We predict a novel electronically driven phase for the recently created $\mathrm{C}/\mathrm{Si}(111)$ surface at $1/3$ monolayer coverage. Whereas the isoelectronic surface $\mathrm{Sn}/\mathrm{Ge}(111)$ is a $3\times 3$ distorted metal and $\mathrm{Si}/\mathrm{SiC}(0001)$ is an undistorted magnetic Mott insulator, the new phase combines both features. Two of three adatoms in $\mathrm{C}/\mathrm{Si}(111)$ should form a distorted ($3\times 3$) honeycomb sublattice, the third an undistorted insulating and magnetic triangular sublattice. The generally conflicting elements, namely, band energy, favoring distortion, and strong electron correlations favoring a Mott state, actually conspire in this case. This kind of state represents the surface analog of the Fazekas-Tosatti state in the charge density wave compound $1T\mathrm{\text{−}}{\mathrm{TaS}}_2$.

• Received 29 July 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.206801