Density-functional calculations are used to identify one-atom-thick metallic In phases grown on the Si(111) surface, which have long been sought in quest of the ultimate two-dimensional (2D) limit of metallic properties. We predict two metastable single-layer In phases, one sqrt[7]×sqrt[3] phase with a coverage of 1.4 monolayer (ML; here 1 ML refers to one In atom per top Si atom) and the other sqrt[7]×sqrt[7] phase with 1.43 ML, which indeed agree with experimental evidences. Both phases reveal quasi-1D arrangements of protruded In atoms, leading to 2D-metallic but anisotropic band structures and Fermi surfaces. This directional feature contrasts with the free-electron-like In-overlayer properties that are known to persist up to the double-layer thickness, implying that the ultimate 2D limit of In overlayers may have been achieved in previous studies of double-layer In phases.
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