Multiple Dirac Cones Research Articles

Thermodynamic properties of topological crystalline insulator SnTe (001) thin film in the presence of Zeeman magnetic field

Abstract Multiple surface Dirac cones in topological crystalline insulators motivate the researchers to tune the topological phase. In the present work, we theoretically study the longitudinal, transverse and in-plane Zeeman magnetic field effects on the electronic density of states (DOS), electronic heat capacity (EHC) and Pauli spin paramagnetic susceptibility (PSPS) [on behalf of the electrical, thermal and magnetical properties, respectively] of topological crystalline insulator SnTe (001) and related alloys thin films. In doing so, we implement the Dirac theory, Green’s function approach, and the Boltzmann method. First, we found that EHC and PSPS decrease with hybridization potential due to the hybridization-induced gap in DOS. Second, the Weyl cones appear [result from the van Hove singularities around the Fermi level] when the Zeeman field is greater than the hybridization potential. Third, the Zeeman splitting and shifting of bands are characterized by the van Hove singularities in the vicinity of the Fermi level and the degenerate states, the Schottky anomaly and the crossover in DOS, EHC and PSPS, respectively. Our findings show that the EHC (PSPS) increases (decreases) with Zeeman fields. The predicted results may be useful for designing nanoelectronic and spintronic TCI-based devices.

Electronic and optical properties of non-hexagonal Dirac material S-graphene sheet and nanoribbons

Abstract In this paper, we have critically explored the electronic, magnetic and optical properties of stable non-hexagonal carbon allotrope S-graphene (SG). The band structure of SG sheet exhibits two Dirac cones at distinct k → points. The ab-initio molecular dynamics study reveals the dynamical stability of the system up to 600 K. Besides, the sheet possesses appreciable mechanical stability. Furthermore, the electronic properties of the ribbons strongly depend on the edge geometry and width. The A-type S-graphene nanoribbons (SGNRs) with even N exhibit width-dependent direct bandgap semiconducting nature. Whereas, A-SGNRs with odd N are semi-metallic. In contrary, B-SGNRs are uniformly semi-metallic except for extremely narrow N = 1 and 2 case. Besides, the unexpected occurrence of Dirac point for the N = 4.5 C-SGNR has been explored. Moreover, the optical response of the sheet and nanoribbons are highly anisotropic. We have critically obtained the plasma frequency for the collective electron oscillation of the sheet at 5.37 eV under parallel incidence of electromagnetic waves. Besides, the effective number of electrons participating in direct interband transitions in sheet show a quasi-saturation between 3-10 eV. We thus expect these theoretical predictions will provide a basic understanding of the opto-electronic responses towards possible application of this non-hexagonal graphene network with multiple Dirac cones.

Weak localization in graphene sandwiched by aligned h-BN flakes

Charge carriers in graphene exhibit distinct characteristics from those in other two-dimensional materials because of their chiral nature. Additionally, multiple Dirac cones that emerge in graphene superlattices have been regarded as an interesting point in condensed-matter physics in recent years. Here, we report an investigation of the magneto-conductance in graphene encapsulated on the top and bottom by aligned h-BN. The bottom h-BN is precisely aligned with graphene, while the top h-BN is rotated a very small angle relative to it. Such a heterostructure could spoil the commensurate state existing in precisely aligned graphene while the giant moiré superlattice remains. A clear signature of weak localization and weak anti-localization is observed at multiple Dirac cones. Both the weak (anti)localization and the universal conductance fluctuations exhibit strong dependencies on the carrier density, temperature and channel length. This artificial heterostructure allows one to explore quantum interference in graphene with a wide spectrum of electronic properties.

