Discovery of Superconductivity in Hard Hexagonal ε-NbN

Since the discovery of superconductivity in boron-doped diamond with a critical temperature (TC) near 4 K, great interest has been attracted in hard superconductors such as transition-metal nitrides and carbides. Here we report the new discovery of superconductivity in polycrystalline hexagonal ε-NbN synthesized at high pressure and high temperature. Direct magnetization and electrical resistivity measurements demonstrate that the superconductivity in bulk polycrystalline hexagonal ε-NbN is below ∼11.6 K, which is significantly higher than that for boron-doped diamond. The nature of superconductivity in hexagonal ε-NbN and the physical mechanism for the relatively lower TC have been addressed by the weaker bonding in the Nb-N network, the co-planarity of Nb-N layer as well as its relatively weaker electron-phonon coupling, as compared with the cubic δ-NbN counterpart. Moreover, the newly discovered ε-NbN superconductor remains stable at pressures up to ∼20 GPa and is significantly harder than cubic δ-NbN; it is as hard as sapphire, ultra-incompressible and has a high shear rigidity of 201 GPa to rival hard/superhard material γ-B (∼227 GPa). This exploration opens a new class of highly desirable materials combining the outstanding mechanical/elastic properties with superconductivity, which may be particularly attractive for its technological and engineering applications in extreme environments.

Hard superconducting materials have attracted considerable interest in materials science, condensed matter physics and solid-state chemistry since the discovery of the superconductivity in superhard boron-doped diamond with a transition temperature of T C ∼ 4 K 1-5 . For transition-metal nitrides, some of them possess very good superconductivity (e.g. 10 K for ZrN, 8.8 K for HfN, 17.3 K for δ-NbN), as well as excellent mechanical properties such as low compressibility, high shear rigidity and high hardness [6][7][8][9][10][11][12][13][14][15][16] . Despite the T C for transition-metal nitrides is not very high, their remarkable mechanical properties make them good candidates of hard superconductors for specific electronic/high-field applications 17 as well as potential applications in motor system, carbon-nanotube junctions and high-pressure devices 18 . In addition, the chemical inertness and high melting points also make these nitrides suitable for protective and wear-resistant coatings 19 .
It is known that rock-salt structured δ-NbN possesses the highest transition temperature among transition-metal nitrides (∼ 17 K), and has several polymorphs 4,8,[20][21][22][23] such as WC-type NbN, δ-NbN (NiAs-type) and hexagonal ε-NbN (#194, P6 3 /mmc), but only cubic δ-NbN has been extensively investigated 1,2,4,8 . Recent first-principles theoretical calculations of the thermodynamic properties and structural stability in NbN polymorphs 22,23 (e.g. NaCl-, NiAs-and WC-type NbN) predicted that the hexagonal-structured NbN (e.g. WC-and NiAs-type) exhibited higher hardness and lower total energy than the cubic δ-NbN. These results indicated that the hexagonal phases were more stable than the cubic counterpart which appeared to be the most energetically unfavorable structure or metastable phase with the rock-salt structure.
For hexagonal ε-NbN polymorph, despite its crystal structure was ever simply referred by Terao 24 and Holec et al. 25 , the experimental studies on hexagonal ε-NbN are very scarce, especially for its superconductivity and mechanical/elastic properties which have never been reported. Recently, the wide and growing interest lies in  Fig. 1C, shows a clear hexagon formed by Nb atoms. Crystal structures of the transition-metal nitrides are generally characterized by strong intermetallic bonding with transition-metal atoms and N atoms occupying octahedral, tetrahedral or trigonal prismatic sites, giving rise to a large cohesive energy. In the hexagonal ε-NbN, each N atom is surrounded by six Nb atoms and there are six N atoms around the Nb atoms (Fig. 1D).
