Pressure-induced superconductivity and modification of Fermi surface in type-II Weyl semimetal NbIrTe4

Weyl semimetals (WSMs) hosting Weyl points (WPs) with different chiralities attract great interest as an object to study chirality-related physical properties, topological phase transitions, and topological superconductivity. Quantum oscillation measurements and theoretical calculations imply that the type-II WPs in NbIrTe4 are robust against the shift of chemical potential making it a good material for pressure studies on topological properties. Here we report the results of electrical transport property measurements and Raman spectroscopy studies under pressures up to 65.5 GPa accompanied by theoretical electronic structure calculations. Hall resistivity data reveal an electronic transition indicated by a change of the charge carrier from multiband character to hole-type at ~12 GPa, in agreement with the calculated Fermi surface. An onset of superconducting transition is observed at pressures above 39 GPa, with critical temperature increasing as pressure increases. Moreover, theoretical calculations indicate that WPs persist up to highly reduced unit cell volume (−17%), manifesting that NbIrTe4 is a candidate of topological superconductor.

The variation of the thermodynamic parameter pressure is a powerful method to modify the Fermi surface of a solid and to tune its carrier density without inducing chemical impurities. The monopnictides TaPn and NbPn (Pn = P, As) were predicted to be type-I WSMs 6 . Subsequently, quantum oscillation and angleresolved photoemission spectroscopy (ARPES) studies confirmed the exotic band structure at ambient pressure [8][9][10][11]13 . Moreover, high-pressure studies on transport properties and superconductivity were performed 7,[19][20][21][22] . Interestingly, pressure induces a phase transition at~14 GPa in TaAs, and the new phase was suggested to exhibit Weyl fermions different from the ambient pressure phase 7 . However, in contrast to other topological materials, only TaP displays superconducting transition at an extremely high pressure of~70 GPa, which is accompanied by a structural transition 20 . TaAs shows tip-induced superconductivity in the point contact spectroscopy 23 . The transition metal dichalcogenides MoTe 2 , WTe 2 , and the ternary compounds MM′′ Te 4 (M = Nb, Ta, M′ = Ir, Rh) were proposed to be type-II WSMs, and some of them were experimentally confirmed 12,[24][25][26][27][28][29][30] . High pressure-driven superconductivity following the dramatic suppression of the large magnetoresistance was reported for WTe 2 and TaIrTe 4 15,16,31 . However, the topological nature of the superconducting state remains an open question under pressure.
NbIrTe 4 features an orthorhombic lattice structure without inversion-symmetry, which is isostructural to TaIrTe 4 and can be considered as a ternary variant of WTe 2 32 . Recently, ARPES studies uncovered two different Fermi arc connections on opposite termination of (001) crystal faces 33 . Quantum oscillation measurements were performed by three different groups [34][35][36] . The magnetoresistance exhibits large values, and no saturation was observed up to a field of 35 T 34-36 . However, Hall measurements reveal that samples of NbIrTe 4 can adopt different Fermi levels, indicating that its Fermi surface is very sensitive to changes of the chemical potential, while the WPs persist against the shift of Fermi level as suggested from calculations [34][35][36] . These features make NbIrTe 4 a good platform to study the effect of pressure on its topological properties.
Here, we report the effects of high pressure on electrical transport properties and crystal structure of the type-II WSM NbIrTe 4 under external pressures up to 65.5 GPa. Hall effect measurements reveal that the Fermi surface changes from a multiband character to hole dominated at~12 GPa. Superconductivity is detected at pressures above 39 GPa, and the onset critical temperature T c increases monotonically with further compression. The observed pressure-induced superconductivity in NbIrTe 4 is in good agreement with the recent results for the isostructural compound TaIrTe 4 31 , demonstrating that the superconductivity under compression is an intrinsic property of this class of compounds.

