Signatures of time-reversal-invariant topological superconductivity in the Josephson effect

Abstract

For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide analogous relations for Josephson junctions involving one-dimensional time-reversal invariant topological superconductors supporting Majorana-Kramers pairs, considering both topological-topological and s-wave-topological junctions. Working in the regime where the junction is much shorter than the superconducting coherence length, we obtain a number of analytical and numerical results that hold for arbitrary normal-state conductance and the most general forms of spin-orbit coupling. The signatures of topological superconductivity we find include the fractional AC Josephson effect, which arises in topological-topological junctions provided that the energy relaxation is sufficiently slow. We also show, for both junction types, that robust signatures of topological superconductivity arise in the DC Josephson effect in the form of switches in the Josephson current due to zero-energy crossings of Andreev levels. The junction spinorbit coupling enters the Josephson current only in the topological-topological case and in a manner determined by the switch locations, thereby allowing quantitative predictions for experiments with the normal-state conductance, the induced gaps, and the switch locations as inputs.

Fragility of the Fractional Josephson Effect in Time-Reversal-Invariant Topological Superconductors

“…Here we show that, when the superconducting phase winds adiabatically, local mixing indeed spoils the fractional Josephson effect and yields either an aperiodic or 2π-periodic current-phase relation depending on localmixing timescales. This result holds even in an otherwise ideal situation for which effects known previously to destroy 4π periodicity [17,49,51,[58][59][60][61][62][63]]-e.g., explicit T breaking, overlap between distant MZMs, energy relaxation, and quasiparticle poisoning-are absent. By mapping the problem onto an effective model that features avoided crossings in the energy spectrum, we further demonstrate that 4π periodicity is recovered when the phase difference evolves sufficiently quickly that local mixing remains benign.…”

“…On one hand, in a TRITOPS Josephson junction that preserves T at phase differences 0 and π, each subgap level is certainly 4π periodic (Fig. 1), suggesting that a fractional Josephson effect appears as predicted in numerous works [26,29,30,43,[49][50][51][52][53][54][55][56][57]. But on the other, the braiding and fractional Josephson connection noted earlier naively implies that nonuniversality of the former spells doom for the latter.…”

Catalog of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires

“…For TRITOPS-S junctions, we find an abrupt discontinuity with a jump of the Josephson current at φ = 0 as in previous works, as well as a strong component with periodicity of half the superconducting flux quantum. 28,32,36 These features are, however, modified in wires of finite length due to the hybridization of the zero modes. For both cases, we find a quench of the 0 − π transition in the presence of an interacting quantum dot in the junction.…”

Floquet Majorana fermions and parafermions in driven Rashba nanowires

“…Under this symmetry transformation U T we find R ησ → (ησ)L ησ and L ησ → (ησ)R ησ , and thus U † T H * (−k)U T = H(k). We note that, in contrast to Kramers pairs protected by the time-reversal symmetry [87][88][89][90][91][92][93][94][95][96][97][98][99], the degeneracy of the pair can be lifted by disorder [100,101]. Thus, these states are similar to fractional fermions, which similar to MFs possess non-Abelian statistics [102] and can be used for quantum computing schemes.…”