Pressure-induced superconductivity in hypercoordinated 5p-block element nitrides MN₆ (M = Sb, Te, I)

INTRODUCTION

The metallization of nitrogen (N) has long been considered particularly challenging due to extreme stability of triple-bonded molecular nitrogen. However, over the past 20 years, it has been shown that the physical and chemical properties of nitrogen significantly change at high pressure^[1,2]. The outer-shell electrons of nitrogen tend to delocalize upon strong compression, which directly leads to the dissociation of molecular nitrogen to form more close-packed polynitrogen structures^[3-6]. Theoretically, pressure-induced nonmetal-to-metal transition in solid nitrogen has been predicted, including the layered black phosphorus phase^[7], the cis-trans and Cmcm chain structures^[5,8], and a potentially superconducting Pnnm phase^[9]. Unfortunately, all the predicted metallic nitrogen phases are metastable structures. Thus far, the metallization of solid nitrogen at high pressure has not yet been verified, although a transition from insulating to conducting has been experimentally demonstrated in dense fluid nitrogen above 125 GPa and 2,500 K^[10,11].

Nitrogen-rich compounds provide an alternative route to the synthesis of solid nitrogen^[12-17]. In particular, various polynitrogen structures occur as a result of the interaction between secondary element and nitrogen under high pressure, which are stabilized in the form of polyanion and result in the anion-driven metallicity. Consequently, Aslandukov et al. synthesized two metallic YN₆ and Y₂N₁₁ with unique N₁₈ macrocycle and polynitrogen double helix structure at 100 GPa and 3,000 K in a laser-heated diamond anvil cell (DAC)^[18]. Conjugated polymeric nitrogen chains and dumbbell units were identified in rhenium nitride ReN₁₀ and Re₂N₄, exhibiting metallicity properties^[19]. The single-bond nitrogen framework and dinitrogen units were stabilized in metallic TaN₅ and WN₁₀^[20,21]. Obviously, anion-driven metallicity has been a regular phenomenon for high-pressure nitrides, except for the transition metal nitrides; it is mainly focused on the alkali metal and alkali earth metal element nitrides^[22-24]. Worth noting is that the planer N₆ hexazine rings have been predicted several times in alkali metal and alkali earth metal nitrogen-rich compounds, such as LiN₃, KN₃, RbN₃, and BaN₆^[25-28]. Following the theoretical research, Wang et al. successfully prepared metallic planar N₆ hexazine dianions that stabilized in K₂N₆^[29]. Recently, Laniel et al. realized the synthesis of the plane aromatic hexazine N₆ anion in the metallic structure of high-pressure potassium nitrogen compound K₉N₅₆^[30].

Compared with the anion-driven metallicity in binary metal-nitrogen compounds of alkali, alkaline earth, and transition metal elements, the high-pressure chemistry and physical properties of p-block element nitrides are quite different. Although the metallic and even superconductive B₄N, PN₃, SN₄, and SeN₃ have been theoretically predicted^[31-34], the strong electronegativity^[35] of the p-block elements makes them prone to form covalent bonding with nitrogen. For this reason, the conventional wisdom holds that p-block element nitrides are undesirable for developing polymeric nitrogen framework topologies^[15]. However, high pressure enables a direct interaction of N₂ and Xe (5p-block element) to form XeN₆ with a three-dimensional covalent bonding network, in which the N atoms are polymerized into a chair-like N₆ hexazine ring, but unfortunately, it exhibits non-metallicity^[36]. Therefore, other candidate p-block elements need to be explored for enlarging and enriching metallic nitrogen structures under compression. Antimony (Sb), tellurium (Te), and iodine (I), as typical 5p-block elements, have large atom sizes and moderate electronegativity, which makes them distinct from the lighter p-block elements and allows them to coordinate with more atoms at high pressure^[37-39]. Furthermore, flexible electronic properties can provide a unique bonding environment, making Sb, Te, and I anticipated to be ideal candidates for inducing novel nitrogen structures with metallicity.

