Chiral Electron-Hole Hybrid Edge Modes from the Lowest Landau Level of Proximitized Graphene*

We study a tight-binding model of a graphene nanoribbon in the integer quantum Hall state with one edge coupled to an s-wave superconductor. Along the superconducting edge at high field, we find two gapless electron-hole hybrid modes related by particle-hole symmetry. These modes have nearly equal electron and hole content and propagate more slowly than the corresponding pure vacuum-quantum Hall edge modes. The momentum difference between these modes leads to accumulation of a relative phase between them. This phase is tunable via gate voltage, magnetic field, or applied bias. We show that such phase variation gives rise to oscillations of the longitudinal resistance between electron-like and hole-like transport similar to those measured recently by Zhao et al. [1]. Armchair and zigzag nanoribbons lead to similar results because the valley degeneracy is broken by the superconductor.

[1] L. Zhao, E. G. Arnault, A. Bondarev, A. Seredinski, T. Larson, A. W. Draelos, H. Li, K. Watanabe, T. Taniguchi, F. Amet, H. U. Baranger, G. Finkelstein; "Interference of Chiral Andreev Edge States"; arXiv:1907.01722.