We report first-principles calculations that clarify atomic structures and coverage of the metallic phases of In overlayers on Si (111) surfaces. Calculated energy bands and scanning tunneling microscopy images along with the obtained energetics of various phases reveal that the two metallic phases with the √ 7 × √ 3 periodicity observed experimentally are single and double In overlayers, as opposed to prevailing assignments. PACS numbers: 68.43.Bc, 73.20.At, Surfaces ubiquitous in nature provide new phases of materials due to symmetry breaking and modification of interactions among constituting elements. A thin layer of metallic elements on a semiconductor surface is an example. It offers a good stage to study two-dimensional electron systems (2DESs), and also a key structure in device fabrication in current technology encountered with the cutting-edge miniaturization [1].Indium adatom layers on Si(111) surfaces are typical and important examples. A particular phase with the lateral periodicity of √ 7 × √ 3 exhibits metallic behavior down to several K [2], as opposed to the metalinsulator transition predicted for the 2DESs [3,4], and eventually becomes superconducting at 3 K [5,6]. This is the first case where superconductivity is found in a deposited layer. Angle-resolved photoemission spectroscopy (ARPES) clarifies the band structure of the metallic phase of the √ 7 × √ 3 surface [7]. However, atom-scale identification, i.e., the In coverage, the stable atomic structure and the resultant electron states, of the metallic phase is still lacking.Various surface reconstructions emerge by depositing In atoms on the Si(111) 7 × 7 surface [8], followed by annealing at ∼ 500• C in ultra-high vacuum: The √ 3 × √ 3, the √ 31 × √ 31, and the 4 × 1 phases appear consecutively with increasing the In dose, all showing insulating behavior at low temperature [9,10]. Then the √ 7 × √ 3 phase [11] appears with the In deposition of 1.5 -1.8 ML. The STM topographs [9,11] show that the two distinctive structures coexist on the √ 7 × √ 3 phase: Bright spots appear in a quasi-hexagonal pattern with protruding trimers in one structure (hex structure hereafter), and they appear in a quasi-rectangular pattern in the other structure (rect structure). The former and the latter have been speculated to be 1.0 ML and 1.2 ML, respectively, In adatoms on the Si(111) surface [9,11]. The excess In atoms are desorbed from the surface in the annealing. The metallic behavior [2,7] and the superconducting gap [5] have been observed on the rect structure, whereas the metallic behavior and the superconducting current has been measured on the hex structure [6]. Identification of the hex and the rect structures based on the firstprinciples calculations is highly demanded.In this Letter, we unequivocally identify the two metallic phases of √ 7 × √ 3 -In/Si(111) by performing totalenergy electronic-structure calculations in the densityfunctional theory. The obtained energetics, energy bands and scanning tunneling microscopy (STM) images are indicative t...