Topological Kondo effect with spinful Majorana fermions
arxiv(2024)
摘要
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(√(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.
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