Half-metallic magnetism and electronic structures of CrPSe<sub>3</sub> monolayers with multiple Dirac cones<span style="background-color: rgb(255, 255, 255);"><span style="color:#ff0000;">（withdraw）</span></span>

According to the first-principles calculation within PBE+<em>U</em> method and tight-binding model, the magnetic properties and electronic structures of two-dimensional (2D) CrPSe<sub>3</sub> monolayer were investigated. Constructed by a Cr-honeycomb hexagonal lattice, 2D CrPSe<sub>3</sub> was predicted to be in a half-metallic ferromagnetic state with dynamic stability, confirmed by the phonon spectrum with no imaginary dispersion. The Curie temperature was estimated as 224 K by Monte Carlo simulation within the Metropolis algorithm under the periodic boundary condition. The thermal stability of CrPSe<sub>3</sub> monolayer was estimated at 300 K by a first-principles molecular dynamics simulation. It is found that the magnetic ground state of CrPSe<sub>3</sub> monolayer is determined by a competition between the antiferomagnetic d-d direct exchange interactions and the Se-p orbitals mediated ferromagnetic p-d superexchange interactions. Most interestingly, in the half-metallic state the band structure exhibits multiple Dirac cones in the first Brillouin zone: two cones at <em>K</em> point showing a very high Fermi velocity<inline-formula><tex-math id="M6">\begin{document}${v_{\rm F}{(K)}} = 15.8 \times 10^5 \;{\rm m \!\cdot\! s^{-1}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M6.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M6.png"></graphic></alternatives></inline-formula> about twice larger than the <inline-formula><tex-math id="M7">\begin{document}$ v_{\rm F} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M7.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M7.png"></graphic></alternatives></inline-formula> of graphene in the vicinity of Fermi level, and six cones at <inline-formula><tex-math id="M8">\begin{document}$ K'/2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M8.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M8.png"></graphic></alternatives></inline-formula> points with <inline-formula><tex-math id="M9">\begin{document}${ v_{\rm F} {(K'/2)}} = 10.1 \times 10^5\;{\rm m \!\cdot\! s^{-1}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M9.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M9.png"></graphic></alternatives></inline-formula> close to the graphene's value. These spin-polarized Dirac cones are mostly composed of Cr <inline-formula><tex-math id="M10">\begin{document}${\rm d}_{xz}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M10.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M10.png"></graphic></alternatives></inline-formula> and <inline-formula><tex-math id="M11">\begin{document}${\rm d}_{yz}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M11.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M11.png"></graphic></alternatives></inline-formula> orbitals. The novel electronic structure of CrPSe<sub>3</sub> monolayer is also confirmed by the HSE06 functional. A tight-binding model was built based on the Cr-honeycomb structure with two Cr-d orbitals as the basic with the first, second and third nearest-neighboring interactions, further demonstrating that the multiple Dirac cones are protected by the Cr-honeycomb lattice symmetry. Our findings indicate that 2D CrPSe<sub>3</sub> monolayer is a candidate with potential applications in the low-dimensional, high speed and temperature spintronics.

R3c-type LnNiO3 (Ln = La, Ce, Nd, Pm, Gd, Tb, Dy, Ho, Er, Lu) half-metals with multiple Dirac cones: a potential class of advanced spintronic materials.

In the past three years, Dirac half-metals (DHMs) have attracted considerable attention and become a high-profile topic in spintronics becuase of their excellent physical properties such as 100% spin polarization and massless Dirac fermions. Two-dimensional DHMs proposed recently have not yet been experimentally synthesized and thus remain theoretical. As a result, their characteristics cannot be experimentally confirmed. In addition, many theoretically predicted Dirac materials have only a single cone, resulting in a nonlinear electromagnetic response with insufficient intensity and inadequate transport carrier efficiency near the Fermi level. Therefore, after several attempts, we have focused on a novel class of DHMs with multiple Dirac crossings to address the above limitations. In particular, we direct our attention to three-dimensional bulk materials. In this study, the discovery via first principles of an experimentally synthesized DHM LaNiO3 with many Dirac cones and complete spin polarization near the Fermi level is reported. It is also shown that the crystal structures of these materials are strongly correlated with their physical properties. The results indicate that many rhombohedral materials with the general formula LnNiO3 (Ln = La, Ce, Nd, Pm, Gd, Tb, Dy, Ho, Er, Lu) in the space group R 3 c are potential DHMs with multiple Dirac cones.

