Absence of supercurrent sign reversal in a topological junction with a quantum dot

Abstract

Experimental techniques to verify Majoranas are of current interest. A prominent test is the effect of Majoranas on the Josephson current between two wires linked via a normal junction. Here, we study the case of a quantum dot connecting the two superconductors and the sign of the supercurrent in the trivial and topological regimes under grand-canonical equilibrium conditions, explicitly allowing for parity changes due to, e.g., quasi-particle poisoning. We find that the well-known supercurrent reversal for odd occupancy of the quantum dot (pi-junction) in the trivial case does not occur in the presence of Majoranas in the wires. However, we also find this to be a mere consequence of Majoranas being zero energy states. Therefore, the lack of supercurrent sign reversal can also be caused by trivial bound states, and is thus not a discriminating signature of Majoranas.

6 pages + 1 page appendix + 2 pages bibilography, 4 figures

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Cited by in corpus (15)

• Singlet-doublet transitions of a quantum dot Josephson junction detected in a transmon circuit
• Theory of Majorana zero modes in unconventional superconductors
• Weak measurement protocols for Majorana bound state identification
• Distinguishing trivial and topological zero energy states in long nanowire junctions
• Quantum-Dot Parity Effects in Trivial and Topological Josephson Junctions
• Parity-to-charge conversion in Majorana qubit readout
• Supercurrent reversal in ferromagnetic hybrid nanowire Josephson junctions
• Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions
• Experimental review on Majorana zero-modes in hybrid nanowires
• Robust topological superconductivity in weakly coupled nanowire-superconductor hybrid structures
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Supercurrent transport through 1$e$-periodic full-shell Coulomb islands
• Enhanced $2\pi$-periodic Aharonov-Bohm Effect as a Signature of Majorana Zero Modes Probed by Nonlocal Measurements
• Enhancement of the Kondo effect in a quantum dot formed in a full-shell nanowire
• Confinement-induced zero-bias peaks in conventional superconductor hybrids