Abstract: I will discuss mesoscopic topological superconductors that can be used to realize quantum impurity models with orthogonal or symplectic symmetries. The first one uses a topological superconductor that hosts many (M>2) Majorana zero modes. Such an "M-Majorana island" coupled to normal metal leads realizes a novel type of topological Kondo effect, where the effective impurity "spin" transforms under the orthogonal group SO(M) stemming from the non-local topological ground state degeneracy of the island. In [1], we introduce a physically motivated N-channel generalization of the topological Kondo model, finding signatures of non-Fermi liquid (NFL) physics and emergent anyons. Our model allows a perturbative large-N limit which we use to obtain a NFL fixed point at weak coupling. In [2], we propose a Majorana-free setup that uses k spinful zero-energy Andreev bound states and can be mapped to a Kondo impurity with Sp(2k) symmetry. We predict conductances and impurity entropies that can be potentially observed in mesoscopic devices. Besides enriching the understanding of quantum impurity and correlations physics, our work may be relevant for topological quantum computation.
[1] Multichannel topological Kondo effect, Li, Oreg, Vayrynen, PRL 130, 066302 (2023)
[2] Topological symplectic Kondo effect Li, Konig, Vayrynen, arXiv:2210.16614 (2022)