Charge-6e superconductivity from doping SU(3) spin liquids

Abstract

We propose doping $SU(3)$-symmetric spin liquids as a route toward charge-$6e$ superconductivity. This generalizes the idea of constructing charge-$4e$ superconductivity from doped $SU(4)$-symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with $SU(3)$ spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped ${\mathbb{Z}}_3$ quantum spin liquid and $SU(3)$-related chiral spin liquids. Doping a ${\mathbb{Z}}_3$ quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge-$3e$ fermionic trions. Pairing these trions gives a time-reversal-symmetric charge-$6e$ superconductor. Doping Abelian $SU(3{)}_1$ and $SU(6{)}_1$ chiral spin liquids yields chiral charge-$6e$ superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian $SU(3{)}_2$ chiral spin liquid leads to a non-Abelian chiral charge-$6e$ superconductor intertwined with $SO(3{)}_{-3}$ topological order and supporting non-Abelian $h/(6e)$ superconducting vortices. We also identify several other phases, including ${\mathbb{Z}}_3$ orthogonal metal, quantum anomalous Hall (crystal) phases enriched by ${\mathbb{Z}}_3$ or ${\mathbb{Z}}_2$ topological order, $SU(3)$-breaking charge-$2e$ superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped $SU(3)$ spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge-$6e$ superconductivity.

11.5 pages, 1 figure

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