Pressure-induced superconductivity in topological semimetal NbAs2

Topological superconductivity with Majorana bound states, which are critical to implement nonabelian quantum computation, may be realized in three-dimensional semimetals with nontrivial topological feature, when superconducting transition occurs in the bulk. Here, we report pressure-induced superconductivity in a transition-metal dipnictide NbAs2. The emergence of superconductivity is not accompanied by any structural phase transition up to the maximum experimental pressure of 29.8 GPa, as supported by pressure-dependent synchrotron X-ray diffraction and Raman spectroscopy. Intriguingly, the Raman study reveals rapid phonon mode hardening and broadening above 10 GPa, in coincident with the superconducting transition. Using first-principle calculations, we determine Fermi surface change induced by pressure, which steadily increases the density of states without breaking the electron–hole compensation. Noticeably, the main hole pocket of NbAs2 encloses one time-reversal-invariant momenta of the monoclinic lattice, suggesting NbAs2 as a candidate of topological superconductors. Superconductivity is observed in NbAs2, indicating that this predicted topological material could host Majorana fermions. Using transport measurements, researchers led by Zhu-An Xu from Zhejiang University and Zhaorong Yang from the National High Magnetic field Laboratory in Hefei have demonstrated a superconducting transition when this compound is placed under high pressure. X-ray diffraction shows that no structural transition accompanies the onset of superconductivity, but Raman scattering and density functional theory calculations suggest that the pressure induces changes in the electron–phonon coupling and electronic density of states that facilitate the superconductivity. The band structure of NbAs2 is predicted to host topological features, indicating that transition metal dipnictides such as this could be time reversal invariant topological superconductors, and may feature Majorana edge modes that can be utilized in fault-tolerant quantum computing.


INTRODUCTION
There have been various proposals in search of quasiparticle excitations of Majorana fermions (MFs) in solids, which are the subject of both fundamental research and error-tolerant topological quantum computing 1,2 .Superconductor-topological insulator (TI) heterostructures turn the surface Dirac fermions of topological insulators (TIs) into p-wave-like Cooper pairs 3 .Majorana zero modes by this superconducting proximity approach have been observed in vortices by scanning tunnelling microscopy in Bi 2 Te 3 /NbSe 2 heterostructures 4,5 .Superconducting proximity effects may also create MFs in semiconducting nanowires with strong spin-orbital coupling 6,7 , or in ferromagnetic atomic chains 8 .Alternatively, chiral Majorana edges states are expected in two-dimensional (2D) chiral topological superconductors, consisting of a topological insulator in proximity to an swave superconductor [9][10][11][12] .It is intriguing that superconducting phase transitions are widely observed in many topological materials when high pressure is applied, such as type II Weyl semimetals of MoTe 2 13 and WTe 2 14,15 , Dirac semimetals of Cd 3 As 2 16 and ZrTe 5 17 , and topological insulators of Bi 2 Se 3 18 , Bi 2 Te 3 19 , and Sb 2 Te 3 20 .Recently tip-induced superconductivity has attracted much attention because it could offer a new platform to study topological superconductivity (TSC) in Dirac 21 and Weyl semimetals 22 .Charge carrier doping is another effective method to induce TSC in topological insulators such as in Cu x Bi 2 Se 3 23 and Sr x Bi 2 Se 3 24 .The experimental obser-vations strongly suggest the feasibility to realize TSC 25,26 in novel topological materials with non-trivial topological features.However, before the emergence of superconductivity (SC), most of these topological compounds undergo structural phase transitions, which usually change the topological states.Very recently, transition-metal dipnictides of the MPn 2 family [27][28][29][30][31][32][33] , where M represents Mo, Nb or Ta atom, and Pn is As or Sb atom, respectively, generate a wide interest as a new prototype of topological semimetals with extremely large magnetoresistance (XMR).When spin orbital coupling (SOC) is included, the band anticrossing in MPn 2 between the M-d xy and M-d x 2 −y 2 orbitals along the I − L − I ′ direction are fully gapped 34 , resulting in weak topological insulator invariants of Z 2 = [0; 111] 28,31,35 .Another interesting point in the MPn 2 family is that magnetic field could induce Weyl points 36 .With its monoclinic lattice (Space group No. 12), which is normally stable under very high pressure 16,17 , it is tempting to study the physical properties of MPn 2 under high pressure.
In this work, we report pressure-dependent transport measurement and structure evolution in NbAs 2 , using the diamond-anvil-cell (DAC) technique to continuously tune the electronic structure.Superconducting transition has been successfully observed at 12.8 GPa with a critical temperature (T c ) of 2.63 K. Further increase in pressure gradually suppresses T c , which disappears completely at 27.9 GPa when bad metal behavior dominates below the helium temperature.Using high-pressure X-ray diffraction and Raman scattering, we confirm that there is no structural phase transition up to the maximum experimental pressure of 29.8 GPa, which implies that the topological state maybe remain undisturbed under high  pressure.Intriguingly, the electron-hole compensation in NbAs 2 changes little even in the superconducting region, as suggested by first-principle calculations, although the electron-hole compensation under pressure is not so perfect.Instead, the dwindling of XMR and the emergence of superconductivity are characterized by continuous Fermi surface change and gradual growth in density of state.Our results thus indicate the coexistence of XMR and SC.The growing density of states is usually beneficial to the occurrence of SC.Moreover, the Cooper pair formation in NbAs 2 may also be correlated to the enhanced electron-phonon coupling under high pressure, since the Raman studies reveal significant phonon mode hardening and broadening above 10 GPa.It is noteworthy that, in the SC region, the main hole pocket of NbAs 2 encloses the time-reversal-invariant (TRI) momenta M .These suggest NbAs 2 as a candidate of TRI topological superconductors.

