Even-odd flux quanta effect in the Fraunhofer oscillations of an edge-channel Josephson junction

Abstract

We calculate the beating of $h/2e$ and $h/e$ periodic oscillations of the flux-dependent critical supercurrent $I_c(\Phi )$ through a quantum spin-Hall insulator between two superconducting electrodes. A conducting pathway along the superconductor connects the helical edge channels via a non-helical channel, allowing an electron incident on the superconductor along one edge to be Andreev reflected along the opposite edge. In the limit of small Andreev reflection probability the resulting even-odd effect is described by $I_c\propto |\cos (e\Phi /\hslash )+f|$, with $|f|\ll 1$ proportional to the probability for phase-coherent inter-edge transmission. Because the sign of $f$ depends on microscopic details, a sample-dependent inversion of the alternation of large and small peaks is a distinctive feature of the beating mechanism for the even-odd effect.

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• Thermoelectric transport in junctions of Majorana and Dirac channels
• A Topological SQUIPT based on helical edge states in proximity to superconductors
• Superconducting Quantum Interference in Edge State Josephson Junctions
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• Majorana fermions on the quantum Hall edge
• Supercurrent Reversal in Two-Dimensional Topological Insulators
• Majorana bound states in topological insulators with hidden Dirac points
• Reconstruction-Induced ${\phi }_0$ Josephson Effect in Quantum Spin Hall Constrictions
• Supercurrent mediated by helical edge modes in bilayer graphene
• Anomalous $h/2e$ periodicity and Majorana zero modes in chiral Josephson junctions
• Fraunhofer pattern in the presence of Majorana zero modes
• Effects of the Spatial Extension of the Edge Channels on the Interference Pattern of a Helical Josephson Junction
• Edge supercurrent in Josephson junctions based on topological materials
• Spin-resolved spectroscopy of helical Andreev bound states
• Josephson junction of minimally twisted bilayer graphene
• Anomalous flux periodicity in proximitised quantum spin Hall constrictions
• Interedge backscattering in time-reversal symmetric quantum spin Hall Josephson junctions