Semi-dirac material based N-S junction

Abstract

We study the Andreev bound states and provide unique signatures of Andreev bound states using the Blonder-Tinkham-Klapwijk model for Normal-Superconductor (N-S) junction. Taking this forward, we have looked into the possibility of getting such Andreev bound states in a semi-Dirac materials-based N-S junction. This report contains the solution of such Andreev bound states in such an N-S junction obtained by solving the Bogoliubov-de-Gennes equation. We find that for the case of the ideal N-S interface if the energy of an incident electron is such that E < ∆ (where ∆ is the superconducting gap), we have a perfect Andreev reflection. But as this ratio E ∆ become greater than 1, the probability of transmission of an electron transmitting into the S region increases since there are no allowed Cooper pair states at such energy. We also studied the differential conductance of such a setup and it shows an anomaly giving a very large conductance at a certain energy. It must be mentioned that the singularity of the differential conductance at eV =∆ also appears (as expected).