Graphite–hexagonal diamond hybrid with diverse properties

Elemental carbon via sp-, sp²-, and sp³-hybridizations can form numerous allotropes with various bonding-determined properties,^1,2 such as the sp³-hybridized ultrahard and insulating diamond, and the sp²-hybridized electrical conductive graphite. In particular, two-dimensional sp²-hybridized graphene has displayed fascinating electronic properties such as Dirac cone and the topological physical feature and has triggered a major research enthusiasm.³ It is expected that carbon materials with coexistent sp²- and sp³-hybridizations may possess unique physical properties contributed from both hybridizations, providing a promising route to broader functionality. One way to this mixed hybridization can occur at the atomic level, where differently hybridized C atoms form a series of crystals, such as T6-carbon, m-C8, Orthorhombic C36, and T-Carbon ranging from insulator to semiconductors and metals.^4–13 This kind of mixed hybridizations (at atomic level) also exists in graphite-like and diamond-like amorphous carbons.^14–17 At a higher scale, mixed hybridizations can be realized in carbon materials, such as graphite/diamond and graphene/diamond composites.^18–21 For example, graphite can be formed on the surface of diamond through high-pressure high-temperature treatment²² and chemical vapor deposition with metallic catalyst.^23,24

Recently, a new type of carbon materials, hybridized graphite and diamond, has been prepared,^25–29 potentially with the advantages of both graphite and diamond. The integration of graphite and diamond may produce a variety of interfaces in the composite. In addition to the Van der Waals interface (without the formation of chemical bonds), the interface can be incoherent, semi-coherent, or coherent depending on the specific bonding relation across the interface. For example, an incoherent interface is featured with the complex and irregular correspondence between carbon layers in graphite and diamond;²¹ a semi-coherent interface in type-2 diaphite is characterized with the correspondence between four carbon layers in graphite to six (or three layers) in diamond.²⁶ Most recently, we identified coherent interfaces with one-to-one correspondence between the atomic layers in graphite and diamond in a graphite–diamond hybrid (termed as Gradia).²⁹ The transformation from graphite to diamond under static compression can occur through the formation of the coherent interface and subsequently the advance of the interface.²⁹ Interestingly, Gradia containing abundant graphite–diamond interfaces and variable graphite/diamond sizes shows a variety of properties that would be inaccessible for diamond and graphite alone, such as the excellent mechanical properties and tunable electronic properties.^27,29 Moreover, Gradia-CO was predicted an intrinsic superconductor with a T_c of 39 K.³⁰ 

In this work, the properties of graphite–hexagonal diamond hybrids were investigated on the basis of the first-principles calculations. With varying graphite width, these hybrids show rich electronic properties, including topological nodal-line semimetal, narrow-bandgap semiconductor, and normal metal as well as tunable mechanical properties. More importantly, these charming electronic structures and excellent mechanical features can be regulated by the size of graphite part, which can be achieved through controlled compression and decompression. This study is curial in understanding the properties of graphite–diamond hybrid and opening the path to potential applications.

The first-principles calculations were performed within the density functional theory (DFT) as implemented in QUANTUM ESPRESSO³¹ and ABINIT packages.^32–34 The exchange-correlation effect was described by the Perdew–Burke–Ernzerhof³⁵ parameterized generalized-gradient approximation (PBE-GGA). The phonon spectra and electron–phonon coupling were calculated using the density functional perturbation theory (DFPT).³⁶ The anisotropic electronic transport characteristics of metal and semiconductors were studied using ABINIT and QUANTUM ESPRESSO, respectively. The electron–phonon coupling with dense k- and q-grids was produced using QUANTUM ESPRESSO's maximally localized Wannier functions (MLWFs) interpolation and ABINIT's Fourier interpolation.^37–40 The calculations of nodal lines and the surface states based on maximally localized Wannier functions were done using the WannierTools package.⁴¹ 

