Crossover of h/e and h/2e oscillations in chiral edge-channel Josephson junctions

Recently, several experiments reported that the magnetic field interference pattern of the quantum hall edge states mediated Josephson junctions can exhibit Fraunhofer oscillations with a periodicity of either h/e or h/2e. However, a unified understanding of such a phenomenon is still absent. In this work, we show that the competition between crossed Andreev reflections and local Andreev reflections results in the crossover between h/e and h/2e quantum oscillations in chiral edge-channel Josephson junctions. Our theory explains why recent experiments observed either h/e or h/2e oscillations in different samples. Furthermore, we predict a thermal-driven h/e to h/2e Fraunhofer oscillations crossover.