Josephson junctions made of conventional superconductors display Fraunhofer-like oscillations of the critical current as a function of the threaded magnetic flux. When the superconductors are deposited on the surface of a three-dimensional topological insulator, this pattern is slightly modified due to the presence of chiral Majorana modes. Here we calculate the critical current of a Corbino Josephson junction, where the fluxoid becomes quantized and the superconducting phase has an integer winding. We discover that circular junctions exhibit similar behavior in both topologically trivial and nontrivial scenarios, while noncircular junctions demonstrate a remarkable and qualitative distinction. Using a simple analytical model, we show that these noncircular junctions exhibit reentrant superconductivity with a period related to their number of corners and numerically we find that this period is halved in the topological case. The period halving may help establish the existence of topological superconductivity in hybrid topological insulator–superconductor junctions. We find that as long as the circular symmetry of the junction's geometry is broken, the topological junction exhibits a superconducting diode effect with unique properties: the polarity alternates with the parity of the number of fluxes independent of microscopic junction details.

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• Critical current
• Superconductivity
• Topological insulators
• Topological superconductors
• Josephson junctions