RESULTS
Crystal structure and transport property measurements at ambient pressure NbIrTe 4 crystalizes in an orthorhombic crystal structure without inversion symmetry and exhibits a characteristic layer stacking along the c-axis (Fig. 1a) 32 . Along a-axis, Nb and Ir atoms each can be viewed as chain structures of edge-sharing octahedral units NbTe 6 or IrTe 6 . The chains extend alternately along b-axis forming an individual layer, and the sequence is Nb-Ir…Ir-Nb. Figure 1b-d show the single crystal x-ray diffraction (SXRD) patterns characterizing different crystallographic axis at room temperature, and the insets are the corresponding optical pictures of the long plate-like crystal. The as-grown orthorhombic crystals are easily cleaved perpendicular to the c-axis, and the longer edge of the obtained ab-plane is the crystallographic a-axis. The clean diffraction pattern and the small width of the reflections confirm the good crystal quality. The space group is Pmn2 1 , and the refined lattice parameters are a = 3.7805(5) Å, b = 12.5146(11) Å, and c = 13.1140 (13) Å, which are consistent with previous results 32 . We note that extra weak spots are detected on the diffraction pattern of a-axis, and the amount is less than 1%. After carefully matching with possible impurity phases, we propose that these extra diffraction spots suggest a modulation of the crystal structure.
We performed electrical resistivity, magnetoresistance, and Hall resistivity measurements at ambient pressure, in which the current was along a-axis, and the magnetic field was perpendicular to the ab-plane. The data are shown in Fig. 1. The inset of Fig. 1e is a photo of the actual crystal used for measurements under ambient pressure and high pressure. The resistivity is 0.6 m cm at room temperature and exhibits metallic behavior down to 1.8 K (Fig. 1e) with a residual resistivity ratio (RRR) of 19. These specific values are comparable with previous reports [34][35][36] . The magnetic field dependence of magnetoresistance MR(B) = (ρ (B) − ρ(0))/ρ(0) × 100%, is shown in Fig. 1f. All MR(B) curves follow a power law behavior~B α without the tendency of saturation, and α changes from 1.5 to 1.9 as temperature increases to 250 K. The same value of 1.5 was reported in TaIrTe 4 at 1.7 K 37 . The MR(9 T) at 2 K is 100%.
Hall resistivity curves as a function of magnetic field ρ xy (B) at selected temperatures are shown in Fig. 1g. For T ≤ 90 K, the ρ xy (B) varies nonlinear, indicating that both electrons and holes contribute to the electrical transport properties in this temperature range. The sign of the slope at 2 K changes from positive to negative as magnetic field increases, as reported in ref. 36 . According to two-band model, electrons are the majority carriers, and adopt low mobility, while the minority hole-type carriers have high mobility. For T ≥ 110 K, the curves exhibit linear magnetic field dependence with positive curvature, suggesting that holes become the dominant carriers. The Hall coefficient R H (R H = ρ xy /B) in linear ρ xy (B) gives the one-band carrier density based on n h = 1/ eR H , and the mobility is derived from μ = 1/neρ, while the nonlinear Hall resistivity is described by two-band model: where n h (n e ) and μ h (μ e ) are the concentration and mobility of holes (electrons). These parameters are constrained with experimental resistivity ρ xx according to Eq. (2). The obtained carrier density and mobility from the fit of ρ xy (B) are displayed in Fig. 1h, i, and the inset of Fig. 1g is the corresponding fit of ρ xx (B) at 2 K. Both fits give similar values of these parameters. As temperature increases, the carrier density of holes increases sharply at first, and then almost keeps constant. The mobility varies slightly, followed with continuous decrease. For the electrons, the concentration reaches a maximum at~50 K, and the mobility keeps decreasing.
Considering that the measured samples of different authors were grown with similar methods, they exhibit obvious differences in Hall resistivity. This suggests a drastic sensitivity of the Fermi surface to the chemical potential due to some unintentional doping. The shift of Fermi level, except for the variation of mobility 36 , is possibly the origin for the evolution of Hall resistivity with respect to temperature in NbIrTe 4 at ambient pressure.

