Bethe ansatz solution of the topological Kondo model

Conduction electrons coupled to a mesoscopic superconducting island hosting Majorana bound states have been shown to display a topological Kondo effect with robust non-Fermi liquid correlations. With $M$ bound states coupled to $M$ leads, this is an SO($M$) Kondo problem, with the asymptotic high and low energy theories known from bosonization and conformal field theory studies. Here we complement these approaches by analyzing the Bethe ansatz equations describing the exact solution of these models at all energy scales. We apply our findings to obtain nonperturbative results on the thermodynamics of $Mrightarrow M-2$ crossovers induced by tunnel couplings between adjacent Majorana bound states.

Multi-channel Kondo impurity dynamics in a Majorana device

We study the multi-channel Kondo impurity dynamics realized in a mesoscopic superconducting island connected to metallic leads. The effective impurity spin is non-locally realized by Majorana bound states and strongly coupled to lead electrons by non-Fermi liquid correlations. We explore the spin dynamics and its observable ramifications near the low-temperature fixed point. The topological protection of the system raises the perspective to observe multi-channel Kondo impurity dynamics in experimentally realistic environments.

Domain wall in a chiral p-wave superconductor: a pathway for electrical current

Superconductors with p+ip pairing symmetry are characterized by chiral edge states, but these are difficult to detect in equilibrium since the resulting magnetic field is screened by the Meissner effect. Nonequilibrium detection is hindered by the fact that the edge excitations are unpaired Majorana fermions, which cannot transport charge near the Fermi level. Here we show that the boundary between p_x+ip_y and p_x-ip_y domains forms a one-way channel for electrical charge. We derive a product rule for the domain wall conductance, which allows to cancel the effect of a tunnel barrier between metal electrodes and superconductor and provides a unique signature of topological superconductors in the chiral p-wave symmetry class.

Quantum limit of the triplet proximity effect in half-metal - superconductor junctions

We apply the scattering matrix approach to the triplet proximity effect in superconductor-half metal structures. We find that for junctions that do not mix different orbital modes, the zero bias Andreev conductance vanishes, while the zero bias Josephson current is nonzero. We illustrate this finding on a ballistic half-metal--superconductor (HS) and superconductor -- half-metal -- superconductor (SHS) junction with translation invariance along the interfaces, and on HS and SHS systems where transport through the half-metallic region takes place through a single conducting channel. Our calculations for these physically single mode setups -- single mode point contacts and chaotic quantum dots with single mode contacts -- illustrate the main strength of the scattering matrix approach: it allows for studying systems in the quantum mechanical limit, which is inaccessible for quasiclassical Greens function methods, the main theoretical tool in previous works on the triplet proximity effect.