Challenges in detecting topological superconducting transitions via supercurrent and phase probes in planar Josephson junctions

Abstract

Topological superconductors harbor, at their boundaries and vortex cores, zero-energy Majorana bound states, which can be the building blocks in fault-tolerant topological quantum computing. Planar Josephson junctions host such topological superconducting phases, highly tunable by external magnetic field or phase difference between the superconducting leads. Despite many theoretical and experimental studies, the signatures of the transition to a topological superconducting phase, based on minima in the critical supercurrent $I_c$ flowing across the junction, $0$-$\pi$ transition in the ground state junction phase and their anisotropic magnetic-field response have remained unsettled. Using rigorous numerical calculations with several experimentally-relevant parameter settings, we show that $I_c$ and ${\phi }_{{}_{\mathrm{GS}}}$ cannot indicate unambiguously topological transition in any realistic planar junctions. Furthermore, the anisotropic variations of $I_c$ and ${\phi }_{{}_{\mathrm{GS}}}$ with in-plane magnetic field appear in junctions that are undoubtedly in trivial superconducting phase, raising concerns on the effectiveness of these probes in identifying topological transitions in planar junctions. We discuss possible strategies to confirm a topological superconducting phase in these platforms.

References in corpus (18)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Scaling of Majorana Zero-Bias Conductance Peaks
• Transport spectroscopy of NS nanowire junctions with Majorana fermions
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum
• To close or not to close: the fate of the superconducting gap across the topological quantum phase transition in Majorana-carrying semiconductor nanowires
• Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling
• Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit
• Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions
• Detecting topological superconductivity using low-frequency doubled Shapiro steps
• ${\mathbb{Z}}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin
• Out of Equilibrium Majoranas in Interacting Kitaev Chains

Cited by in corpus (4)

• Progress in superconductor-semiconductor topological Josephson junctions
• Multiple Majorana bound states and their resilience against disorder in planar Josephson junctions
• Magnetic field-free braiding and nontrivial fusion of Majorana bound states in high-temperature planar Josephson junctions
• Diode effect in a skyrmion-coupled high-temperature Josephson junction