Non-Abelian Anyon Superconductivity

Abstract

Non-Abelian Anyons exist in certain spin models and may exist in Quantuam Hall systems at certain filling fractions. In this work we studied the ground state of dynamical SU(2) level-$\kappa$ Chern Simons non-Abelian anyons at finite density and no external magnetic field. We find that in the large-$\kappa$ limit the topological interaction induces a pairing instability and the ground state is a superconductor with $d+id$ gap symmetry. We also develop a picture of pairing for the special value $\kappa =2$ and argue that the ground state is a superfluid of pairs for all values of $\kappa$.

5 pages, no figures

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• Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
• Quantized conductance with non-zero shot noise as a signature of Andreev edge state
• Local characterization and engineering of proximitized correlated states in graphene-NbSe${}_2$ vertical heterostructures