ArXiv · 2026
Doping a quantum spin liquid is expected to produce a superconductor. We show that for the Dirac spin liquid on the kagome lattice the doped charge orders first. The charge is carried by a chargon doublet whose two gauge components are degenerate on the square and triangular lattices, and the kagome lattice, as the line graph of the honeycomb lattice, splits them. One component disperses and condenses in four valleys. The other has flat lowest bands and stays empty over a window in the bare mass whose width, (√6-1)t, follows from the band structure alone. Within that window, in the mean-field chargon theory constructed from the projective symmetry group of the spin liquid, the doped state forms charge and loop-current crystals with the electromagnetic U(1) unbroken and no superconductivity. Pairing requires a gapped descendant of the spin liquid as the parent and then takes the form of a pair-density wave, with no uniform d+id channel at leading order and none at any order for the crystals at the M point. The predicted charge order is odd under the twofold rotation and has no cubic invariant, which distinguishes it from the charge order of the kagome metals.
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