions [13][14][15][16][17][18][19][20][21][22][23][24][25]. However, the effect of tuning of the Fermi velocity on the characteristics of these contacts has not been investigated so far.…”