A new three-dimensional graphite–hexagonal diamond hybrid structure, named Gradia-HZ, was constructed based on our previous research.^27,29,44 In Fig. 1(a), the atoms in hexagonal diamond (HD) part and graphite (G) part are colored in blue and red, respectively. The structure can be considered as a bulk superlattice composed of graphite-like and HD units. We labeled this structure as Gradia-HZ(m, n), where m is the number of six-numbered rings to be formed between adjacent layers in graphite domain and n is the number of six-numbered rings formed in the hexagonal diamond domain as reported in our previous works.^28–30 The coherent junction is (210)_HD, and the two domains have the orientation relationship of [210]_G//[001]_HD. Obviously, Gradia-HZ is different from Gradia-HB and Gradia-HC,²⁹ where G and HD units exhibited an orientation relationship of [010]_G//[010]_HD (see supplementary material Fig. S1). Note that there are two interlayer distances (Δd₁ = 3.12 Å and Δd₂ = 3.60 Å) between adjacent graphite layers, alternately distributing along the a-direction. The armchair edge of each graphite layer, commonly known for graphene, is connected to HD, as illustrated by the green dotted line in Fig. 1(a) from an appropriate view angle of Gradia-HZ(m, n). Here, we systematically study the physical properties of Gradia-HZ(m, n) with m and n vary from 2 to 6, including mechanical properties, electronic structures, and electronic transport properties.

The stability of the hybrid structures was confirmed by molecular dynamics simulation and phonon dispersion. As shown in Fig. 1(b), the total energies of Gradia-HZ(2,2), Gradia-HZ(3,2), and Gradia-HZ(4,2) show oscillation behaviors within a small energy range during the long-time molecular dynamics simulations at 300 K, with no sign of C–C bond breaking and structural instability (see the supplementary material for molecular dynamics simulations at 1000 K, Fig. S2). The absence of imaginary frequency in phonon dispersion [Fig. 1(c)] indicated the dynamic stability of Gradia-HZ(2,2), Gradia-HZ(3,2), and Gradia-HZ(4,2).

The mechanical characteristics of Gradia-HZ, such as elastic modulus, bulk modulus (B), shear modulus (G), Young's modulus (E), etc., are estimated from the elastic constants with the Voigte–Reusse–Hill approximations.⁴⁵ As shown in Fig. 2, both B and G increase with increasing HD percentage. For example, B and G of Gradia-HZ(2,6) with the highest diamond proportion are both about 360 GPa, indicating incompressibility and resistance to shear deformation. The Vickers hardness (H_v) of Gradia-HZ was also calculated with the microscopic hardness model.⁴⁵ Like B and G, the Vickers hardness increases with increasing HD percentage [Fig. 2(c)]. Again, Gradia-HZ(2,6) shows the maximum H_v of 59.3 GPa, only slightly lower than that of T-carbon (61.1 GPa) and cubic BN (64.5 GPa).^9,46 The yellow line in Fig. 2(c) highlights the superhard threshold (H_v > 40 GPa) of Gradia-HZ(m, n).

Based on the calculated electronic properties, Gradia-HZ(m, n) can be categorized into three groups, i.e., topological nodal-line semimetal, semiconductor, and normal metal, which are represented by Gradia-HZ(2,2), Gradia-HZ(3,2), and Gradia-HZ(4,2) in Fig. 3, respectively. For Gradia-HZ(2,2), there are several bands crossings with a linear dispersion around the Fermi level, originating from the graphite component in the crystal. The calculated topological properties show that the linear band crossings form the nodal lines in the Brillouin zone, as discussed later. Furthermore, the presence of linear band crossings remains unchanged with the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional (see supplementary material Fig. S3), indicating an intrinsic semi-metallic feature of Gradia-HZ(2,2). With one more armchair edge added in the graphite part, the band crossings disappear in Gradia-HZ(3,2); meanwhile, an indirect bandgap of 0.52 eV created with the valence band maximum (VBM) and conduction band minimum (CBM) located at X (0.5, 0.0, 0.0) and Z (0.0, 0.0, 0.5), respectively [Fig. 3(b)]. Further broadening the graphite part by adding another armchair edge leads to Gradia-HZ(4,2), a typical metal with a peak DOS at the Fermi level [Fig. 3(c)].

