Checkerboard ordered state in a superconducting FeSe/SrTiO3(001) monolayer

Ordered electronic states have been extensively explored in cuprates and iron-based unconventional superconductors, but seldom observed in the epitaxial $\mathrm{FeSe}/\mathrm{SrTi}{\mathrm{O}}₃(001)$ monolayer (FeSe/STO) with an enhanced superconducting transition temperature $({T}_c)$. Here, by using scanning tunneling microscopy/scanning tunneling spectroscopy (STM/STS), we reveal a checkerboard charge order in the epitaxial FeSe/STO monolayer, with a period of four times the inter-iron-atom distance along two perpendicular directions of the iron lattice. This ordered state is uniquely present in the superconducting FeSe/STO monolayer, even at liquid nitrogen temperature, but is absent in the nonsuperconducting FeSe monolayer or bilayer. Quasi-particle interference measurements further confirm it as a static order without an energy-dependent dispersion and is gapped out within the superconductivity gap. The intensity of the charge order shows an enhancement near the superconducting transition temperature, thus implying a correlation with the $\text{high-}{T}_c$ superconductivity in the FeSe/STO monolayer. This study provides a new basis for exploring the ordered electronic states and their interplay with $\text{high-}{T}_c$ superconductivity in the FeSe monolayer.