Prediction of two-dimensional nodal-line semimetals in a carbon nitride covalent network

Abstract

Carbon nitride compounds have emerged recently as a prominent member of 2D materials beyond graphene. The experimental realizations of 2D graphitic carbon nitride g-C 3 N 4 , nitrogenated holey grahpene C 2 N, polyaniline C 3 N have shown their promising potential in energy and environmental applications. In this work, we predict a new type of carbon nitride network with a C 9 N 4 stoichiometry from first principle calculations. Unlike common C-N compounds and covalent organic frameworks (COFs), which are typically insulating, surprisingly C 9 N 4 is found to be a 2D nodal-line semimetal (NLSM). The nodal line in C 9 N 4 forms a closed ring centered at  point, which originates from the p z orbitals of both C and N. The linear crossing happens right at Fermi level contributed by two sets of dispersive Kagome 2 and Dirac bands, which is robust due to negligible spin-orbital-coupling (SOC) in C and N. Besides, it is revealed that the formation of nodal ring is of accidental band degeneracy in nature induced by the chemical potential difference of C and N, as validated by a single orbital tight-binding model, rather than protected by crystal in-plane mirror symmetry or band topology. Interestingly, a new structure of nodal line, i.e., nodal-cylinder, is found in momentum space for AA-stacking C 9 N 4 . Our results imply possible functionalization for a novel metal-free C-N covalent network with interesting semimetallic properties.

Topological band evolution between Lieb and kagome lattices

“…We note that hopping terms can also be tuned by a chain of waveguide 20,49 , which could possibly be used to tune the band dispersion to realize the transition between type-I and type-II Dirac states. On the other hand, the Lieb and Kagome lattices have been separately proposed in real material systems, such as the 2D metal-organic and covelent-organic frameworks (MOF/COF) 24,[50][51][52][53] . Considering the high tunability of the MOF/COFs 54,55 , it is also possible to find suitable real 2D material systems to realize such phase transition.…”

The Tetragonal Monoxide of Platinum: A New Platform for Investigating Nodal-Line and Nodal-Point Semimetallic Behavior

“…Topological nodal point semimetals (Hosur et al, 2012 ; Zyuzin and Burkov, 2012 ; Hosur and Qi, 2013 ; Vazifeh and Franz, 2013 ; Liu et al, 2014 ; Lundgren et al, 2014 ; Kobayashi and Sato, 2015 ; Miransky and Shovkovy, 2015 ; Xu et al, 2015a ; Young and Kane, 2015 ) enjoy 0-D nodal points in momentum space. Topological nodal line semimetals (Cai et al, 2018 ; Chen et al, 2018 ; Gao et al, 2018 ; Zhou et al, 2018 ; He et al, 2019 ; Jin et al, 2019a ; Pham et al, 2019 ; Yi et al, 2019 ; Zou et al, 2019 ; Zhao et al, 2020 ) host 1-D topological nodal lines in momentum space via band crossing along a line in momentum space. Topological nodal surface semimetals (Wu et al, 2018 ; Zhang et al, 2018 ; Fu et al, 2019a ; Qie et al, 2019 ; Yang et al, 2020 ) host 2-D nodal surface states that are composed of continuous band crossing points.…”

Pure Zirconium: Type II Nodal Line and Nodal Surface States

“…Weyl and Dirac materials (Ouyang et al, 2016 ; Zhong et al, 2016 ; Zhou et al, 2016 ; Liu et al, 2017 ; Fu et al, 2018 ; Meng et al, 2019 , 2020a ; Zhang et al, 2020 ), which host 2-fold and fourfold degenerate band-crossing points, have been explored in real materials and their exotic properties have been confirmed in experiments. Moving forward, a series of three-dimension materials, with 1D and 2D band crossing points, have been predicted to be nodal line semimetals/metals (Phillips and Aji, 2014 ; Gan et al, 2017 ; Jin et al, 2017 , 2019 , 2020 ; Lu et al, 2017 ; Yang et al, 2017 ; Chen et al, 2018 ; Gao et al, 2018 ; Liu et al, 2018 ) and nodal surface semimetals/metals (Wu et al, 2018 ; Zhang et al, 2018 ; Wang et al, 2020 ), respectively.…”