Pressure-induced superconductivity
The results of pressure dependent studies on electrical resistivity are presented on Fig. 2. The data (Fig. 2a, b) at pressures up to 40.6 GPa were collected on sample 1 using a diamond anvil cell (DAC) with 500 μm culet. The sample demonstrates-similar to the ambient pressure data-metallic behavior upon cooling down to 1.8 K. Interestingly, the pressure dependence of electrical resistivity is nonmonotonic. Upon applying pressure, the room temperature resistivity decreases to a minimum as pressure approaches tõ 12 GPa and turns to increase as pressure is further increased. Finally, the resistivity decreases continuously as pressure is abovẽ 28 GPa. Electrical resistivity of NbIrTe 4 was further studied at higher pressures up to 65.5 GPa by employing a DAC adopting a smaller culet 300 μm (see Fig. 2c). At pressures >39 GPa, drops of resistivity are detected at low temperature, indicating the onset of a superconducting transition. Electrical resistivity in normal state displays metallic behavior similar to that at lower pressures. For demonstrating the superconducting transition clearly, the temperature dependence of resistivity at low temperature is normalized to the value at 5 K (see Fig. 2d, the inset is the expanded view at 39.1 GPa displaying a weak drop below 2 K). With further compression, the drop becomes more obvious, and the onset T c is slightly increasing to 2.9 K at 65.5 GPa. However, the superconducting transition is broad and no zero-resistivity state is achieved in the applied pressure range. Higher pressure is required to further investigate the pressure-induced superconductivity. The pressure-induced superconductivity in NbIrTe 4 crystals was confirmed by measuring the resistivity ρ(T) under various static magnetic fields up to 1.5 T at 65.5 GPa applied along the c-axis (Fig. 2e). With magnetic field increase, the onset T c shifts to lower temperature, and the drop of resistivity lifts. No superconducting transition can be detected above 1.8 K when magnetic field increases to 1.5 T. The onset T c (for zero field marked with an arrow in Fig. 2e) is determined by the temperature where the resistivity deviates from normal resistivity. The corresponding upper critical fields are plotted as a function of temperature and shown in Fig. 2f. According to Ginzburg-Landau theory, H c2 (T) = H c2 (0)(1 − t 2 )/(1 + t 2 ) with t = T/T c , the upper critical field at zero temperature μ 0 H c2 (0) is estimated to be 2.2 T, which is larger than the value~0.87 T from TaIrTe 4 31 . It is noted that this is much lower Pressure-driven modification of electronic structure To study pressure effects on electronic structure, we carried out Hall resistivity ρ xy (B) and magnetoresistance MR(B) measurements at pressures up to 40.6 GPa (Fig. 3). At pressure of 1.3 GPa, the sign of the slope for ρ xy (B) changes from positive to negative as magnetic field increases from 0 to 9 T (Fig. 3a) similar to the behavior at ambient pressure. This suggests that the multiband character of the Fermi surface remains, and the majority carriers are electrons with low mobility. The multiband feature survives up to 11.7 GPa as indicated by the nonlinear ρ xy (B) curves (Fig. 3a). However, with further increase of pressure, the ρ xy (B) curves display a linear magnetic field dependence (Fig. 3b), indicating that holes are the main charge carriers. The slope of the linear ρ xy (B) curves becomes larger when pressure approaches to 23.1 GPa, and is followed by a reduction upon further compressing, implying that the concentration of hole decreases slightly at first, and then increases. We did the same analysis of ρ xy (B) as done at ambient pressure, and the extracted carrier density and mobility are summarized in the phase diagram. Similar to ambient pressure data, MR(B) exhibits a power law dependence~B α . The exponent α is 1.4 below 11.7 GPa, and increases to 1.6 at pressure of 32.9 GPa upon compression. These values are close to the value of 1.5 at ambient pressure.

