Topological Kondo effect with spinful Majorana fermions

Journal Article · Fri Jul 12 00:00:00 EDT 2024 · Physical Review. B

DOI:https://doi.org/10.1103/PhysRevB.110.035136· OSTI ID:2397350

Bollmann, Steffen; Väyrynen, Jukka I.; König, Elio J.

Motivated by the importance of studying topological superconductors beyond the mean-field approximation, we here investigate mesoscopic islands of time-reversal-invariant topological superconductors. 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 $\frac{1}{2}$ 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-type point using Abelian bosonization. We demonstrate a residual ground-state entropy of $ln\left(2\right)$ , which is protected by spin-rotation symmetry, but reduced to $ln\left(\sqrt{2}\right)$ (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.

Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• OSTI ID: 2397350
• Alternate ID(s): OSTI ID: 2582536
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 110; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English