Correspondence between Andreev reflection and Klein tunneling in bipolar graphene

TL;DR

This paper reveals a fundamental connection between Andreev reflection in superconductors and Klein tunneling in graphene, showing they share identical energy spectra under certain conditions, leading to novel zero-density states and pseudo-superconducting phenomena.

Contribution

It establishes a theoretical correspondence between Andreev reflection and Klein tunneling, predicting new equilibrium states and extending the concept to other band-structure systems.

Findings

Identical energy spectra for Andreev reflection and Klein tunneling at low energies.

Bipolar graphene junctions can have zero density of states at the Fermi level.

Potential for pseudo-superconducting behavior in non-electronic systems with similar band structures.

Abstract

Andreev reflection at a superconductor and Klein tunneling through an n-p junction in graphene are two processes that couple electrons to holes -- the former through the superconducting pair potential Delta and the latter through the electrostatic potential U. We derive that the energy spectra in the two systems are identical, at low energies E<<Delta and for an antisymmetric potential profile U(-x,y)=-U(x,y). This correspondence implies that bipolar junctions in graphene may have zero density of states at the Fermi level and carry a current in equilibrium, analogously to superconducting Josephson junctions. It also implies that nonelectronic systems with the same band structure as graphene, such as honeycomb-lattice photonic crystals, can exhibit pseudo-superconducting behavior.