Comparative First-Principles Study of Antiperovskite Oxides and Nitrides as Thermoelectric Material: Multiple Dirac Cones, Low-Dimensional Band Dispersion, and High Valley Degeneracy

We perform a comparative study on thermoelectric performance of antiperovskite oxides $Ae_3Tt$O and nitrides $Ae_3Pn$N ($Ae=$ Ca, Sr, Ba; $Tt=$ Ge, Sn, Pb; $Pn=$ As, Sb, Bi) by means of first-principles calculation. As for the oxides with the cubic structure, Ca$_3$GeO with a sizable band gap exhibits high thermoelectric performance at high temperatures, while Ba$_3$PbO with Dirac cones without the gap is favorable at low temperatures. The latter high performance owes to high valley degeneracy including the multiple Dirac cones and the valleys near the $\Gamma$ and R points. For the nitrides with the cubic structure, insulator with strong quasi-one-dimensionality exhibits high thermoelectric performance. We also find that the orthorhombic structural distortion sometimes sizably enhances thermoelectric performance, especially for Ba$_3$GeO and Sr$_3$AsN where the high valley degeneracy is realized in the $Pnma$ phase. Our calculation reveals that antioerpvskites offer a fertile playground of various kinds of characteristic electronic structure, which enhance the thermoelectric performance, and provides promising candidates of high-performance thermoelectric materials.

DFT-Based Study on Electronic, Magnetic and Thermodynamic Properties of HoMnO3: A Half-Metallic Material with Nearly Linear Band Crosses

A novel half-metallic family of materials, the multiple Dirac cones half-metals, has received considerable interest from researchers. Benefiting from its novel electronic structure, they are promising candidates for ultra-performance spintronic devices. In this paper, we propose a new half-metallic material, perovskite-type [Formula: see text] HoMnO3, which possesses similar Dirac-like multiple linear band crosses. We investigated its electronic, magnetic and thermodynamic properties in detail on the basis of density functional theory. The excellent band structures are robust enough against spin-orbit coupling and electron and hole doping. Through calculations, we confirmed its multi-aspect stability. Based on the current study, we confirm that HoMnO3 has potential for next-generation spintronic applications.

Understanding the thermodynamic and magnetic properties, remarkable multiple Dirac-cones, and fully spin-polarization in a new half-metal TbNiO3 with R3¯c phase via first-principles

Abstract This current investigation builds upon previous results (Ma et al., 2018), which have shown that LaMnO3 is a novel Dirac half metal with multiple Dirac-like cones. In this work, a new R 3 ¯ c phase material, TbNiO3, with 100% spin-polarization and robust multiple Dirac-cones has been focused on. By means of first-principles and quasi-harmonic Debye model, its electronic, magnetic and thermodynamic properties have been studied, and also, the effects of uniform strain and on-site Coulomb interaction U on its electronic structures have been discussed. Moreover, the magnetic states, including FM, NM, and AFM, were fully considered in a 1 × 1 × 1 unit cell and two superlattice cells, i.e., 1 × 1 × 2 and 2 × 2 × 1 systems. We hope this work will trigger further research about R 3 ¯ c type Dirac half-metallic materials with multiple Dirac cones in experimental and theoretical regions.

Insight into the robust multiple Dirac-cones in perovskite [formula omitted] phase CuBO3 semimetal from first-principles

Motivated by a related recent study (Jiao et al. PRL 119, 016403 (2017)), in this work, a new R3¯c type semimetal has been calculated based on the first-principles method. We observed that CuBO3 showed robust multiple Dirac-cones (DCs) near the Fermi level. Also, we found that these DCs were coming from the hybridization between O-p and Cu-d orbits. As a medium state between normal insulating state and topological insulating state, Dirac semimetal is a new class of materials due to its novel physical properties. Moreover, for CuBO3, the Dirac-like band crossings are dispersed in a linear pattern across a very large energy range. In order to guide the experiment, the thermal stability of CuBO3 has been studied through ab initio molecular dynamic simulations. Finally, we are keen to emphasize that the specific space of this group allows for the three-dimensional Dirac point to be used as a symmetric protection for degeneracy. There may be many other three-dimensional Dirac semimetals in the R3¯c phase of crystallization that have not yet been discovered. Thus, more attention to these materials is required in the future.