Topological nodal-line semimetal, semiconductor, and normal metal arise, in turn, from Gradia-HZ(2,2) to Gradia-HZ(6,2) when the width of the graphite component grows, as shown in Fig. 3(f) [see the supplementary material for the band structures of other Gradia-HZ(m, n), Figs. S4–S8]. Notably, the electronic states around the Fermi level or near the bandgap in the three types of materials are primarily derived from the graphite part. In comparison, the electronic states contributed from HD part are far from the Fermi level, as illustrated by the gray lines of the band structures in Fig. 3. Therefore, this cyclic evolution is mainly caused by changes in the electronic structure of armchair graphite nanoribbons with varying widths. It is well known that the bandgap of armchair graphite nanoribbons varies periodically with the width and closes at the appropriate width, which can be understood with the ladder network.^47,48 Connecting HD to graphite in Gradia-HZ produces sp²-hybridized C–C bonds with the length of approximately 1.41 ± 0.01 Å, which benefits the closure of bandgap and is different from the obvious change caused by the passivation of dangling bonds with H atoms.⁴⁹ For Gradia-HZ(m, n), m = 2, 3, and 4 correspond to the graphite part with 1, 2, and 3 armchair rows, respectively. The graphite width of nodal-line Gradia-HZ (m = 2 or 5) is the same as that of armchair graphite nanoribbons with the closed bandgap. While it is reasonable to extend this law to larger graphite width (m > 6) for Gradia-HZ, the law is absent for Gradia-HB with zigzag graphite nanoribbons (see supplementary material Fig. S1). In addition, the change in the diamond width does not affect the electronic properties of Gradia-HZ(m, n) apparently. For example, Gradia-HZs with m = 2 are all topological nodal-line semimetals, while those with m = 3 are narrow-bandgap semiconductors. Yet, the proportion of HD part does affect the bandgap of the semiconductors, such as bandgap size and positions of VBM or CBM (see supplementary material Figs. S4–S8).

The electronic structure analysis of Gradia-HZ(2,2) indicates that the bands near the Fermi level are primarily contributed from the out-of-plane orbitals of the graphite part. The touchpoints between valence and conduction bands in the reciprocal space yield linear crossing points, which form four continuous nodal lines [Fig. 3(d)], evidencing Gradia-HZ(2,2) as a topological nodal-line semimetal. Two lines are located near k_x = 0.5, while the other two are located near k_x = 0 [see the supplementary material for the three-dimensional (3D) band structures near the Fermi level, Fig. S9]. These nodal lines are protected by space-inversion and time-reversal symmetry (PT) due to the P-1 symmetry of Gradia-HZ(2,2) (space group No. 2). Therefore, Gradia-HZ(2,2) is a type-B topological nodal line semimetal,⁵⁰ similar to the topological property of bco-C16.⁵¹ Moreover, the surface electronic structure was further computed to investigate the topological electronic features of Gradia-HZ(2,2). When the electronic structure is projected onto the (010) surface, topologically protected surface states are generated around the Fermi level, which dictate the characteristics of topological nodal lines, as shown in red in Fig. 3(e). From the calculations of Z₂ topological invariance of six time-reversal invariant planes after considering spin–orbital coupling, Z₂ topological index (1;101) ensures that Gradia-HZ(2,2) is a topological insulator, similar to other type-B nodal-line semimetals.⁵⁰ 

