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Morphed Graphene of BCO-C16: A Novel Topological Node-Line Semimetal

Date:24-05-2016 Print

Carbon is extremely versatile in its ability to form a rich variety of allotropes with a wide range of fascinating properties. At ambient conditions graphite is the thermodynamically most stable carbon allotrope and that many structural transformations and modifications of carbon structures in various sp2 and sp3 bonding networks can be produced under various pressure and temperature conditions. Under high static pressure and high temperature conditions, graphite can be converted to cubic diamond or twinned cubic diamond with {111} hexagonal-diamond-like stacking faults in all-sp3 bonding networks; meanwhile, the discovery of fullerenes, nanotubes, and graphene has ignited tremendous interest in recent years to explore additional carbon structures in all-sp2 bonding networks. Various hypothetical sp2 carbon modifications have been proposed, including the hexagonal H6 carbon, fcc-C20, ThSi2-type tetragonal bct4 carbon, and SrSi2-type cubic K4 carbon; most of them, however, are dynamically unstable due to the presence of twisted π states. Recent studies unveiled a new type of stable chiral framework structures comprising 3-fold, 4-fold and 6-fold helical chains in all-sp2 bonding networks connected by ethene-type planar π conjugation.

For three-dimensional chiral crystalline modification of carbon in all-sp2 bonding networks, the structures with matching helical chains of complementary chirality are energetically more favorable than structures with helical chains of same chirality. Based on this concept, recently, Prof. WANG Jiantao, WENG Hongming, FANG Zhong in IOP (including graduate student NIE Simin) in collaboration with Prof. KAWAZOE Yoshiyuki from Tohoku University, Japan and Prof. CHEN Changfeng from University of Nevada, Las Vegas, USA, reported a new all-sp2 carbon allotrope in Imma symmetry. This new carbon phase has a 16-atom body-centered orthorhombic unit cell, thus termed bco-C16, and it can be regarded as a three-dimensional modification of graphite, consisting of benzene linear chains connected by ethene-type planar π conjugation (see Fig. 1a). Total-energy calculations show that bco-C16 is comparable to solid fcc-C60 in energetic stability (see Fig. 1b), and its dynamic stability is verified by phonon and molecular dynamics simulations. An excellent match of simulated and measured x-ray diffraction spectra indicates the presence of bco-C16 in detonation and chimney soot. Electronic band structure calculations show that bco-C16 belongs to a new class of topological node-line semimetals. The valence and conduction bands exhibit linear dispersion near the Fermi energy and cross at the Fermi level (see Fig. 2a), and further analysis of the band structure in the full Brillouin zone indicates that the band crossing points (or nodal points) of the valence and conduction bands in bco-C16 form a continuous nodal ring inside a mirror plane (the shaded region in Fig. 2b). Moreover, the states near the crossing points around the nodal ring are formed by the inversion of the valence and conduction bands and protected by the coexistence of the time-reversal and inversion symmetry. When the nodal ring is projected onto the (100) surface, it produces topologically protected surface flat bands either inside or outside of the ring, depending on the termination of the surface, as shown in Fig. 2(c,d). These flat bands can be detected by photoelectron spectroscopy.

Our findings should facilitate further exploration of this class of intriguing materials. A major challenge is to find a route toward more effective synthesis of bco-C16 for more detailed studies. The structural identification and characterization of bco-C16 reported in the present work provide crucial knowledge for fundamental understanding and further exploration of this new carbon allotrope.

This study entitled “Body-Centered Orthorhombic C16: A Novel Topological Node-Line Semimetal” was published on Physical Review Letters 116, 195501 (2016).

This study was supported by the National Natural Science Foundation of China (Grant No. 11274356, No. 11274359, and No. 11422428) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB07000000). H.W., S.N. and Z.F. acknowledge the National 973 program of China (Grant No. 2011CBA00108 and No. 2013CB921700). C.F.C. acknowledges support by DOE under Cooperative Agreement No. DE-NA0001982.

Fig.1 Structure of bco-C16 and its phonon dispersion. (a) Top and side view of the all-sp2 bco-C16 in Imma symmetry with one-third double (d2, d3) and two-thirds single (d1) carbon-carbon bonds. It has a 16-atom body-centered orthorhombic structure with lattice parameters a = 7.8061 Å, b = 4.8772 Å, c = 3.2372 Å, occupying the 8i (0.3231, 0.25, 0.1258) and 8f (0.0885, 0.5, 0.5) Wyckoff positions, denoted by C1 and C2, respectively. (b) Calculated energy versus volume per atom for bco-C16 compared to graphite, fcc-C60, cR6, cT8, and rh6 carbon in all-sp2, and diamond in all-sp3 bonding networks. The dashed line indicates the energy level of carbyne chain. (Image by Institute of Physics)
Fig.2 Calculated bulk and surface band structures of bco-C16 at equilibrium lattice parameters.
(a) The bulk band structure along several high-symmetry directions. G1 and G2 indicate the irreducible representation of the two crossing bands, respectively. (b) The Brillouin zone with several high-symmetry momenta indicated. The nodal ring (red circle), formed by the band crossing points, is in the shaded mirror plane. (c) and (d) show the surface states for different zigzag-like (c) and beard-like (d) terminations of the (100) surface. The surface flat band (red line) can be outside or inside the surface projected nodal ring. (Image by Institute of Physics)

Contact:
Institute of Physics
WANG Jiantao
Email:wjt@iphy.ac.cn

Key word:
Morphed graphene nanostructures; All-sp2 bonding networks; Topological node-line semimetal.

Abstract:
We identify by ab initio calculations a novel topological semimetal carbon phase in all-sp2 bonding networks with a 16-atom body-centered orthorhombic unit cell, termed bco-C16. Total-energy calculations show that bco-C16 is comparable to solid fcc-C60 in energetic stability, and phonon and molecular dynamics simulations confirm its dynamical stability. This all-sp2 carbon allotrope can be regarded as a three-dimensional modification of graphite, and its simulated x-ray diffraction (XRD) pattern matches well a previously unexplained diffraction peak in measured XRD spectra of detonation and chimney soot, indicating its presence in the specimen. Electronic band structure calculations reveal that bco-C16 is a topological node-line semimetal with a single nodal ring. These findings establish a novel carbon phase with intriguing structural and electronic properties of fundamental significance and practical interest.