6π Josephson Effect in Majorana Box Devices

Fermi-Liquid Approach for Superconducting Kondo Problems

We present a Fermi liquid approach to superconducting Kondo problems applicable when the Kondo temperature is large compared to the superconducting gap. To illustrate the theory, we study the current-phase relation and the Andreev level spectrum for an Anderson impurity between two s-wave superconductors. In the particle-hole symmetric Kondo limit, we find a 4π periodic Andreev spectrum. The 4π periodicity persists under a small voltage bias which however causes an asymmetric distortion of Andreev levels. The latter distinguishes the present 4π effect from the one in topological Majorana junctions.

Exact Nonequilibrium Transport in the Topological Kondo Effect

A leading candidate for the experimental confirmation of the nonlocal quantum dynamics of Majorana fermions is the topological Kondo effect, predicted for mesoscopic superconducting islands connected to metallic leads. We identify an anisotropic, Toulouse-like, limit of the topological Kondo problem where the full nonequilibrium conductance and shot noise can be calculated exactly. Near the Kondo fixed point, we find novel asymptotic features including a universal conductance scaling function and fractional charge quantization observable via the Fano factor. In the universal regime, our results apply for generic anisotropy and even away from the Kondo limit as long as the system supports an emergent topological Kondo fixed point. Our approach thus provides key new qualitative insights and exact expressions for quantitative comparisons to future experimental data.

Non-Fermi-liquid behavior in quantum impurity models with superconducting channels

We study how the non-Fermi-liquid nature of the overscreened multi-channel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap Δ. We find that the low-energy spectrum in the limit Δ → 0 actually does not correspond to the spectrum strictly at Δ = 0. In particular, in the two-channel Kondo model the Δ → 0 ground state is an orbitally degenerate spin-singlet, while it is an orbital singlet with a residual spin degeneracy at Δ = 0. In addition, there are fractionalized spin-1/2 sub-gap excitations whose energy in units of Δ tends towards a finite and universal value when Δ → 0; as if the universality of the anomalous power-law exponents that characterise the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by Δ ≠ 0. This intriguing phenomenon can be explained by the renormalisation flow towards the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi liquid features at finite Δ: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a non-monotonic function of temperature. The persistent sub-gap excitations are characteristic of the non-Fermi-liquid fixed-point of the model, and thus depend on the impurity spin and the number of screening channels.