Raman spectroscopy studies
We performed Raman spectroscopy study of NbIrTe 4 under pressures up to 40.1 GPa to detect possible structural transitions in connection with the observed variations of the transport behavior at~12 GPa. Raman spectra under selected pressures are plotted in Fig. 4a. Both the incident laser (unpolarized) and backscattered laser beams were parallel to the c-axis. Based on group analysis, 23A 1 and 12A 2 optical modes can be detected with this backscattering geometry. Several obvious peaks were observed at 0.8 GPa, and the Raman shifts are in accordance with previous Raman measurements using polarized laser 38 . The pressure dependence of Raman shift is shown in Fig. 4b. Upon compressing, the Raman spectra show blue shift due to the shrinkage of lattice. Note that a shoulder peak appears near the peak with frequency 70 cm −1 under 3.5 GPa, and the peak becomes obvious under 4 GPa. The two newly emerging small peaks that can be recognized are marked by asterisks in Fig. 4a. In contrast to the total modification of the Raman spectrum at a major (reconstructive) structural transition, the observed profiles of the Raman spectra of NbIrTe 4 under different pressures remain the same. Additionally, in comparison with the spectrum of the isostructural TaIrTe 4 39 , more weak vibrational modes should be detected. Further considering that no structural transition was observed from synchrotron XRD in TaIrTe 4 31 . We suggest that a lattice distortion instead of major structural transition occurs at 3.5 GPa. In contrast, no anomaly is observed in Raman spectra and in the pressure coefficient of Raman shift at~12 GPa. Just the peak width increases, and the intensity decreases with pressure further increase due to nonhydrostatic pressure conditions at high pressure and the enhanced luminescence of the stressed diamond anvils. The vibrational peaks are too weak to be detected when pressure is above 40.1 GPa. As the pressure is released to 0.8 GPa (Fig. 4a), the Raman spectrum is well consistent with the one at low pressure besides peaks have broadened due to the poorer sample quality after compression. Also, the observed Raman shifts are in good agreement with the data obtained upon compression (Fig. 4b). This indicates that the crystal structure of NbIrTe 4 is reversible with respect to pressure.

Electronic structure calculations
Using density-functional theory (DFT) calculations, we simulated the pressure effects on the electronic structure of NbIrTe 4 . Since no major structural transition was detected from Raman spectroscopy, we compressed the lattice volume within the range of β = (V − V 0 )/ V 0~[ −17%, 0] based on the experimental crystal structure above, where β is shrinkage rate, and V 0 is the volume at ambient pressure. The band structure at ambient pressure is shown in Fig. 5a. Two hole bands (band 1 and 2) and two electron bands (band 3 and 4) cross the Fermi level doing contribution to the conductivity. Figure 5b, c are the Fermi surfaces of band 1-4 with β = 0 and −17%, respectively. In Fig. 5b, the Fermi surfaces of band 3 and 4 are much larger than the Fermi surfaces of band 1 and 2. In Fig. 5c, all the four Fermi surfaces shrink, but the Fermi surface of band 2 (with hole character) is much larger than the other three ones. As a consequence, holes dominate the transport behavior. Thus, comparing Fig. 5b, c, we can find the switch of the charge carrier character from electrons to holes, which is consistent with the above Hall effect measurements. Correspondingly, the density of states near Fermi level decreases slightly and then increases continuously with further compression (Fig. 5d). NbIrTe 4 is a type-II WSM 30 , and we have also investigated the evolution of its WPs in momentum space. All the WPs locate in the k z = 0 plane slightly above the Fermi level, and in the k z = 0.21 plane below Fermi level at ambient pressure. Upon compressing, such kinds of WPs exist all the way up to the maximum considered shrinkage −17% (Table 1).