Pressure-dependent structure analysis
The structure evolution of NbAs 2 under pressure is determined by synchrotron radiation-based high-pressure X-Ray diffraction (XRD) and Raman spectroscopy, as shown in Fig. 1.The XRD data are refined using the Rietveld method, and the Bragg peaks are well indexed by the space group C2/m for both the 0.6 GPa and 25.3 GPa data (See Supplementary Fig. S1).Within 30 GPa, the pressure-induced lattice changes are reversible.In Fig. 1a, we show the XRD results of NbAs 2 when the DAC is slowly decompressed from 29.8 GPa to 0.3 GPa.The data are essentially identical to the bottom curve of 0.6 GPa.In Fig. 1b, the high pressure dependent unit-cell volumes can be fitted by the third−order Birch-Murnaghan equation of state 37 , and no distinct drop of the unit-cell volume is observed with the increase of pressure, which suggests stability of this structure.The mon- oclinic lattice is also manifested in pressure-dependent Raman scattering measurements, showing six fingerprinting peaks between 180 and 350 cm −1 , namely A 2g , A 3g , B 3g , A 4g , A 5g , and A 6g , respectively (see Fig. 1c).It is intriguing that Raman spectroscopy shows distinctive enhancement of A 2g , A 3g , B 3g , A 4g and A 5g above 10 GPa, when the data are normalized by the A 2g peak intensity.The distinct broadening in A 2g , A 4g and A 5g , which could be an indication of stronger electron-phonon coupling or pressure-enhanced defect scattering 38 , is also discernable above 10 GPa.
Resistivity measurements Fig. 2a and 2b summarize the resistance vs temperature (R − T ) characteristics of NbAs 2 at various pressures from 0.5 GPa to 27.9 GPa.Below 9.8 GPa, NbAs 2 shows typical metallic behaviour, which is characterized by monotonic increase in resistance with increasing temperature, and exhibits a lower residual-resistivity-ratio (RRR) with enhancement of pressure.The trend is reversed at 9.8 GPa, when the whole R − T curve is upshifted by ∼ 0.03 Ω compared to 6.1 GPa.Superconductivity with a transition temperature of 2.63 K emerges at 12.8 GPa, but the resistance does not drop to zero even at 1.8 K (Fig. 2a).Further increase in pressure surprisingly starts to suppress T c , although the SC transition becomes sharper, and zero-resistance behaviour is observed at 16 GPa.Noticeably, the zero-resistance transition is accompanied by a positive resistance kink, which is very sharp and only extends within a temperature range of 0.2 K. Subsequently, the superconducting transition is gradually suppressed when the positive resistance kink becomes broader and its onset shifts to lower T .Above 23 GPa, the positive resistance kink completely dominates.
In previous studies, the emergence of SC is generally accompanied with a suppression of the XMR effect in topological SMs 14,15,39 .There are different interpreta- tions in the XMR suppression mechanism.Cai et al. suggest that pressure weaken the electron-hole compensation in WTe 2 by gradually decreasing the hole carrier population 39 .In-situ pressure-dependent Hall measurements by Kang et al. indeed observe the change from a positive sign to negative sign in the Hall coefficients 14 , suggesting increasing population of the electron carriers and decreasing hole carriers density.Moreover, Pan et al. report that the SC transition is induced by rapid increase in the density of states at the Fermi surface, as a result of the compression of the unit cell 15 , while the difference between hole pockets and electron pockets is enhanced with applied pressure.