Herein, we introduce a new class of 5p-block element nitrides with novel structure and exotic properties. An extensive structure prediction at high pressure was performed using the CALYPSO code, and we uncovered a nitrogen-based superconductor MN₆ (M = Sb, Te, I) with distorted N₆ hexazine rings and hypercoordinated features. Under high pressure, the vacant 5d orbitals of the 5p-block elements become valence orbitals and participate in the covalent bonding with N atoms. First-principles calculations for different 5p-block element nitrides MN₆ predict diverse T_c values among the same stoichiometry, in which TeN₆ has a noteworthy T_c of 36.8 K at 100 GPa. Crucially, we reveal the superconducting mechanism of 5p-block element nitrides. High T_c is attributed to the strong electron-phonon coupling (EPC) derived from the phonon softening and the hybridized electronic states between N and 5s and 5p orbitals of 5p-block elements, while the pressure-induced 5d electron is negatively correlated with the superconductivity.

METHODS

Structural optimization and total energy calculation were based on density functional theory (DFT) with the implementation of the Vienna ab initio simulation (VASP) code^[40,41]. The exchange-correlation functional was given by Perdew-Burke-Ernzerhof (PBE)^[42] of generalized gradient approximation (GGA)^[43]. Electron-ion interactions were represented employing the all-electron projector augmented wave (PAW) method^[44] with 5s²5p³ valence configurations for Sb, 5s²5p⁴ for Te, 5s²5p⁵ for I, and 2s²2p³ for N. Electronic wavefunctions were expanded using a plane wave basis set with a cutoff of 520 eV. Monkhorst-Pack grids were generated per cell with a reciprocal space resolution of 2π × 0.03 Å^-1, ensuring that the enthalpy calculations converged to better than 1 meV per atom. Electron localization function (ELF) was calculated by VASP and displayed by the Visualization for electronic and structural analysis (VESTA)^[45]. Ab initio molecular dynamics (AIMD) simulations within the canonical ensemble (NVT) were used to examine the thermal stability at 300 K and 1,000 K for 5,000 fs^[46]. Chemical bonding analyses were carried out using the crystal orbital Hamilton population (COHP) as implemented in the LOBSTER package^[47]. The three-dimensional Fermi surface (FS) was depicted using the FermiSurfer software^[48].

Phonon dispersion and EPC calculation were performed with the Quantum-ESPRESSO package^[49], where the structure is fully re-optimized from the results of PAW. Based on convergence tests, we adopted an appropriate kinetic energy cutoff of 80 Ry and a 12 × 12 × 12 Monkhorst-Pack mesh for Brillouin zone integration. The ultrasoft pseudopotentials of Sb, Te, I, and N were used. Phonon dynamic matrix elements were performed in the first Brillouin zone on a 6 × 6 × 6 q-mesh. To ensure the convergence of the EPC matrix elements for the electron-phonon interaction coefficients, a large 24 × 24 × 24 q-mesh was required. Here, The EPC parameter λ can be defined as the first reciprocal moment of the spectroscopic function α²F(ω)^[50]:

where q is a wavevector in the first Brillouin zone, j is the phonon mode label, and ω_qj is the phonon frequency of mode qj. Other important frequency moments are defined as:

where the ω_log is the logarithmic average phonon frequency, and $$ \left \langle \omega ^{2} \right \rangle $$ represents the average phonon frequency.

RESULTS AND DISCUSSION

Extensive structure searches were performed in binary 5p-block element nitrides M_xN_y (M = Sb, Te, I) with different stoichiometric ratios to predict stable structures^[51,52], ultimately focusing on the most characteristic nitrogen-rich compounds MN₆ at 100 GPa. Detailed descriptions and results for the structure prediction are displayed in Supplementary computational details, Supplementary Figure 1 and Table 1. Conspicuous in the predicted crystal structure of the 5p-block element nitrides MN₆ is the chair-like N₆ hexazine ring, which crystallizes in a rhombohedral primitive cell with $$ R\bar{3}m $$ space group symmetry [Figure 1A and B]. The 5p-block elements are occupied at the vertex position of the primitive cell and hypercoordinated with twelve N atoms from eight hexazine N₆ rings to form an MN₁₂ icosahedral cage [Figure 1C], which is the building block in the construction of the three-dimensional crystal structure. Within the chair-like N₆ hexazine ring, N atoms adopt sp³ hybridization to form a fourfold coordination structure, which is substantially different from the typical sp² hybridization caused by the alternating single-double bonding patterns on well-known hypothetical planar N₆ hexazine ring^[53,54]. The structural stability of 5p-block element nitrides MN₆ was preliminarily verified by elastic constants calculation [Supplementary Table 2] and molecular dynamic simulation [Supplementary Figure 2]. Subsequently, we focus our analyses mainly on TeN₆ to exhibit its prominent properties while also discussing crucial data and change trends involving other MN₆ compounds.

