Driven Dissipative Majorana Dark Spaces.

Pure quantum states can be stabilized in open quantum systems subject to external driving forces and dissipation by environmental modes. We show that driven dissipative (DD) Majorana devices offer key advantages for stabilizing degenerate state manifolds ("dark spaces") and for manipulating states in dark spaces, both with respect to native (non-DD) Majorana devices and to DD platforms with topologically trivial building blocks. For two tunnel-coupled Majorana boxes, using otherwise only standard hardware elements (e.g., a noisy electromagnetic environment and quantum dots with driven tunnel links), we propose a dark qubit encoding. We anticipate exceptionally high fault tolerance levels due to a conspiracy of DD-based autonomous error correction and topology.

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.

Josephson effect in junctions of conventional and topological superconductors.

We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green's function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S-TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S-QD-TS setup can support φ0-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S-TS-S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.

Non-Fermi-liquid manifold in a Majorana device.

We propose and study a setup realizing a stable manifold of non-Fermi-liquid states. The device consists of a mesoscopic superconducting island hosting N≥3 Majorana bound states tunnel coupled to normal leads, with a Josephson contact to a bulk superconductor. We find a nontrivial interplay between multichannel Kondo and resonant Andreev reflection processes, which results in the fixed point manifold. The scaling dimension of the leading irrelevant perturbation changes continuously within the manifold and determines the power-law scaling of the temperature-dependent conductance.