Topological Kondo effect with spinful Majorana fermions

TL;DR

This paper investigates the topological Kondo effect in spinful Majorana fermions within topological superconductors, revealing unique ground state entropies and mixed Fermi liquid behaviors through analytical solutions and transport analysis.

Contribution

It introduces a novel Kondo Hamiltonian for spinful Majorana modes in topological superconductors and analyzes their complex thermodynamic and transport properties.

Findings

Residual ground state entropy of ln(2) protected by spin symmetry

Reduction to ln(√2) entropy with symmetry breaking

Presence of both Fermi liquid and non-Fermi liquid thermodynamics

Abstract

Motivated by the importance of studying topological superconductors beyond the mean-field approximation, we here investigate mesoscopic islands of time reversal invariant topological superconductors (TRITOPS). We characterize the spectrum in the presence of strong order parameter fluctuations in the presence of an arbitrary number of Kramers pairs of Majorana edge states and study the effect of coupling the Coulomb blockaded island to external leads. In the case of an odd fermionic parity on the island, we derive an unconventional Kondo Hamiltonian in which metallic leads couple to both topological Majorana degrees of freedom (which keep track of the parity in different leads) and the overall spin-1/2 in the island. For the simplest case of a single wire (two pairs of Majorana edge states), we demonstrate that anisotropies are irrelevant in the weak coupling renormalization group flow. This permits us to solve the Kondo problem in the vicinity of a Toulouse-like point using Abelian Bosonization. We demonstrate a residual ground state entropy of $\ln(2)$, which is protected by spin-rotation symmetry, but reduced to $\ln(\sqrt{2})$ (as in the spinless topological Kondo effect) by symmetry breaking perturbations. In the symmetric case, we further demonstrate the simultaneous presence of both Fermi liquid and non-Fermi liquid like thermodynamics (depending on the observable) and derive charge and spin transport signatures of the Coulomb blockaded island.