Figure 1. Crystal structure of 5p-block element nitrides MN₆ (M = Sb, Te, I). (A) MN₆ has $$ R\bar{3}m $$ space group; (B) Rhombohedral primitive cell structure without showing any M–N bonds, and the chair-like N₆ hexazine ring is located in the center; (C) The hypercoordinated MN₁₂ icosahedral cage. The large pink spheres and small yellow spheres represent the 5p-block elements and nitrogen, respectively.

We first examine the high-pressure electronic structure and chemical bonding of TeN₆. As shown in Figure 2A, the contour plots of the ELF are projected on the (111) plane, cutting through the center of the N₆ hexazine ring. Regions with ELF values of 0.85 are found to localize between N atoms in the N₆ hexazine ring, showing evidence for N–N covalent bonding. A hypothetical N₆ hexazine ring structure (Te₀N₆) is constructed by removing Te from the lattice of TeN₆ and leaving the N sublattice unchanged. Compared with the ELF of TeN₆, the original lone electron pairs of N in the hypothetical N₆ hexazine ring [Figure 2A, middle] collapse and form covalent bonding with Te atoms, which is extremely similar to that of N in XeN₆^[36]. Intriguingly, the chair-like N₆ hexazine ring transforms into a planar ring after structural relaxation but remains in the original N sublattice [Figure 2A, right], directly proving that the introduction of 5p-block element Te causes structural distortion of the N₆ hexazine ring. A covalent interaction with an ELF of 0.89 between the N atoms in the planar ring is stronger than that in the chair-like N₆ hexazine ring (0.85), which results from the accommodation by the N₆ ring of excess electrons from Te. We employ the quantum theory of atoms in molecules (QTAIM) to quantify the number of transferred charges in TeN₆^[55], and Bader charge analysis reveals that the N₆ hexazine ring accepts ~2.4 e from the nearly Te atoms. These electrons reside in the N–N antibonding π* orbitals, prolongating the N–N bond length and weakening the N–N bonding, thereby decreasing the repulsion of lone electron pairs of N and finally stabilizing the distorted N₆ hexazine ring in TeN₆.

Figure 2. Electronic structures and chemical bonding of TeN₆. (A) ELF of TeN₆ (left), Te₀N₆ (middle), and relaxed N₆ hexazine ring (right). Its value ranges from 0 to 1, and the closer to 1, the stronger the electron localization, corresponding to the region of bonding and the lone electron pairs; (B) Electron band structure; (C) PDOS; (D) pCOHP of Te–N pairs, the negative and positive -pCOHP values denote antibonding and bonding interactions, respectively. Horizontal dotted lines indicate the Fermi level. ELF: electron localization function; PDOS: projected density of states; pCOHP: projected crystal orbital Hamilton population.

The stable TeN₆ exhibits metallic features, corresponding to two distinct bands (labeled band I and band II) crossing the Fermi level (E_F) and dispersing from about 2 eV below E_F to 3 eV above E_F in the electron band structures [Figure 2B]. The projected density of states (PDOS) shows that the N atoms make a substantial contribution to the conduction bands [Figure 2C]. Moreover, obvious hybridizations between N and Te 5s, 5p, and 5d orbitals near the E_F indicate that in addition to the 5s and 5p electrons of Te, the pressure-induced 5d electrons also participate in the chemical bonding of nitrogen-rich compound TeN₆. The calculated COHP is displayed in Figure 2D, in which the fully occupied bonding states and partially occupied antibonding states lend strong support to the N–Te 5s, N–Te 5p, and N–Te 5d covalent bonding within the TeN₆. Therefore, Te not only has the basic properties of typical 5p-block elements but also exhibits electron occupation characteristics similar to those of d-block transition metal elements under high pressure.