NbAs 2 is a well compensated semimetal at ambient pressure 28 .When high pressure is applied, XMR at 8 T is effectively suppressed from 5.16 at 0.5 GPa to 0.08 at 14.6 GPa, as shown in Fig. 2c.The dwindling of XMR as a function of pressure can be explained well by pressure-induced decrease in the average mobility μ40 , using the power-law relation of MR = (μB) l .Using logarithmic scale, it is clear that the XMR curves at different pressures have nearly the same linear slope (l = 1.43), which is a simple measure of the electron-hole compensation accuracy 34 , and the electron-hole compensation here is not so perfect.By fitting the experimental data to the aforementioned equation, we found that μ decreases quasi-linearly as a function of pressure, and only shows a slight upward curvature as entering the SC region above 10 GPa (see Fig. 2d).Our results thus imply that a distinct phase boundary does not exist between SC and XMR, and the mechanism of SC in NbAs 2 may be different compared to other topological semimetals 14 .The positive resistance kinks, which become broader and shift to lower temperature as a function of pres- sure (P ), may be rooted in different mechanisms, such as superconductor to metal transition (SMT) in disordered system 41 , a probable foreshadow of p-wave superconductivity in superconductor-ferromagnet nanowires structure 42 , or highly anisotropic superconducting gap 43 , but should not be the same as the semiconductor-like behaviour in LaO 0.5 F 0.5 BiSe 2 44 .When external magnetic field (B ) is applied, T c monotonically shifts to lower temperatures and the positive resistance kinks gradually become predominant.As shown in Fig. 3a, it is surprising that the superconducting transition at 16 GPa is completely suppressed at 1000 Oe.This may be due to the predominant resistivity upturn, which pushes T c to below 1.8 K. Nevertheless, with the available experimental data, we can define an empirical critical T 90% c by those points at which R is 90% of the normal state, as seen in inset of Fig. 3b.In Fig. 3b, the deduced T 90% c can be well fitted by the Werthamer-Helfand-Hohenberg (WHH) model 45 , which yields the orbital-limited upper critical field in dirty-limited system by Interestingly, by plotting the pressure-dependent R at different T (4.5 K, 100 K, 200 K and 300 K, respectively) in Fig. 3c, we are able to clearly see an anomaly at 12.8 GPa, which corresponds to the emergence of superconductivity.However, there is no structural phase transition up to 29.8 GPa, so the origin of this behavior needs further investigation.By including the characteristic pa-rameters of XMR, T 90% c as a function of pressure, we can draw the P −T phase diagram for NbAs 2 .As summarised in Fig. 3e, high pressure suppresses the XMR effect (the blue region) by reducing the average mobility μ.The emergence of SC may be related to the enhance of density of states 15,46 , and calculated density of states increase as a function of pressure, as seen in Fig. 3d.Moveover, there is a significant overlap between the XMR (the blue region) and SC region (the magenta region) when superconductivity emerges at 12.8 GPa.Such a coexistence of XMR and SC is in contrast to the other cases like WTe 2 where XMR is significantly suppressed as entering the SC state under high pressure 14 .Above 16 GPa, there is a probable phase competition between SC and the bad metal (BM) transition (the green region), which maybe lead to the vanishing of T c at 27.9 GPa.

