Moiré superlattice and two-dimensional free-electron-like states of indium triple-layer structure on Si(111)

We studied the growth of an indium triple-atomic-layer film and the two-dimensional free-electron-like electronic states on Si(111) by low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), and angle-resolved photoelectron spectroscopy (ARPES). By depositing In on the In/Si(111)-$\sqrt{7}\times \sqrt{3}$-rect surface below 100 K, followed by brief postannealing up to 140 K, we successfully obtained well-crystalline films exhibiting sharp superstructure LEED spots. We revealed an $(11\times 11)$ superlattice of the triple-layer structure, while both LEED and STM showed a $(5.5\times 5.5)$ pseudoperiodicity. This pseudoperiodicity was attributed to the moiré interference between the Si(111)-($11\times 11$) lattice ($a$ = 3.84 Å) and the In $(13\times 13)$ hexagonal lattice, which has a lattice constant of 3.25 Å, with the ratio very close to 13/11. ARPES measurements unveiled two free-electron-like states with Fermi wave vectors of 1.32 and 1.46 ${\AA }^{-1}$. We also observed replica Fermi surfaces, which are associated with the reciprocal lattice vectors of both the $(1\times 1)$ Si(111) and the In hexagonal layers. This further confirms the hexagonal atomic arrangement of the In triple-layer structure.