Time-reversal anomaly and Josephson effect in time-reversal invariant topological superconductors

Abstract

Topological superconductors are gapped superconductors with protected Majorana surface/edge states on the boundary. In this paper, we study the Josephson coupling between time-reversal invariant topological superconductors and s-wave superconductors. The Majorana edge/surface states of time-reversal invariant topological superconductors in all physical dimensions 1, 2, 3 have a generic topological property which we named as time-reversal anomaly. Due to the time-reversal anomaly, the Josephson coupling prefers a nonzero phase difference between topological and trivial superconductors. The nontrivial Josesphon coupling leads to a current-flux relation with a half period in a SQUID geometry, and also a half period Fraunhofer effect in dimension higher than one. We also show that an in-plane magnetic field restores the ordinary Josephson coupling, as a sharp signature that the proposed effect is a consequence of the unique time-reversal property of the topological edge/surface states. Our proposal provides a general approach to experimentally verify whether a superconductor is topological or not.

6 pages, 3 figures

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• Intrinsic Time-reversal-invariant Topological Superconductivity in Thin Films of Iron-based Superconductors
• Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states
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• Quantum Computing with Majorana Kramers Pairs
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• Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires
• Dislocation Majorana zero modes in perovskite oxide 2DEG
• Friedel oscillations and Majorana zero modes in inhomogeneous superconductors
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• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
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• Topological superconducting phases and Josephson effect in curved time-reversal-invariant superconductors
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
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• Topological multiband s-wave superconductivity in coupled multifold fermions
• Topology from Triviality
• Exact analytical solution of a time-reversal-invariant topological superconducting wire
• Magnetic resonance in a singlet-triplet Josephson junction
• $(1+3)$D topological superconductors: screening and confinement in presence of external fields
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Changes of Kondo effect in the junction with DIII-class topological and $s$-wave superconductors