Electronic, magnetic, and thermodynamic properties of rhombohedral Dysprosium Manganite and discussions of effects of uniform strain, spin-orbit coupling, hole and electron doping on its electronic structures

In recent years, the search for new Dirac half-metallic materials has been one of the hotspots in the field of spintronics because they have very good physical properties, such as massless Dirac fermions and full spin polarization. In this study, using density function theory combined with the quasi-harmonic Debye model, we show that perovskite-type dysprosium manganite is a novel half metal with multiple Dirac cones. A detailed study of the electronic, magnetic, and thermodynamic properties of DyMnO3 was carried out. Furthermore, the effects of uniform strain, the on-site Coulomb interaction U, spin-orbit coupling, and hole and electron doping on the multiple Dirac cones and full spin polarization were investigated. We should point out that such a spin-polarized Dirac material is rare among perovskite-type compounds. Hence, we hope that, through this work, this kind of material will receive more extensive attention in future studies.

Perovskite R{\bar 3}c phase AgCuF3: multiple Dirac cones, 100% spin polarization and its thermodynamic properties.

Very recently, experimentally synthesized R{\bar 3}c phase LaCuO3 was studied by Zhang, Jiao, Kou, Liao & Du [J. Mater. Chem. C (2018), 6, 6132-6137], and they found that this material exhibits multiple Dirac cones in its non-spin-polarized electronic structure. Motivated by this study, the focus here is on a new R{\bar 3}c phase material, AgCuF3, which has a combination of multiple Dirac cones and 100% spin polarization properties. Compared to the non-spin-polarized system LaCuO3, the spin-polarized Dirac behavior in AgCuF3 is intrinsic. The effects of on-site Coulomb interaction, uniform strain and spin-orbit coupling were added to examine the stability of its multiple Dirac cones and half-metallic behavior. Moreover, the thermodynamic properties under different temperatures and pressures were investigated, including the normalized volume, thermal volume expansion coefficient, heat capacity at constant volume and Debye temperature. The thermal stability and the phase stability of this material were also studied via ab initio molecular dynamic simulations and the formation energy of the material, respectively.

Rhombohedral HoNiO3: A new half-metallic material with a high T, full spin-polarization and multiple Dirac-cones for advanced functional applications

Abstract A recent work by Du et al. [ACS Applied Materials & Interfaces 10 (2018): 36088-36093] showed that LaMnO3 was a novel Dirac half metal with multiple Dirac cones. Our current work was based on their study, and the main task of our manuscript was to predict a new R 3 ¯ c phase material, HoNiO3, with 100% spin-polarization and multiple Dirac-cones from first principles. The magnetic states, including FM, NM and AFM, were examined by building a 1 × 1 × 1 unit cell and two superlattice cells, i.e., 1 × 1 × 2 and 2 × 2 × 1 systems. The results showed that the FM state was the most stable magnetic state for this system. From mean-field theory (MFT), we roughly estimated the Curie temperature of the HoNiO3 material. Although the real Curie temperature of a material is often overestimated by MFT, the high Curie temperature (TC) value of HoNiO3 (∼902.04 K) ensured that the TC of the material was higher than room temperature. Furthermore, the effect of spin-orbit coupling was added to examine the stabilities of the multiple Dirac cones. The results indicate that this material has long-term spin coherence, which is favourable for spin transport. The effects of the on-site Coulomb interaction U and on-site exchange constant J values on the electronic structures and magnetic moments were also examined. Moreover, the thermodynamic properties under different temperatures and pressures were investigated. We believe our current work will trigger further experimental and theoretical research on R 3 ¯ c -type Dirac half-metallic materials with multiple Dirac cones.

Ab initio study of rhombohedral ErMnO3 as a high Tc half-metal with multiple Dirac cones and promising applications in spintronics

Abstract Advanced materials with high spin polarization and Dirac features have attracted widespread attention due to their potential applications in the field of spintronics. But this type of material is still very rare, especially for three-dimensional bulk materials. In this manuscript, via first-principles, we predicted a new rhombohedral type material ErMnO3. Remarkably, this material possesses the following excellent characteristics: (1) robust half-metallic properties, (2) multiple Dirac-cones, (3) strong resistance to the spin-orbit coupling, (4) high Curie temperature and (5) very resistant to the hole and electron doping. Therefore, ErMnO3 could potentially have broad application prospects in spintronics. Also, to better understand the specific behaviors of ErMnO3 under extreme conditions as high temperature or pressure, we further investigated its thermodynamic properties through the quasi-harmonic Debye model.

