Semimetallic carbon allotrope with topological nodal line in mixed $sp^2$-$sp^3$ bonding networks

TL;DR

This paper reports a new 3D carbon allotrope, $m$-$C_8$, with a topological nodal line semimetallic electronic structure, discovered via evolutionary search, and characterized by stability, unique bonding, and potential experimental identification.

Contribution

The discovery and characterization of a novel stable 3D carbon allotrope with topological nodal line features, expanding the understanding of carbon's structural and electronic diversity.

Findings

$m$-$C_8$ is more energetically favorable than other topological carbon allotropes.

$m$-$C_8$ exhibits a protected nodal line in its electronic structure.

Phonon spectra and molecular dynamics confirm its dynamical stability.

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 analogues 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 by using an evolutionary structure search method. The new carbon phase in monoclinic $C$2$/m$ space group, termed $m$-$C_8$, consists of five-membered rings with $sp^3$ bonding interconnected by $sp^2$-bonded carbon networks. Enthalpy calculations reveal that $m$-$C_8$ is more favorable over recently reported topological semimetallic carbon allotropes, and the dynamical stability of $m$-$C_8$ is verified by phonon spectra and molecular dynamics simulations. Simulated x-ray diffraction spectra propose that $m$-$C_8$ would be one of the unidentified carbon phases observed in detonation shoot. The analysis of electronic properties indicates that $m$-$C_8$ exhibits the 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.