As a prototypical one-dimensional electron system, self-assembled indium (In) nanowires on the Si(111) surface have been believed to drive a metal-insulator transition by a charge-density-wave (CDW) formation due to electron-phonon coupling. Here, our first-principles calculations demonstrate that the structural phase transition from the high-temperature 4×1 phase to the low-temperature 8×2 phase occurs through an exothermic reaction with the consecutive bond-breaking and bond-making processes, giving rise to an energy barrier between the two phases as well as a gap opening. This atomistic picture for the phase transition not only identifies its firstorder nature but also solves a long-standing puzzle of the origin of the metal-insulator transition in terms of the ×2 periodic lattice reconstruction of In hexagons via bond breakage and new bond formation, not by the Peierls instability-driven CDW formation. PACS numbers: 73.20.At, 68.35.Md, 71.30.+h Low-dimensional electronic systems are of great interest in contemporary condensed-matter physics because of their susceptibility to charge density wave (CDW) instability [1], non-Fermi liquid behavior [2], spin ordering [3,4], and superconductivity [5,6] at low temperatures. Specifically, metalatom adsorption on semiconductor surfaces provides a unique playground for the exploration of such exotic physical phenomena [7,8]. We here focus on a prototypical example of quasi-one-dimensional (1D) systems, self-assembled indium (In) atom wires on the Si(111) surface [9][10][11]. Each In wire consists of two zigzag chains of In atoms [see the left panel of Fig. 1(a)] [10]. Below ∼120 K, this quasi-1D system undergoes a reversible phase transition initially from a 4×1 structure to a 4×2 one, then to an 8×2 structure [9,12], showing a period doubling both parallel and perpendicular to the In wires. This (4×1)→(8×2) structural phase transition is accompanied by a metal-insulator (MI) transition [9,13,14]. For the explanation of such a MI transition, the CDW mechanism due to a Peierls instability was initially proposed [9,[13][14][15], but subsequently other mechanisms based on an orderdisorder transition [19,20] and many-body interactions [21] have been proposed. Despite such debates, the CDW mechanism has been most widely believed to drive the observed MI transition [9,[13][14][15][16][17][18]. It is noted that the CDW formation invokes the strong coupling between lattice vibrations and electrons near the Fermi level E F , caused by Fermi surface nesting with a nesting vector 2k F = π/a x (a x : the 4×1 lattice constant along the In wires) [9,22]. The resulting Peierls dimerization was believed to occur on each chain, and the two dimerized chains further interact with each other, leading to a coupled double Peierls-dimerized chain model [23] [see Fig. 1(b)].Regarding the phase transition of the In/Si(111) system, there are still some unsettled issues. Although it is well established that the structural model of the 8×2 phase is constituted by the basic building block of In ...

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Graphene has been the subject of much research, with structural engineering frequently used to harness its various properties. In particular, the concepts of graphene origami and kirigami have inspired the design of quasi-three-dimensional graphene structures, which possess intriguing mechanical, electronic, and optical properties. However, accurate controlling the folding process remains a big challenge. Here, we report the discovery of spontaneous folding growth of graphene on the h-BN substrate via adopting a simple chemical vapor deposition method. Folded edges are formed when two stacked graphene layers share a joint edge at a growth temperature up to 1300 °C. Using first-principles density functional theory calculations, the bilayer graphene with folded edges is demonstrated to be more stable than that with open edges. Utilizing this novel growth mode, hexagram bilayer graphene containing entirely sealed edges is eventually realized. Our findings provide a route for designing graphene devices with a new folding dimension.