Magnetotransport in graphene nanoribbons sandwiched by superconductors at side edges

Magnetotransport properties of the graphene nanoribbons (GNR) that are in contact with superconductors at side edges are investigated numerically with respect to oscillations caused by the cyclotron motion. In terms of the modelling, the superconductors are incorporated as superconducting GNRs to make the Andreev reflection at the graphene-superconductor interface almost perfect. The classical commensurability oscillation appears at low magnetic fields where the cyclotron radius is larger than the width of the nanoribbons. A transition to the circumstance dominated by the quantum interference between Andreev- and normal-reflected components takes place when the Andreev reflection probability is reduced by introducing a barrier at the interface. The near perfection of the Andreev reflection enlarges the period of the oscillation associated with skipping orbits a few orders of magnitude in the quantum limit. Chaotic fluctuations emerge furthermore in the regime of Hofstadter's butterfly. The periodicity of a transmission modulation at the onset of the chaos is revealed to change continuously over eight orders of magnitude of the magnetic-field variation. The commensurability and edge-state oscillations are examined additionally for the situations with specular Andreev reflection.

Automated summary

The study focuses on the magnetotransport properties of graphene nanoribbons in contact with superconductors, showing that nearly perfect Andreev reflection results in significant increases in the period of oscillations induced by cyclotron motion. Additionally, chaotic fluctuations are observed in the regime of Hofstadter's butterfly, with transmission modulation periodicity changing continuously over eight orders of magnitude of magnetic-field variation. Commensurability and edge-state oscillations are also examined in situations with specular Andreev reflection.