Interplay of Andreev physics and quantum Hall effect in graphene

The interplay of Andreev physics and the quantum Hall effect has recently attracted a lot of interest and gained experimental relevance. A quantizing out-of-plane magnetic field in the normal region (N) leads to propagating states confined along the interface with the superconducting region (S). If N is a normal metal, there are magnetoconductance oscillations that can be understood as a result of an interference between the two interface states with wave vectors ±k, where k≈π/2l_c and l_c=2\hbar k/eB can be semiclassically interpreted as a cyclotron diameter. When N is graphene which is characterized by a Dirac dispersion, the conductance was found to be independent of the magnetic field [1]. This is confirmed in our numerical simulations in a certain range of parameters. Outside this range we find magnetoconductance oscillations if the pair potential Δ is larger than the Fermi energy E_F (measured from the Dirac point) and (or) the penetration depth of the magnetic field λ_B is larger than the graphene lattice constant a.

[1] A. R. Akhmerov and C. W. J. Beenakker, Phys. Rev. Lett. 98, 157003 (2007)