In fact, a primitive cell of TeN₆ can be seen as composed of a N₆ hexazine ring and a Te atom [Figure 1B], its electron band structure near the E_F is modified from N₆ due to the hybridization between N and Te 5s, 5p, and 5d orbitals. Supplementary Figure 3 presents the electronic band structure of Te₀N₆, where two conduction bands are half-filled. The introduction of Te adds approximately two electrons to the N₆ hexazine ring, partially occupying the degenerate band near the E_F in TeN₆ [Figure 2B]. The occupancy of the degenerate band causes the electronic state to have orbital degeneracy, which is affected by the Jahn-Teller effect (JTE). Conventional JTE involves the coupling of electron and nuclear degrees of freedom and states that stability and degeneracy are not possible simultaneously unless all the nuclei in the equilibrium configuration lie on a straight line^[56]. In short, the orbitally degenerate state means potential instability that causes the spontaneous distortion characteristic of the JTE^[57]. Herein, the N₆ hexazine ring undergoes structural distortion and reduces the symmetry of the original configuration (from a planar ring with D_6h symmetry to a chair-like ring with D_3d symmetry), thereby lifting the orbital degeneracy and enhancing the structural stability. It is worth mentioning that the dynamic JTE is particularly favorable for superconductivity, which has been employed to explain the superconductivity in high-pressure hydride cI14-CaH₆ and B-doped diamond^[58,59]. Furthermore, a Van Hove singularity (VHS) near the E_F in the PDOS of TeN₆ [Figure 2C] corresponds to the flat band structure at L, but the bands passing through the E_F along the Γ–L and P2–Γ directions are steeping [Figure 2B]. The existence of the VHS and Flat/Steep band indicates that TeN₆ may be a potential high-temperature superconductor.

To investigate this possibility, EPC calculations were performed for the nitrogen-rich compound TeN₆ at 100 GPa. The phonon dispersion results are depicted in Figure 3A; the absence of imaginary frequencies in the entire Brillouin zone indicates the dynamical stability of this compound. Two gaps separated the phonon dispersion curves into three regions [Figure 3B]: the low-frequency acoustic branches are associated with the lattice vibrations of Te owing to its large atomic mass (0~215 cm^-1), the high-frequency optical branches correspond to the vibrations of N atoms (980~1180 cm^-1), whereas the mid-lying region is attributed to the strong interaction between Te and N atoms. By analyzing the Eliashberg spectral function α²F(ω), it can be concluded that the combined contribution of three regions (6%, 53%, and 41%, respectively) gave an EPC parameter λ of 1.01 [Figure 3C]. The vibration of the mid-frequency region plays a dominant role in EPC, which is derived primarily from the twofold degenerate E_g modes along the Γ–P2 direction (474 cm^-1 and 605 cm^-1). Incidentally, these bands are the rock and breathing vibrations between I and N atoms, leading to the distortions in the N₆ hexazine ring structure. In addition, the contribution of lattice vibrations in the low-frequency region cannot be ignored, which will be discussed later. Superconducting critical temperature T_c is evaluated through the following Allen-Dynes modified McMillan equation^[60]:

Figure 3. EPC in TeN₆. (A) Phonon dispersion curve. Blue circles represent the q-resolved EPC parameter λ_q; the radii of circles are proportional to the strength; (B) PHDOS. The illustrations and percentages are the contribution of the vibration modes to the EPC parameter λ; (C) Eliashberg spectral function α²F(ω) and integral EPC parameter λ(ω) as a function of frequency. EPC: electron-phonon coupling; PHDOS: phonon density of states.

where the ω_log is calculated logarithmic average phonon frequency, and μ^* is Coulomb pseudopotential. At 100 GPa, the predicted T_c of nitrogen-rich compound TeN₆ reaches 36.8 K, close to the McMillan limit (40 K). The EPC calculations are also performed for 125 GPa and 150 GPa, and the pressure evolution of important parameters involved with the superconductivity of TeN₆ are displayed in Supplementary Table 3. There is a negative pressure dependence of T_c (28.6 K at 125 GPa and 20.8 K at 150 GPa), with a pressure coefficient (dT_c/dP) of -0.31 K/GPa.

