Charge-4$e$ Anyon Superconductor from Doping $\text{SU}(4)_1$ chiral spin liquid

Previous studies have shown that $\text{SU}(4)_1$ chiral spin liquid can emerge in the SU($4$) Hubbard model on triangular lattice. A natural question then arises: What is the phase upon doping? In this work, we show the possibility that hole doping can give rise to an anyon superconductor and propose that both spinons and holons form integer quantum Hall states with opposite chiralities. Using topological field theory we demonstrate that the phase is a topological charge-$4e$ superconductor with chiral central charge $c_-=4$. We further identify the deconfined excitations and anyonic excitations bound to the vortex. This unusual superconductor may be realized in moir'e bilayer and detected through quantized thermal Hall effect and spin quantum Hall effect.