Prediction of robust multiple Dirac-cones in newly designed perovskite R3¯c phase AgBO3 from first-principles

Abstract In this paper, a new R 3 ¯ c type semimetal has been predicted based on first-principles computations. We found that AgBO3 exhibited robust multiple Dirac-cones which come from the hybridization between O-p and Ag-d orbitals around the Fermi level. As an intermediate state between a trivial insulator and topological insulator, the research regarding this type of Dirac semimetal has great theoretical academic significance. Importantly, for AgBO3, the Dirac-cone bands are linearly dispersed over a very large energy range. The thermal stability of this material has also been examined via ab-initio molecular dynamics simulations. The specific space of this group allows for the three-dimensional Dirac point to be used as a symmetric protection for degeneracy. Therefore, there may be many 3D Dirac semimetals in the perovskite ( R 3 ¯ c ) phase, that have not yet been discovered. Therefore, we hope that our present work can give some inspiration to the subsequent experimental and theoretical work, and that more R 3 ¯ c -based Dirac materials will receive attention.

Dual Dirac cones in elastic Lieb-like lattice metamaterials

Double-zero-index properties of electromagnetic and acoustic waveguides have been recently realized based on Dirac/Dirac-like cones at the Brillouin zone (BZ) center. However, very limited research has been devoted to double-zero-index structural systems of elastic waveguides, and almost no lattice system has been able to achieve multiple separated Dirac cones generated around different frequencies at the BZ center. Here, we report two separated elastic-wave Dirac-like cones, which are simultaneously achieved around different Dirac points at the BZ center, due to the accidental degeneracy and frequency repulsion effect in a Lieb-like lattice metamaterial. Using the proposed elastic medium, the double-zero-index properties of various elastic wave modes are theoretically analyzed, numerically computed, and experimentally observed at the neighborhood of both Dirac-like points. The performance of near total transmission without the phase change and the ability of wave-front shaping are unambiguously verified by numerical simulation and experimental measurements.

Localization physics in graphene moiré superlattices

Non-trivial Berry phase of graphene leads to unusual quantum correction to the conductivity. Berry phase of pi in single layer graphene (SLG) and 2pi in bi-layer graphene (BLG) is expected to reveal weak anti-localization (WAL) and weak localization (WL), respectively. However, experimentally both WAL and WL have been observed in graphene devices depending on the strength of different scattering mechanisms. Graphene superlattice having multiple Dirac cones is expected to exhibit pi to 2pi Berry phase transition from primary Dirac cone (PDC) to cloned Dirac cone (CDC). However, its effect on localization physics has not been explored yet. In this letter we present the magneto-conductance study in a hexagonal Boron-nitride (hBN)-graphene moire superlattice. Our results reveal a transition from WAL at PDC to WL at CDC in a single device by tuning the Fermi energy. The transition is supported by the quantum oscillation measurements showing a shift of pi phase from PDC to CDC and corresponding theoretical calculation capturing the Berry phase transition. Thus, our studies on localization physics in graphene superlattice pave the way to understand the carrier dynamics at multiple Dirac cones.

Electric field manipulation of multiple nonequivalent Dirac cones in the electronic structures of hexagonal CrB4 sheet**Project supported by the National Natural Sciences Foundation of China (Grant Nos. 11704294 and 11504281), the Natural Science Foundation of Hubei Province, China (Grant No. 2016CFB586), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2017IVA078, 2018IVB017, 2017IB013, 2018IB009, and 2018IB011).

