# Andreev reflection in graphene-superconductor junction

Pushpendra Kumar

Center For Basic Sciences Raipur, Amanaka, Raipur, Chhattisgarh 492010

Dr. Sourin Das

Indian Institute of Science Education and Research Kolkata, Mohanpur, West Bengal 741264

## Abstract

Andreev reflection is the type of scattering process of electron-hole conversion at the interface of metal and superconductor junction. The charge is not conserved but momentum is conserved in this mechanism. The electron incident from metal sides with some momentum and get reflect as positively charged hole with same momentum but opposite velocity. In normal reflection, where the electron incidents at insulator surface, this process charge is conserved but momentum is not conserved. The conservation of momentum is an approximation, valid if excitation gap ∆ is much smaller then the Fermi energy ΕF of the normal metal. The missing 2${e}^{-}$enters as a Cooper pairs and flows as supercurrent inside the superconductor. This electron-hole conversion process is determined by solving through Bogoliubov-De-Geenes equation and the probability of electron-hole conversion is calculated by solving the reflection matrices. For that, we seperately calculated the BDG equation for both region of interface and analysed the electron-hole conversion at the interface.

Keywords: excitation gap, Fermi energy, BDG equation

abbreviations
 BDG Bogoliubov -de-Geenes ${e}^{-}$ electron charge U electrostatic potential ${E}_{F}$ Fermi energy $∆$ Pair potential ε excitation energy ħ Planck's constant/2π

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