Wave packet scattering at a normal-superconductor interface in two-dimensional materials: a generalized theoretical approach
12 December 2019
UAntwerp, Campus Groenenborger, G.U.241 - Groenenborgerlaan 171 - 2020 Antwerpen (route: UAntwerpen, Campus Groenenborger
4:00 PM - 5:00 PM
Organization / co-organization:
Condensed Matter Theory
CMT Lecture presented by Prof Andrey Chaves from Universidade Federal do Ceara, Brazil
It is widely known that electron states convert to holes after being reflected by a normal - superconductor interface, in an effect known as Andreev reflection. If the system consists of a semiconductor material, the hole component of the reflected wave function travels back in a trajectory that is parallel to that of the incident electron, which is then coined the term retro-reflection. However, it has been demonstrated that in monolayer graphene, where low energy electrons behave as massless Dirac fermions, the energy dispersion is so that the reflected hole travels parallel to the reflected electron, thus undergoing a specular Andreev reflection. Theoretical models describing specular and retro-reflection are usually based on analytical calculations only for one dimensional potentials and for specific system dispersions.
In this work, I will present a wave packet time evolution method suitable to investigate the scattering of quasi-particles by a normal-superconductor interface with arbitrary profile and shape. As a practical application, we consider a system where low energy electrons can be described as Dirac particles, but the method is easily adapted for other cases such as electrons in phosphorene, or any Schroedinger quasi-particles within the effective mass approximation. Particularly, we use the method to revisit Andreev reflection in graphene, where specular and retro reflection cases are naturally observed for an uniform step-like superconducting gap. The effect of opening a zero-gap channel across the superconducting region on the electron and hole scattering is also addressed, as an example of the versatility of the technique proposed here.
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