Electronic structures under pressure
To get insights into the aforementioned experimental results, we have studied the pressure-dependent electronic structure of NbAs 2 using density-functional theory (DFT) calculations, which adopt the experimental lattice parameters determined by XRD.Fig. 4 displays the DFT calculations at ambient pressure, 15.6 GPa, and 22.7 GPa, respectively.In excellent agreement with the XMR measurements, the DFT results confirm that pressure simultaneously increases electron and hole populations in NbAs 2 , which is displayed in Fig. 4d,e,f where the electron pockets (magenta) and hole pockets (blue) all enlarge with increasing pressure.This is not surprising since the monoclinic lattice is retained under high pressure.Equally important, the steady growth in charge carrier does not show any anomaly, neither in density of states in Fig. 3d nor in Fermi surface topology, in the vicinity of 12.8 GPa when SC starts to emerge.According to the proposed theory by Fu et al., time-reversal-invariant topological superconductivity in a centrosymmetry system requires odd-parity spin pairing and an Fermi surface enclosing an odd number of TRIM points 26 .Although the pairing symmetry is not explicitly known, the latter condition is well satisfied in NbAs 2 .As shown in Fig. 4, the main hole pocket of NbAs 2 enlarges under pressure, centering the TRIM point of M .In addition, the electronic specific-heat coefficient of γ = 0.45mJ/mol/K 2 is observed from the specific heat measurements (see Fig. S3 in Supplementary Materials), suggesting weak electronic correlation in NbAs 2 at ambient pressure.With increasing pressure, the sudden hardening and broadening phonon modes may start to play a critical role in the emergence of SC, and the phonon-mediated pairing maybe have an odd-parity symmetry in NbAs 2 to possess the singular behavior of the electron-phonon interaction at long wavelength 47,48 .In addition, no structural transition is observed as entering the superconducting states with increasing pressure and thus the topological surface state should remain undisturbed at high pressure, which suggests the possibility of topologically superconducting surface states in NbAs 2 because of superconducting proximity effect 3 .Therefore, NbAs 2 with time-reversal and inversion symmetries may be a candidate for topological superconductor.It is necessary to be checked by further experiments.
In summary, we study the high pressure-induced superconductivity in topological semimetal NbAs 2 , which shows a superconducting transition temperature of 2.63 K at 12.8 GPa.Unlike previously reported topological semimetals, no structural phase transition occurs near the superconducting region, which is supported both by the high-pressure synchrotron X-ray diffraction and Raman data.Raman spectroscopy, resistance and specific heat data all suggest the critical importance of electronphonon interactions on the SC pairing in NbAs 2 , which may be a candidate of time-reversal-invariant topological superconductor with odd spin paring parity.Strikingly, the SC phase emerges with a nearly invariable electronhole compensation and shows no anomaly in the density of states in the vicinity of the critical pressure of 12.8 GPa.Our results illustrate that high-pressure induced SC may be more complex in physical origins than the prevailing explanations, and the monoclinic family of MPn 2 may provide a platform to test various theoretical proposals and to search for topological superconductivity.