We calculated the phonon-limited electronic transport properties of three representative Gradia-HZ(m, n), including the electrical resistivity of semimetal and normal metal, and the carrier mobility of semiconductor. The transport spectrum function, α_tr²F(ω), for Gradia-HZ(2,2) nodal-line semimetal indicates that phonons in three frequency ranges (i.e., the obvious phonon bands at 400, 1200, and 1400 cm⁻¹) have considerable scattering effects on the electrons, as shown in Fig. 4(a). Particularly, low-frequency phonon scattering along the b-direction (armchair direction of graphene nanoribbons) is visibly lower than the other two directions, but the difference in the high-frequency range is not obvious. With only phonon scattering being considered, Gradia-HZ(2,2) has a room-temperature electronic relaxation time (τ) along b-direction (approximately 138 fs) substantially longer than those along a and c directions, as illustrated in Fig. 4(b). As mentioned earlier, the electronic states near the Fermi level mainly come from the sp²-hybridized C atoms in graphite part. Along the a-direction, the insulator HD obviously weakens the overlap of the conducting electronic wave packets, and the interlayer vacuum is the main factor to weaken the wave packet overlap along the c-direction. Due to the restriction of HD part or the interlayer gap between graphite layers, the electronic transport in a- and c-directions is inferior. The obvious anisotropy indicates a quasi-one-dimensional (1D) characteristic, which also exists in semiconductor Gradia-HZ(3,2) and metal Gradia-HZ(4,2) (see more details later). The room-temperature resistivity (ρ) is predicted to be 3.8 × 10⁻⁸ Ω m along the b-direction for Gradia-HZ(2,2), close to that of aluminum (2.83 × 10⁻⁸ Ω m). The electronic relaxation time attenuates noticeably with increasing temperature, leading to a quick increase in ρ, as demonstrated in Figs. 4(b) and 4(c). Furthermore, the long electronic relaxation time along the b-direction also contributes to a high electronic thermal conductivity (see supplementary material Fig. S10). In Gradia-HZ(2,3), the larger HD part does not show significant influence on the electronic transport along the b-direction. Instead, it weakens the overlap of conducted electron wave packets contributed by the graphite part, thus increasing the resistivity along the a-direction (see supplementary material Fig. S11).

The carrier transport features are analyzed for the semiconductor Gradia-HZ(3,2). From the electronic structure, it is obvious that one roughly parabolic band edge locates around VBM at X point; meanwhile, many bands exist adjacent to CBM and result in more complex band structures and electronic states. Correspondingly, more scattering processes would occur near CBM, and electron scattering rates are higher than those of hole, as shown in Fig. 4(d). Furthermore, with elevating temperature, more high-frequency phonons participate in the electron–phonon scattering, increasing the scattering rates even further. The room-temperature carrier mobility of electron and hole in Gradia-HZ(3,2) along the b-direction is 1088 and 1527 cm²/V s, respectively, as shown in Figs. 4(e) and 4(f). Finally, we calculated the resistivity of Gradia-HZ(4,2) with wider graphite part. Compared with the nodal-line semimetal Gradia-HZ(2,2), the scattering effect of low-frequency phonons of Gradia-HZ(4,2) is negligible, as revealed from the transport spectrum function [Fig. 4(g)]. Furthermore, the peak of α_tr²F(ω) occurred at frequency range (1300–1600 cm⁻¹) higher than that of Gradia-HZ(2,2), with much reduced values. As the result, Gradia-HZ(4,2) tends to have a substantially longer electronic relaxation time [Fig. 4(h)], e.g., 2245 fs along the b-direction at room temperature. Correspondingly, the electrical resistivity reached 1.38 × 10⁻⁸ Ω m, even lower than that of gold, silver, and copper [Fig. 4(i)].

Gradia-HZ applications await the establishment of an executable route to accurate regulation of graphite width for the tunable electronic structure.⁴⁴ As one of the promising methods of materials synthesis, we explore the structure and physical properties of semiconducting Gradia-HZ(6,6) under hydrostatic pressure. As the pressure steadily rises to 30 GPa, carbon atoms form new sp³ bonds across neighboring layers at the graphite edge, resulting in diamond growth at the expense of graphite part. Higher pressure at 35 and 38 GPa advances the coherent interfaces into graphite part steps further. Specifically, Gradia-HZ(6,6) transforms into Gradia-HZ(5,7), Gradia-HZ(4,8), and Gradia-HZ(3,9) at pressure of 30, 35, and 38 GPa, respectively, which are retainable to ambient pressure, as shown in Fig. 5. The calculated electronic structures [Fig. 5(d)] at ambient pressure indicate that they are nodal-line semimetal, normal metal, and semiconductor, respectively, consistent with the evolution of electronic properties with varying graphite width [Fig. 3(f)]. Moreover, according to the summary of mechanical properties (Fig. 2), increasing diamond proportion can enhance the mechanical properties of Gradia-HZ. Therefore, a relative change in graphite proportion (e.g., via structural phase transition under high pressure) may induce intriguing cyclic evolution of electronic properties among semimetal, semiconductor, and normal metal. We also study the effect of uniaxial strain in the direction perpendicular to the interface. Large tensile strain can break the C–C bonds near the interface and results in the graphitization of HD, which can be recovered by applying compressive strain afterward (see supplementary material Fig. S12). These Gradia-HZ structures with diverse and interesting properties call for further research works in materials synthesis, purification, and characterization. Due to the thermal stability issue (HD is less stable than cubic diamond), it is challenging to find large HD sections in current experiments. Based on the proposed phase transformation mechanisms, more HD sections may be retained with appropriately increased pressure to minimize the phase transition temperature, thus increasing the likelihood to obtain Gradia-HZ. Furthermore, advanced sample preparation techniques, such as focused ion beam (FIB), can be utilized to extract pure Gradia-HZ phases from multiphase samples, enabling the realization of the unique electrical properties predicted in this work. Previously, we prepared Gradia possessing complex interface structures and different graphite–diamond orientational relations, resulting in diverse metal–semiconductor, semimetal–semiconductor, and semimetal–metal combinations that may bring in more abundant physical phenomena. It is expected that Gradia, with the advantages of properties combination and multifunctionality, will expand its applications to a great range of research areas.