The crystal structure of ε-NbN has been further explored by the refinement of high-resolution in situ angle-dispersive X-ray diffraction pattern ( Fig. 2A), yielding a = 2.9599(4) Å, c = 11.2497(22) Å and V 0 = 85.352(19) Å 3 (Rwp = 5.65%, Rp = 2.60%, chi^2 = 0.5977) with a space group of P6 3 /mmc (No. 194). The lattice parameters are in good agreement with the previous experimental results (a = 2.960 Å, c = 11.270 Å) reported by Terao 24 , and comparable to our theoretically calculated results from GGA (a = 2.947 Å, c = 11.611 Å) and LDA (a = 2.908 Å, c = 11.464 Å), as well as the previous theoretical study (a = 2.993 Å, c = 11.415 Å) 25 . According to the well-known Born stability criteria 32 , the hexagonal ε-NbN is found to be mechanically stable, whereas the cubic δ-NbN is mechanically unstable based on our first-principles calculations of the elastic constants. Selected angle-dispersive synchrotron in situ X-ray diffraction patterns of ε-NbN upon compression in a diamond anvil cell (DAC) are shown in Fig. 2B. For comparison, the X-ray diffraction patterns of the specimen during decompression are also shown in Fig. 2B. Clearly, no phase transitions are observed throughout this experiment and the hexagonal-structured ε-NbN remains stable at pressure up to ∼ 20.5 GPa. Figure 3A shows normalized magnetization for a bulk polycrystalline hexagonal ε-NbN as a function of temperature below 20 K under a magnetic field of 3 mT (or 30 Oe). Clearly, the magnetic susceptibility measurements reveal obvious diamagnetic responses at temperatures of ∼ 11.6 K and ∼ 17.5 K, respectively. The magnetic anomaly occurring at ∼ 17.5 K is ascribed to the superconducting transition of NaCl-structured cubic δ-NbN, while the magnetic anomaly at ∼ 11.6 K is related to the hexagonal ε-NbN phase. The existence of the hysteresis between the two magnetization curves for the zero-field cooling (ZFC) and field cooling (FC) modes shows that the hexagonal ε-NbN specimen is a typical type-II superconducting material.

Superconductivity in bulk polycrystalline hexagonal ε-NbN.
The observed superconducting transition temperatures of T C = 11.6 K and 17.5 K for the hexagonal ε -NbN and cubic δ-NbN, have been further addressed/confirmed by the current energy-dispersive X-ray diffraction pattern where the two-phase coexisting specimen is identified (Fig. 1A). As shown in Fig. 1A, the as-synthesized bulk polycrystalline hexagonal ε-NbN is coexisting with a minor amount of cubic δ-NbN. Using the Voigt bound for our theoretical calculations, we know that the abundance of δ-NbN of ∼ 2% will result in less than 1% difference in elastic moduli as compared with those for pure hexagonal ε-NbN 28 . This difference is within the experimental uncertainties, indicating that the effect of the minor δ-NbN on the elasticity of the nominal hexagonal-structured ε-NbN can be negligible. In contrast, the appearance of the minor δ-NbN (∼ 2%) has a significant effect on its electrical/magnetic properties. On the basis of the previous studies on the superconducting transition temperature 14 (T C ≈ 17.3 K) of δ-NbN and our XRD measurements, we thus conclude that the observed superconductivity at temperatures around 17.5 K should be attributed to minor phase of cubic δ-NbN, and the relatively low transition at 11.6 K is due to the hexagonal ε-NbN major phase. The nature of superconductivity in bulk hexagonal ε-NbN has further confirmed by our direct electrical resistivity measurements, exhibiting two resistive transitions at temperatures of ∼ 11.6 K and ∼ 17.5 K, respectively (Fig. 3B). These observed resistivity anomalies occur at almost the same temperatures with those obtained by magnetic susceptibility measurements (Fig. 3A). As shown in Fig. 3B, the onset transition temperature of ε-NbN is about 11.6 K, and zero resistivity is achieved at T C = 10.5 K. By using the 90/10 criterion of superconducting transition temperature, we find that the midpoint of the electrical resistivity transition (i.e. the resistivity drops to 50% of that at 11.6 K) is about 11.1 K. The transition width is as small as ∼ 1 K, suggesting that the bulk polycrystalline hexagonal ε-NbN (nominal) specimen owns high quality and the homogeneous nature of the crystals.

Anisotropic behavior and mechanical/elastic properties of hexagonal ε-NbN. Niobium nitride
polymorphs are attractive also due to their excellent mechanical/elastic properties (elastic behavior) besides their superconductivity, so understanding their hardness, elastic behavior, especially the Young's modulus (E) and shear modulus (G), are of great importance for technological and engineering applications 4 . Compressibility measurements upon compression revealed a significant degree of anisotropy in the elastic behavior of hexagonal ε-NbN, where ε-NbN is more compressible along the a-axis direction, while stiffer along the c-axis. The least-squares fit of the lattice constants as a function of pressure yields d(a/a 0 )/dP = − 0.00096(1) GPa −1 and d(c/c 0 )/dP = − 0.00077(2) GPa −1 , as shown in Fig. 4. For comparison, our theoretical first-principles calculations of the pressure-dependent lattice constants are also displayed here, agreeing well with our experimental data, especially for the compressibility of c-axis.