DISCUSSION
The obtained results demonstrate that applying pressure significantly modifies the Fermi surface of NbIrTe 4 , and a superconducting transition is observed. According to DFT calculations, these WPs persist with the volume reduced by 17%, indicating that NbIrTe 4 is promising to exhibit topological superconductivity.
Magnetoresistance curves MR(B) measured under high pressure follows the same power law behavior as at ambient pressure, and shows no hint of saturation. The amplitude at 9 T is suppressed with pressure increase, and it follows the evolution of mobility very well (Fig. 6a). However, the suppression of MR is not as sharp as reported for other topological materials 15,16,31 , and the MR even exhibits a slight enhancement at low pressures. Pressure effects on resistivity and Hall resistivity are complex (Fig. 6b). Hall effect measurements reveal that the conduction behavior changes from two-type (with electron being the majority) to dominant hole-type at~12 GPa, and the carrier concentration decreases at first, and then increases continuously. The resistivity shows nonmonotonic pressure dependence, and reaches a minimum at~12 GPa, the same pressure where hole concentration achieves a maximum. Such nonmonotonic pressure effects on resistivity were observed for topological insulator β-Bi 4 I 4 , topological material ZrTe 5 , and type-I semimetal TaP and NbP 22,40,41 . Such behavior may be explained by a possible topological phase transition with an energy gap opening at the crossing point, a pressure-induced competition of multiband or pressure-induced Lifshitz transition 22,40,41 . According to our DFT calculations, holes dominate the Fermi surface at a lattice compression by 17%, giving rise to the experimentally observed variation of Hall resistivity and resistivity.
An onset of superconducting transition is observed below 2 K at 39.1 GPa where the hole concentration is much enhanced. The onset T c increases along with increase of pressure, as it is also observed in TaIrTe 4 31 . The modification of the Fermi surface as well as the increased carrier density plays a significant role in the pressure-induced superconductivity. With regard to the topological property, the persistence of WPs when the volume shrinks by up to 17% makes NbIrTe 4 a candidate of topological superconductivity. However, the relationship between superconductivity and topological property calls for further investigations. Note that no anomalies are detected on the pressure dependence of the resistivity at~3.5 GPa, the pressure at which the Raman spectra suggest a possible pressure-induced lattice distortion.
In conclusion, we performed electrical transport property characterization and Raman spectroscopy measurements on NbIrTe 4 single crystals at pressures up to 65.5 GPa. Superconducting transition is observed when pressure exceeds 39 GPa, and the onset T c increases continuously along with pressure increase. T c at the highest applied pressure is 2.9 K. From the Hall resistivity characterization, the charge carrier changes from multiband character to hole-type at~12 GPa due to modification of Fermi surface. According to DFT calculations, WPs survive with volume reduction up to 17%, implying that NbIrTe 4 is a candidate for topological superconductor. Our studies on pressure effect on NbIrTe 4 provide a promising platform for investigating the relationship between topological properties and superconductivity.

Crystal growth
The NbIrTe 4 single crystals were grown out of excess Te which was used as flux. The mixture of high purity Nb powder (99.99% Alfa Aesar), Ir powder (99.9+% Alfa Aesar), and Te pieces (99.9999% Alfa Aesar) with atomic ratio 1:1:12 was put into an alumina crucible and sealed in a quartz tube with 200 mbar Ar inside. The sealed quartz tube was heated to 1273 K in 20 h and kept for 48 h, followed by cooling down to 973 K at a rate of 1 K h -1 . Finally, the excess Te flux was removed by centrifugation of the ampule at 973 K, and long plate-like single crystals were harvested. The crystals are shining and exhibit good ductility. Fresh surface was obtained by cleaving many times with Scotch tape.

Transport property measurements and crystal structure characterization
The crystal structure at ambient pressure was characterized with SXRD at room temperature, and the transport properties at ambient pressure were collected on Quantum Designed PPMS-9 using low-frequency ac excitation and the standard four-probe method. For high-pressure studies, nonmagnetic