A positive correlation between λ and T_c indicates that λ dominates the superconductivity of the nitrogen-rich compound TeN₆ [Figure 4A]. To elucidate the underlying superconducting mechanism, we extend the calculation of λ by adopting the simplified Hopfield expression^[60]:

Figure 4. Superconductive mechanisms of TeN₆. (A) Calculated pressure variation of superconducting critical temperature T_c and EPC parameter λ; (B) Phonon dispersion curves at different pressures; (C) Fermi surface nesting function ξ(q) along special q trajectories; (D) Three-dimensional Fermi surface and the cross-section at 100 GPa. The color bar represents the Fermi velocity on the Fermi surface; it makes blue as the minimum and red as the maximum. FSN occurs along the Γ–P2 direction (black arrow); (E) Pressure-induced variations of electronic DOS N(ε_F). Red and blue spheres represent the content of 5s, 5p, and 5d occupied orbitals in the IPDOS of atomic Te at Fermi level (s+p% and d%). FSN: fermi surface nesting; DOS: density of states; IPDOS: integral projected density of states.

where η is the Hopfield parameter, N(ε_F) is the electronic density of states (DOS) at E_F, I is the average electron-phonon matrix element, and Mω² is the average lattice force constant. In this way, the EPC is separated into the lattice-related Hopfield parameter and a purely electron-related contribution given by the DOS.

Firstly, the lattice-related Hopfield parameter η decreases with the increase of pressure (0.15 at 100 GPa and 0.10 at 150 GPa), which is consistent with the evolution of λ [Supplementary Table 3]. Comparing the phonon dispersion curves under different pressures shows a striking feature that there is an obvious phonon softening in the low-frequency acoustic branches [Figure 4B], mainly near the L point and Γ–P2 direction. Furthermore, the q-resolved λ_q is particularly strong in these softened regions [Figure 3A], indicating that soft phonon mode is beneficial to enhance EPC. In order to clearly uncover the reason for the phonon softening, we assess the Fermi surface (FS) properties in rhombohedral TeN₆ at high pressure. The three-dimensional FS is mapped at 100 GPa using Fermisurfer, and the nesting function ξ(q) is applied to describe the FS nesting (FSN). The ξ(q) in Figure 4C quantifies the overlap of FS with an image of itself shifted by a vector q^[60]:

where N is the number of k points, n and m are the indices of energy bands, and ε_k,n is the Kohn-Sham eigenvalue. As shown in Figure 4D, a wave vector q connects two parallel FS pockets along the Γ–P2 direction, labeled as a black arrow in the cross-section, which usually represents effective nesting. The calculated ξ(q) exhibits a strong feature (sharp peak) along the Γ–P2 direction with the exception of the maximum at Γ point (q = 0), demonstrating the occurrence of FSN, and this FSN disappears with increasing pressure from 100 GPa to 150 GPa [Figure 4C]. Surprisingly, the nesting direction corresponds to the phonon softening region, so it can be concluded that the soft phonon modes induced by FSN contribute to strong EPC of the nitrogen-rich compound TeN₆.

