Moir\'e-resonant surface state in ultrathin RuO₂

RuO$_2$ has emerged as a prototypical candidate for altermagnetism. In the face of daunting evidence for magnetic order in the bulk, the focus naturally shifted to surfaces and ultrathin films, where Coulomb interactions are dimensionally quenched and electron correlations strongly enhanced. Here, we examine atomically ordered, ultrathin RuO$_2$(110) grown on Ru(0001) using a combination of scanning tunneling microscopy (STM), density functional theory, and density matrix renormalization group methods. We observe a nonmagnetic charge order that is imprinted by the incommensurate moir\'e stacking with the substrate and enhanced by the electronic Fermi surface scattering within the flat-band surface state. We further identify a nonmagnetic, metastable $c(2 \times 2)$ surface reconstruction that arises from surface phonon softening and can be toggled reversibly via STM tip manipulation. Spin-polarized STM measurements, however, reveal no evidence of magnetic order on the RuO$_2$(110) surface. Our findings of a nonmagnetic charge-modulation position ultrathin RuO$_2$(110) as an intriguing platform for exploring moir\'e-assisted electronic orders.