Hardness measurements were performed on the synthesized polycrystalline hexagonal ε-NbN by means of the Vickers indentation method using a pyramidal diamond indenter. The loading force of the hardness tester is adjusted from 2.94 to 9.  Fig. 5A. Clearly, the hexagonal ε-NbN exhibits a Vickers hardness of 22∼ 30 GPa, which is significantly harder than the high-pressure synthesized polycrystalline ReB 2 (17∼ 19 GPa) as reported by Qin et al. 34 and is almost as hard as sapphire Al 2 O 3 4 . Figure 5B shows a summary  It is widely accepted that bulk and/or shear moduli can reflect the hardness in an indirect way 27,35 . To further explore the correlations between the elastic modulus (B, G, E) and other physical properties, we have performed in situ ultrasonic measurements on hexagonal ε-NbN at high pressure. The experimental procedure in details can be seen elsewhere [26][27][28][29][30][31] . The high-pressure elasticity and sound velocities of hexagonal ε-NbN are out of the current scope of this paper and will be published elsewhere 28 . The ambient-condition bulk and shear moduli derived from the acoustic measurements on ε-NbN yielded B S0 = 373(2) GPa and G 0 = 201(1) GPa 28 . Clearly, hexagonal ε-NbN exhibits a remarkable incompressibility, which is as incompressible/stiff as superhard material cBN (∼381 GPa) 36 . The shear rigidity of ε-NbN (∼201(1) GPa) rivals that for superhard γ-B (∼ 227 GPa) 37 , which is well consistent with the theoretical shear modulus/rigidity of G 0 = 199 GPa by our first-principles calculations. According to our experimentally obtained bulk (B S ) and shear (G) moduli, the Young's modulus (E) is derived to be 510(1) GPa by applying the equation E = 9B S G/(3B S + G), which surpasses that of superhard B 6 O-B 4 C composite (501 GPa) 38 , and can be comparable to that of polycrystalline cBN (587 GPa) 39 , indicating that the hexagonal ε-NbN will also be a good candidate for mechanical applications.

Mechanism of superconductivity in hexagonal ε-NbN. It is well known that the rock-salt structured
transition-metal nitrides (e.g. ZrN, NbN, HfN) and the rhombohedral β-ZrNCl (∼13 K) and β-HfNCl (∼ 26 K) compounds show good superconductivity 8,15,40,41 . The structures of cubic δ-NbN, hexagonal ε-NbN and rhombohedral β-ZrNCl along a axis are shown in Fig. 6. In the hexagonal-structured ε-NbN, each N atom is surrounded by six Nb atoms and there are six N atoms around the Nb atoms (Fig. 6B). The rhombohedral β-ZrNCl can be considered to be composed of alternate stacking of honeycomb ZrN bilayers sliced from a ZrN crystal of the hexagonal structure and sandwiched by chloride layers, as shown in Fig. 6B,C. Therefore, the Nb-N layer in hexagonal-structured ε-NbN, as shown in Fig. 6B, is considered a critical component to stabilizing its superconductivity.
To gain insight into the mechanism of superconductivity in hexagonal ε-NbN against those for the rock-salt structured nitrides as well as rhombohedral β-ZrNCl, their crystal structures (Fig. 6) and their structural parameters have been further investigated. The lattice constants, average bond length, bond angle and superconducting transition temperatures (T C ) of niobium nitrides derived from our first-principles calculations and magnetic/ electrical measurements are summarized in Table 1, in comparison with those of cubic ZrN and β-ZrNCl superconductors 40,41 . Our theoretical calculations show that the average bond length of Nb-N for hexagonal ε-NbN (2.2219 Å) is longer than those of the NaCl-structured NbN (2.2077 Å) and rhombohedral β-ZrNCl (2.2127 Å), but shorter than that of cubic ZrN (2.2890 Å). As shown in Fig. 6, the average bond angle (N-Nb-N) for the distorted NbN 6 (trigonal prismatic coordination) of ε-NbN is ∼82.25°, and the layered hexagonal-structured ε-NbN is almost coplanar against the NaCl-structured NbN/ZrN with the bond angle of 90°. Therefore, the weaker bonding in the Nb-N network and the co-planarity may be the reason for the relatively lower T C (∼11.6 K) compared with the cubic δ-NbN counterpart (∼17.5 K). This correlation is further supported by the rock-salt  (Table 1), where a stronger bonding of Zr-N in β-ZrNCl (2.2127 Å) results in a higher T C (∼ 13.0 K), in comparison with the NaCl-structured ZrN (2.2890 Å, 10.7 K). On the other hand, the shorter average bond length of N-N (2.9728 Å) for ε-NbN together with the lower total energy, compared with δ-NbN (N-N: 3.2122 Å), indicated that the hexagonal ε-NbN is more stable than the cubic counterpart.