Next, we study the purely electron-related contribution to the EPC. As shown in [Figure 4E], the electronic DOS N(ε_F) gradually decreases with increasing pressure. Due to the hybridizations between N and Te 5s, 5p, and 5d orbitals near the E_F, we quantify the occupied states of electrons at E_F to further analyze the contribution of these hybridized electronic states to the EPC. The integral PDOS (IPDOS) in Supplementary Figure 4 shows that the total number of electronic states occupied by atomic Te at E_F gradually increases under compression, and the content of occupied 5s, 5p, and 5d states is quite different. Among them, the content of pressure-induced 5d states (d%) has a steady increase, while that of the 5s and 5p states (s+p%) shows a decreasing trend [Figure 4E]. The greater the content of pressure-induced 5d states, the more hybridized electronic states between N and Te 5d orbitals, significantly enhancing the covalent bonding between them. Integrated COHP (ICOHP) is used to quantitatively describe the bonding strength. The ICOHP value of Te 5d–N is negative, and its absolute value increases under compression [Supplementary Table 4]. This means that the covalent bonding between N and Te 5d orbitals gradually strengthens, contributing to the stability of the high-pressure nitrogen-rich compound TeN₆. However, the pressure dependence (positive) is opposite to that of λ (negative), hindering the improvement of EPC. Consequently, the strong EPC in nitrogen-rich compound TeN₆ mainly originates from the hybridized electronic states between N and Te 5s and 5p orbitals; the pressure-induced 5d electron of Te weakens the EPC and depresses the superconductivity.

The 5p-block elements successfully polymerize the nitrogen into the metallic and superconductive N₆ hexazine ring, opening a new avenue for further enlarging and enriching polynitrogen arrangements under compression. Unsurprisingly, Sb and I, located in the same period as Te, can also induce the superconductivity of the distorted N₆ hexazine ring [Supplementary Figures 5 and 6]; the resulting critical temperatures of SbN₆ and IN₆ are 28.4 K and 22.1 K, respectively [Figure 5A]. To the best of our knowledge, this is the first time to predict the nitrogen-based superconductor with N₆ rings, and the T_c is the highest among the known nitrides with ring-like polynitrogen structure [Figure 5B and Supplementary Table 5]. The associated EPC properties of MN₆ (M = Sb, Te, I) are listed in Supplementary Table 3, and the difference in superconducting behavior among these nitrogen-rich compounds with the same stoichiometry mainly stems from the electronic DOS at E_F. From the PDOS in Supplementary Figure 7, one can see that the 5d orbitals of Sb and I also hybridize with N near the E_F, which directly proves that high pressure effectively activates the vacant 5d orbital of 5p-block elements, making them participate in chemical bonding together with the 5s and 5p orbitals. The covalent bonding characteristics of the M–N bonds can be observed from the COHP and the ELF in Supplementary Figures 8 and 9. By projecting the electron band structure onto the pressure-induced 5d orbitals, we find that the contribution of the 5d orbital at E_F does not change monotonically with increasing atomic number [Supplementary Figure 10], so the T_c of different MN₆ compounds may be related to these pressure-induced 5d states. To verify this conjecture, the occupied states of electrons of 5p-block elements at E_F are quantified, and the results are shown in Figure 5C. Te has the lowest content of 5d states, but TeN₆ has the highest T_c, elucidating that the pressure-induced 5d electron is negatively correlated with the superconductivity of 5p-block element nitrides.

Figure 5. Formation mechanism of nitrogen-based superconductors MN₆ (M = Sb, Te, I). (A) Calculated T_c and EPC parameter λ at 100 GPa; (B) The superconductivity dependence on pressure of the reported binary superconducting nitrides including SbN₆, TeN₆, and IN₆ proposed in this work; (C) Electronic DOS N(ε_F) and the content of occupied orbitals in the IPDOS of 5p-block element at Fermi surface. Red and blue spheres represent the 5s, 5p, and 5d orbitals, respectively. EPC: electron-phonon coupling; DOS: density of states; IPDOS: integral projected density of states.

CONCLUSIONS

Using first-principles calculations, the first nitrogen-based superconductor with the distorted N₆ hexazine ring is designed at high pressure. The 5p-block element acts as precompressors and electron donors for the N sublattice, resulting in Jahn-Teller distortion of the N₆ hexazine ring and endowing the 5p-block element nitrides a T_c up to 36.8 K at 100 GPa. This critical temperature, close to the McMillan limit, is attributed to the strong EPC caused by the phonon softening and the hybridized electronic states between N and 5s and 5p orbitals of the 5p-block element. The discovery of metallic and even superconducting N₆ hexazine ring in the 5p-block element nitrides provides new insights into achieving the metallization of solid nitrogen at high pressure. Moreover, our present works open an avenue for further exploring many other p-block element nitrides, enriching nitrogen chemistry under extreme conditions.