Semimetallic carbon allotrope with a topological nodal line in mixed sp2-sp3 bonding networks

Ha-Jun Sung,Kee Joo Chang,In-Ho Lee,Sunghyun Kim

doi:10.1038/am.2017.26

Abstract

Graphene is known as a two-dimensional Dirac semimetal, in which electron states are described by the Dirac equation of relativistic quantum mechanics. Three-dimensional analogs of graphene are characterized by Dirac points or lines in momentum space, which are protected by symmetry. Here, we report a novel 3D carbon allotrope belonging to a class of topological nodal line semimetals, discovered using an evolutionary structure search method. The new carbon phase in the monoclinic C2/m space group, termed m-C8, consists of five-membered rings with sp3 bonding interconnected by sp2-bonded carbon networks. Enthalpy calculations reveal that m-C8 is more favorable than recently reported topological semimetallic carbon allotropes, and the dynamic stability of m-C8 is verified by phonon spectra and molecular dynamics simulations. Simulated X-ray diffraction patterns indicate that m-C8 could be one of the unidentified carbon phases observed in detonation shoot. The analysis of electronic properties indicates that m-C8 exhibits a nodal line protected by both inversion and time-reversal symmetries in the absence of spin-orbit coupling and the surface band connecting the projected nodal points. Our results may help design new carbon allotropes with exotic electronic properties.

Highlights

Carbon, which is one of the most abundant elements in nature, has a rich variety of structural allotropes due to its capacity to form sp, sp[2] and sp[3] hybridized bonds
Enthalpy calculations reveal that m-C8 is more favorable than recently reported topological semimetallic carbon allotropes, and the dynamic stability of m-C8 is verified by phonon spectra and molecular dynamics simulations
The topological semimetals (TSMs) phase has been reported for 3D carbon networks constructed from graphene, such as Mackay-Terrenes crystals,[17] interpenetrated graphene networks (IGNs)[18] and bco-C16.19 Due to the negligible spin-orbit coupling (SOC),[20] the nodal lines of these semimetallic carbon allotropes are protected by a combination of inversion and time-reversal symmetry

Summary

INTRODUCTION

Carbon, which is one of the most abundant elements in nature, has a rich variety of structural allotropes due to its capacity to form sp, sp[2] and sp[3] hybridized bonds. 11), Ca3P2,12 and alkaline-earth metals (Ca, Sr, Yb)[13] and compounds AX2 (A = Ca, Sr, Ba; X = Si, Ge, Sn).[14] When SOC is included, additional non-symmorphic symmetry is necessary to protect the nodal line against gap opening in ZrSiS.[15] In non-centrosymmetric PbTaSe2, the nodal line is protected by mirror reflection symmetry even in the presence of SOC.[16] the TSM phase has been reported for 3D carbon networks constructed from graphene, such as Mackay-Terrenes crystals,[17] interpenetrated graphene networks (IGNs)[18] and bco-C16.19 Due to the negligible SOC,[20] the nodal lines of these semimetallic carbon allotropes are protected by a combination of inversion and time-reversal symmetry. H6 carbon arises from the twisted π states that make these allotropes dynamically unstable.[26]

Method

METHODS

RESULTS AND DISCUSSION