For phonon-mediated superconductivity, T C is given by where Θ D is the Debye temperature, μ* is the Coulomb pseudopotential or electron-electron interaction constant and λ is the electron-phonon coupling 42 . Based on the obtained elastic bulk and shear moduli together with the ambient-condition density ρ = 8.30(2) g/cm 3 of hexagonal ε-NbN as derived from our ultrasonic measurements 28 , the Debye temperature Θ D is determined to be ∼ 738 K from the equation 28

Table 1. Structural parameters and superconducting transition temperatures (T C ) of transition-metal nitrides.
It is clearly seen from the McMillan's formula 42 that the effects of λ (as the exponential term) on the T C is much more significant than Θ D (as the linear term), which can shed light on the relatively smaller T C = 11.6 K, compared with T C = 17 K for δ-NbN 44 . The relatively small value of λ for ε-NbN can be understood qualitatively from the relation of λ ω = N I M (0) /( ) 2 2 , where N(0) is the density of electronic states at the Fermi energy, < I 2 > is the average square of the electron-phonon matrix element, M is the ionic mass and < ω 2 > is a characteristic phonon frequency averaged over the phonon spectrum having ω = . Θ 0 5 D 2 2 (ref. 42). Although the ionic mass of ε-NbN is similar to that of δ-NbN, its stronger covalent bonds in ε-NbN imply a smaller N(0) and larger < ω 2 > , compared to those for δ-NbN. These results have been further confirmed by experimentally measured Θ D = 738 K for ε-NbN, which is larger than the Θ D = 629 K for δ-NbN 43 .
First-principles calculations show that the superconducting and mechanical properties for transition-metal nitrides/carbonitrides are closely related to their electronic properties 45,46 . For a good understanding of the mechanical/superconducting properties of ε-NbN, electronic properties of the total densities of states (TDOS) and partial densities of states (PDOS) for hexagonal ε-NbN at ambient pressure have been calculated, in comparison with those for cubic δ-NbN counterpart (see Supplementary Materials: Fig. S1). Both hexagonal ε-NbN and cubic δ-NbN show similar metallic bonding features with a finite DOS at the Fermi level (E F ), originating mostly from the 4d electrons of Nb and 2p electrons of N and agree well with our electrical measurements that ε-NbN is a metallic electrical conductor at ambient conditions. Clearly, there is a strong hybridization between Nb 4d and N 2p states in ε-NbN as revealed by the appearance of "pseudogap" just below and/or above the Fermi level, indicating the covalent and/or ionic bonding between Nb and N atoms (Fig. S1(A)). When comparing with the electronic structures of hexagonal ε-NbN and cubic δ-NbN, we note that there is a small peak dominated by the Nb-d orbital at about − 0.68 eV in the DOS for ε-NbN (Fig. S1(A,B)). The appearance of this peak with low energy indicates a stronger bonding arising from the metal d orbitals in ε-NbN as compared to δ-NbN, resulting in an enhancement of the elastic/mechanical strength of ε-NbN. Fig. S1(A) shows that the TDOS around the Fermi level (E F ) lies in a dip for ε-NbN, whereas the density of states increases monotonically at E F for δ-NbN ( Fig. S1(B)). This agrees well with the result from the total-energy calculations that the hexagonal ε-NbN is more stable than the cubic counterpart.
As reported by Oya et al. 47 , tetragonal phases γ-Nb 4 N 3 and Nb 4 N 5 with long-range-ordered arrangement of vacancies exhibited superconductivity 47 , whereas the hexagonal NbN and Nb 5 N 6 didn't show superconductivity at temperatures down to 1.77 K. For the mechanism of superconductivity in transition-metal nitrides, it is suggested that the continuous promotion of s, p electrons to the d shell in all solids under pressure is one of the factors which will induce superconductivity. As seen from Fig. S1, the contribution of the 4d-state is larger than those of the 5s and 5p states. The larger contribution of 4d state electrons clearly shows the possibility of superconductivity in hexagonal-structured NbN at ambient pressure.