Samples and experimental technique
Single crystals of NbAs 2 were grown by means of a vapour transport technique 28 .High pressure was generated by a screw-pressure-type DAC consisting of nonmagnetic Cu-Be alloy and two diamonds with the culet of 300 µm diameter.A T301 stainless-steel gasket with a 280 µm diameter hole was used for different runs of highpressure resistance measurement by the standard fourprobe method.The single crystal was placed in the hole and a mixture of fine cubic boron nitride (CBN) powder with epoxy was compressed firmly to insulate the electrodes from the gasket.Pressure medium was daphne 7373 oil and some ruby powder was applied to demarcate the pressure by the ruby fluorescence method at room temperature.High-pressure synchrotron powder XRD (λ = 0.4246 Å) was performed at room temperature at the beamline 16 BM-D 49 , High Pressure Collaborative Access Team (HPCAT).

DFT calculations
The electron structure calculations were performed with the Vienna ab initio simulation package (VASP) 50,51 by the method of the projector augmented wave 52 and the generalized gradient approximation (GGA) 53 in order to introduce the exchange-correlation potential.Spinorbit coupling has been included using the second variation perturbation method 54 .In addition, the plane-wave cutoff energy is setting about 500 eV and 21*21*13 kpoints sampling is performed based on the Monkhorst-Pack scheme 55 .The total energy is ensured to be converged within 10 −6 eV.We use the structure parameters of high-pressure synchrotron X-ray diffraction to relax the structure with the tolerance of 0.01eV/ Å.s on the npj Quantum Materials website.
Competing interests: The authors declare no competing interests.
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FIG. 1 .
FIG. 1. High pressure structure of NbAs2.(a) X-ray diffraction patterns of NbAs2 at various pressures display no structural phase transition.(b) Unit-cell volume decreases with increasing pressure, while the volume diminishes by 13% at 25.3 GPa.(c) The Raman shifts at various pressures show the hardening and broadening of Raman scattering peaks.

9 FIG. 2 .
FIG.2.Pressure-induced superconductivity in single-crystal NbAs2.(a) Temperature-dependent resistance is measured from 0.5 GPa to 14.6 GPa and superconducting transition appears at 12.8 GPa.The enlarged view of low temperature resistance is shown in the inset.(b) The resistance as a function of temperature at different pressures between 16 GPa and 27.9 GPa is displayed with a enlarged plot around the superconducting transition in the inset.(c) Magnetoresistance (MR=(R(8T)-R(0T))/R(0T)) at 4.5 K is suppressed slowly as pressure increases from 0.5 GPa to 14.6 GPa.The MR at 12.8 GPa and 8 T is nearly 22%, which is still very large.(d) Average mobility μ obtained by fitting to the formula MR = (μB)1.43decreases monotonously with increasing pressure.

FIG. 3 .
FIG. 3. Determination of upper critical field for superconductivity and temperature-pressure phase diagram of NbAs2.(a) Temperature-dependent resistance at different magnetic fields is measured at 16 GPa.(b) Hc2 as a function of temperature and its WHH fitting are displayed.The inset shows the definition of different superconducting transition temperatures and transition temperature of bad metal.(c) Resistance at 4.5 K, 100 K, 200 K and 300 K in the normal state at different pressures shows the peak near 12.8 GPa where superconducting transition emerges.(d) Calculated density of states of NbAs2 at the Fermi level versus pressure.The squares are the density of states as a function of pressure, and the red line indicates the tendency of density of state under the pressure.(e) Tc is plotted against pressure as well as evolution of MR, and superconductivity appears at 12.8 GPa following the suppression of XMR with increasing pressure.The BM transition appears after 16 GPa.The regions of XRM, SC, and BM in the phase diagram are marked by blue, magenta, and green colors, respectively.

FIG. 4 .
FIG. 4. Pressure-dependent band structures of NbAs2, showing increasing electron and hole pockets.(a, b and c) Band structures in NbAs2 are shown at ambient pressure, 15.6 GPa and 22.7 GPa, respectively.The red points are TRIM points.(d, e and f ) 3D Fermi surface diagram at ambient pressure, 15.6 GPa and 22.7 GPa indicates that the TRIM (M) is enclosed by the hole-type Fermi surface (the magenta pockets), and blue pockets are electron-type Fermi surface.TRIM points are marked in the Fig.4d.
.Li synthesized and characterized the single crystals.C.An, Y.H.Zhou, and Z.R.Yang conducted the high-pressure transport measurements.Y.Zhou, C.An and R.R.Zhang carried out the Raman experiments, X.L.Chen and C.Y.Park performed the high-pressure synchrotron X-ray diffraction experiments.C.Q.Hua and Y.H.Lu did the DFT calculations.Y.P.Li, C.Q.Hua, Y.H.Lu, Z.R.Yang, Y.Zheng and Z.A.Xu wrote the paper.All the authors analysed the data and discussed the results.Y.P.Li, C.An and C.Q.Hua were co-first authors to this work.Z.R.Yang and Z.A.Xu co-supervised the project.