Two-dimensional materials with Dirac cones have significant applications in photoelectric technology. The origin and manipulation of multiple Dirac cones need to be better understood. By first-principle calculations, we study the influence of external fields on the electronic structure of the hexagonal CrB4 sheet with double nonequivalent Dirac cones. Our results show that the two cones are not sensitive to tensile strain and out-of-plane electric field, but present obviously different behaviors under the in-plane external electric field (along the B–B direction), i.e., one cone holds while the other vanishes with a gap opening. More interestingly, a new nonequivalent cone emerges under a proper in-plane electric field. We also discuss the origin of the cones in CrB4 sheet. Our study provides a new method on how to obtain Dirac cones by the external field manipulation, which may motivate potential applications in nanoelectronics.

Multiple Dirac cones and topological magnetism in honeycomb-monolayer transition metal trichalcogenides

The discovery of monolayer graphene has initiated two fertile fields in modern condensed matter physics, Dirac semimetals and atomically-thin layered materials. When these trends meet again in transition metal compounds, which possess spin and orbital degrees of freedom and strong electron correlations, more exotic phenomena are expected to emerge in the cross section of topological states of matter and Mott physics. Here, we show by using ab initio calculations that a monolayer form of transition metal trichalcogenides (TMTs), which has a honeycomb network of transition metal cations, may exhibit multiple Dirac cones with tunable gaps in the electronic structure. Furthermore, we elucidate that electron correlations and carrier doping turn the multiple-Dirac semimetal into a topological ferromagnet with high Chern number. Our findings raise the honeycomb-monolayer TMTs to a new paradigm to explore correlated Dirac electrons and topologically-nontrivial magnetism. In turn, the unique wide-ranging properties of the materials will deliver new building blocks for atomically thin heterostructures.

Graphene analogue in (111)-oriented BaBiO3 bilayer heterostructures for topological electronics

Topological electronics is a new field that uses topological charges as current-carrying degrees of freedom. For topological electronics applications, systems should host topologically distinct phases to control the topological domain boundary through which the topological charges can flow. Due to their multiple Dirac cones and the π-Berry phase of each Dirac cone, graphene-like electronic structures constitute an ideal platform for topological electronics; graphene can provide various topological phases when incorporated with large spin-orbit coupling and mass-gap tunability via symmetry-breaking. Here, we propose that a (111)-oriented BaBiO3 bilayer (BBL) sandwiched between large-gap perovskite oxides is a promising candidate for topological electronics by realizing a gap-tunable, and consequently a topology-tunable, graphene analogue. Depending on how neighboring perovskite spacers are chosen, the inversion symmetry of the BBL heterostructure can be either conserved or broken, leading to the quantum spin Hall (QSH) and quantum valley Hall (QVH) phases, respectively. BBL sandwiched by ferroelectric compounds enables switching of the QSH and QVH phases and generates the topological domain boundary. Given the abundant order parameters of the sandwiching oxides, the BBL can serve as versatile topological building blocks in oxide heterostructures.

Na2C monolayer: a novel 2p Dirac half-metal with multiple symmetry-protected Dirac cones.

A Dirac half-metal material, which has a gapped band structure in one spin channel but Dirac cones in the other, combines two intriguing properties of 100% spin polarization and massless Dirac fermions and has recently started to attract increasing attention. In this work, using first-principles calculations we predict that the disodium carbide (Na2C) monolayer is an intrinsic 2p Dirac half-metal material with 12 fully spin-polarized and symmetry-protected Dirac cones, and a slightly gapped (53 meV) spin-polarized nodal line coexisting in one spin channel, leaving the other spin channel insulated with a gap of 1.9 eV. There are two kinds of Dirac cones in Na2C, protected by different crystalline symmetries, both of which are robust against biaxial strains (±5%) and spin-orbit coupling effects, with Fermi velocities of up to 5.2 × 105 m s-1. Ferromagnetism is mainly contributed to by the unpaired 2p electrons in the carbon, with a Curie temperature estimated to be 382 K, and the origin of the 2p magnetism could be explained by the superexchange mechanism between C2- anions with the Na+ cation as a bridge. Our results not only indicate a promising candidate for high-speed spintronic devices, but also reveal the hidden mechanism of the origin of symmetric protection and ferromagnetic exchange interactions in a Dirac semi-metal, which would provide a feasible strategy for the design of Dirac materials.