In summary, we have discovered the superconductivity at ∼ 11.6 K in bulk polycrystalline hexagonal ε-NbN, which was synthesized at high pressure and high temperature in a high-pressure multi-anvil apparatus. The weaker bonding in the Nb-N network and the co-planarity may be the reason for the relatively lower T C (∼ 11.6 K) compared with the cubic δ-NbN counterpart (∼ 17.5 K). Our theoretical calculations reveal that the contribution of the 4d-state is larger than those of the 5s and 5p states, and the relatively larger contribution of 4d state electrons may be responsible for the superconductivity in hexagonal ε-NbN. In addition, the hexagonal ε-NbN was found to exhibit excellent mechanical properties, which is as hard as sapphire Al 2 O 3 (21∼ 23 GPa) 4 and possessed a remarkable incompressibility 36 (as stiff as superhard cBN of ∼ 381 GPa). The shear rigidity of ε-NbN (∼ 201(1) GPa) rivals that for superhard γ-B (∼ 227 GPa) 37 , and the Young's modulus (∼ 510(1) GPa) is surpassing that for B 6 O-B 4 C composite (501 GPa) 38 . Our theoretical calculations indicate that the hexagonal ε-NbN is more stable than the cubic δ-NbN, and the stronger bonding arising from the metal d orbitals in ε-NbN compared to δ-NbN results in an enhancement of the elastic/mechanical strength of ε-NbN. This study opens a new window for the design of desirable materials with the combination of excellent mechanical properties and superconductivity, which may be particularly attractive for its technological and engineering applications in extreme conditions.

Methods
Magnetization and electrical resistivity measurements on polycrystalline hexagonal ε-NbN. Magnetization measurements of the high-pressure synthesized bulk polycrystalline hexagonal ε-NbN were performed in a Superconducting Quantum Interference Device (SQUID) based magnetometer (MPMS, Quantum Design). Electrical resistivity measurements on hexagonal ε-NbN were conducted in a Physical Property Measurement System (PPMS, Quantum Design) using the standard four-probe method 48 . In situ X-ray diffraction study of hexagonal ε-NbN at high pressure. High-pressure synchrotron X-ray experiments using diamond-anvil cell (DAC) techniques were performed at the X17C beamline of National Synchrotron Light Source, Brookhaven National Laboratory. Stainless T301 steel plates with an initial thickness of 250 μm were used as gaskets. The ε-NbN powder, a tiny ruby ball, and the methanol-ethanol pressure medium (4:1) were loaded into the hole in the gasket. The experimental cell-pressure was determined by the pressure-induced fluorescence shift of ruby 49 . The incident synchrotron radiation beam was monochromatized to a wavelength of 0.40722 Å. The collected two-dimensional X-ray diffraction patterns were analyzed by integrating 2D images as a function of 2θ using the program Fit2D to obtain conventional, one-dimensional profiles 50 .
First-principles calculations. Our first-principles calculations were performed with the CASTEP code 51 , based on density functional theory (DFT) using Vanderbilt-type ultrasoft pseudopotentials and a plane-wave expansion of the wave functions 52 . The local density approximation (LDA) and generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) were employed for determination of the exchange and correlation potentials for electron-electron interactions. The Broyden-Fletcher-Goldfarb-Shanno Scientific RepoRts | 6:22330 | DOI: 10.1038/srep22330 optimization method was applied to search for the ground states of ε-NbN. For the Brillouin-zone sampling, the Monkhorst-Pack scheme was adopted 53 . To confirm the convergence of our calculations, we have carefully analyzed the dependences of the total energy on the cutoff energy and the k-point set mesh according to the Monkhorst-Pack grid. During our first-principles calculations, the difference in total energy was minimized to below 5 × 10 −7 eV/atom, the maximum ionic Hellmann-Feynman force is converged to less than 0.01 eV/Å, and the total stress tensor is reduced to the order of 0.02 GPa by using the finite basis-set corrections. The valance configuration is 4p 6 5 s 1 4d 4 and 2s 2 2p 3 for Nb and N, respectively. Integrations in the Brillouin zone are performed using special k points generated with 10 × 10 × 2. One-electron valence states are expanded on a basis of plane waves with a cutoff energy of 600 eV in the electronic property calculations. All these parameters have been tested to be sufficient for the convergence.