We have extensively investigated the physical properties of Gradia-HZ with varying unit cell and graphite/diamond proportions, such as elastic constants, electronic structures, and electronic transport properties. The Vickers hardness of Gradia-HZ with a small graphite part can exceed 40 GPa, showing a superhard material character. Furthermore, increasing the width of graphite part in Gradia-HZ unit cell leads to the cyclic evolution of materials electronic properties, from nodal-line semimetal to semiconductor to normal metal, which can be attributed to the bandgap variation of armchair graphene nanoribbons regulated by the ribbon width. The electronic transport properties computations indicate desirable properties for three types of materials, such as the excellent carrier mobility comparable to Si for Gradia-HZ semiconductors, and the extreme resistivity even lower than that of gold, silver, or copper for Gradia-HZ metals. The pressure-induced structural phase transformation may regulate the graphite width in Gradia-HZ and realize transition among semimetal, semiconductor, and normal metal.

See the supplementary material for the stiffness tensor of Gradia-HZ(6,6), lattice structure and band structure of Gradia-HB, molecular dynamics simulation at high temperature, band structure of Gradia-HZ(2,2) obtained using HSE06 functionals, the band structures of Gradia-HZ(m,n) obtained using PBE functionals, 3D band structures of Gradia-HZ(2,2) near the Fermi level, electronic thermal conductivity of Gradia-HZ(2,2), electronic transport of Gradia-HZ(2,3), and structural transition of Gradia-HZ(6,6) under uniaxial strain along the direction perpendicular to the graphite–diamond interfaces.

This work was supported by the National Natural Science Foundation of China (Nos. 52288102, 52090020, 11904312, 21873017, 52202071, 91963203, U20A20238, 52025026, 52073245, and 51722209), the National Key R&D Program of China (Nos. 2018YFA0305900 and 2018YFA0703400), the Innovation Capability Improvement Project of Hebei province (No. 22567605H), the Natural Science Foundation of Jilin Province (No. 20190201231JC), the Hebei Natural Science Foundation (Nos. B2021203030, E2022203109, and A2022203006), Talent Research Project in Hebei Province (No. 2020HBQZYC003), and Science and Technology Project of Hebei Education Department (No. BJK2022002).

The authors have no conflicts to disclose.

Yanfeng Ge and Kun Luo contributed equally to this work.

Yanfeng Ge: Investigation (equal); Writing – original draft (equal). Guoying Gao: Writing – review & editing (equal). Xiang-Feng Zhou: Writing – review & editing (equal). Zhisheng Zhao: Conceptualization (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Bo Xu: Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Yongjun Tian: Funding acquisition (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Kun Luo: Data curation (equal); Investigation (equal); Writing – original draft (equal). Yong Liu: Writing – review & editing (equal). Guochun Yang: Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Pan Ying: Writing – review & editing (equal). Yingju Wu: Methodology (equal); Writing – review & editing (equal). Ke Tong: Writing – review & editing (equal). Bing Liu: Writing – review & editing (equal). Baozhong Li: Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.