PHYSICAL REVIEW B 83, 235417 (2011) Perpendicular growth of carbon chains on graphene from first-principles C. Ataca 1,2 and S. Ciraci 1,2,* 1 Department of Physics, Bilkent University, TR-06800 Ankara, Turkey 2 UNAM-Institute of Materials Science and Nanotechnology, Bilkent University, TR-06800 Ankara, Turkey (Received 21 April 2011; published 14 June 2011) Based on first-principles calculations we predict a peculiar growth process, where carbon adatoms adsorbed to graphene readily diffuse above room temperature and nucleate segments of linear carbon chains attached to graphene. These chains grow longer on graphene through insertion of carbon atoms one at a time from the bottom end and display a self-assembling behavior. Eventually, two allotropes of carbon, namely graphene and cumulene, are combined to exhibit important functionalities. The segments of carbon chains on graphene become chemically active sites to bind foreign atoms or large molecules. When bound to the ends of carbon chains, transition metal atoms, Ti, Co, and Au, attribute a magnetic ground state to graphene sheets and mediate stable contacts with interconnects. We showed that carbon chains can grow also on single-wall carbon nanotubes. DOI: 10.1103/PhysRevB.83.235417 PACS number(s): 73.22.−f, 63.22.−m, 81.05.ue I. INTRODUCTION Graphene, 1,2 a strictly two-dimensional allotrope of carbon, has a planar honeycomb structure that underlies a number of exceptional properties. A segment of carbon atomic chain (CAC), a strictly one-dimensional allotrope, is characterized with its high strength, linear geometry, and even-odd disparity occurring in its structural, quantum transport, and magnetic properties. CACs have been explored theoretically for a long time 3–5 and synthesized only recently. 6–8 Here, we portend a unique growth process of CACs on graphene: When two carbon atoms adsorbed on graphene are at close proximity, the potential barrier between them collapses and they form C 2 attaching perpendicularly to graphene. A CAC can continue to grow longer on graphene through insertion of carbon atoms one at a time from the bottom end as described in Figs. 1(a)–1(c). This process leads to a number of unusual artificial structures combined of the two allotropes of carbon, namely graphene and CACs. Graphene sheets with protruding CACs can achieve chemical activity and attain functionalities through CACs capped by foreign atoms or other graphene sheets. A single hydrogen molecule readily dissociates, once it is attached to the top of a CAC. This self-assembling behavior of carbon adatoms can also be exploited for the synthesis of free carbon atomic chains and other artificial nanostructures promising important applications, such as a medium of high-capacity hydrogen storage. That the binding energy of a single carbon adatom on graphene is smaller than the cohesive energy of a linear carbon chain underlies the present self-assembling growth process. The sp D hybrid orbitals are indigenous to the dimension- ality (D = 1,2,3) of these allotropic forms. The sp 2 bonding together with π bonding assures the planar stability of the honeycomb structure of graphene. Covalent bonding of sp D=1 hybrid orbitals along the chain axis together with π bonding of perpendicular p x and p y orbitals are responsible for the high strength and linear stability of the chain. π bonds having nodes at the atomic sites behave as if they are 1D-nearly free electron system with an effective mass, m ∗ ∼ m e (free electron mass) and mediate long-ranged Friedel oscillations. 4 Unusual geometric forms and emerging properties of CACs have been revealed 5 and free-standing CACs were produced 7 from graphene flakes using a high-energy transmission mi- croscope (TEM). Theoretically, it is also shown that CACs can be produced by stretching a graphene nanoribbon in the plastic deformation range. 9 Much recently, polyene consisting of 44 carbon atoms have been produced. 8 In an earlier experimental study, carbon adatoms and segments of carbon atomic chains were observed using TEM and attributed to vacuum contamination. 10 Since free carbon atomic chains did not form by themselves to exist as contamination, reported TEM images and video taken at a finite temperature present strong evidence for our theoretical predictions. II. METHOD The growth mechanism we hyphothesize is accurately described by first-principles calculations based on density functional theory (DFT) combined with ab initio, finite- temperature molecular-dynamics (MD) calculations. The state-of-the-art spin-polarized, first-principles plane-wave cal- culations within DFT 11 are carried out using projector augmented-wave (PAW) potentials 12 and local density ap- proximation (LDA). 13 PAW potential with small core radius of 1.1 ˚ A is close to all electron treatment and hence better represents C−C bond, as well as magnetic interactions in graphene + C ∗ systems. 14 In addition, a high cutoff assures convergence of energies even if the sizes of superlattice are varied for different systems. We also performed calculations with generalized gradient approximation (GGA) 15 with and without van der Waals (vdW) corrections 16 for the sake of comparison with previous studies. All structures are treated within the supercell geometry, where the distance larger than 11 ˚ A between any two C atoms in different cells is assured. A plane-wave basis set with kinetic energy cutoff of 900 eV is used to achieve high precision. 11 The Brillouin zone (BZ) is sampled in the k space within a Monkhorst-Pack scheme, 17 where the convergence of total energy and magnetic moments with respect to the number of k-points in BZ are carefully tested. All atomic positions and lattice constants are optimized by use of the conjugate gradient method, where the total energy and atomic forces are minimized. The convergence for energy is chosen as 10 −5 eV between two consecutive steps, the maximum Hellmann-Feynman forces acting on each atom is 235417-1 1098-0121/2011/83(23)/235417(10) ©2011 American Physical Society