Pressure-induced superconductivity and topological phase transitions in the topological nodal-line semimetal SrAs3

Topological nodal-line semimetals (TNLSMs) are materials whose conduction and valence bands cross each other, meeting a topologically-protected closed loop rather than discrete points in the Brillouin zone (BZ). The anticipated properties for TNLSMs include drumhead-like nearly flat surface states, unique Landau energy levels, special collective modes, long-range Coulomb interactions, or the possibility of realizing high-temperature superconductivity. Recently, SrAs3 has been theoretically proposed and then experimentally confirmed to be a TNLSM. Here, we report high-pressure experiments on SrAs3, identifying a Lifshitz transition below 1 GPa and a superconducting transition accompanied by a structural phase transition above 20 GPa. A topological crystalline insulator (TCI) state is revealed by means of density functional theory (DFT) calculations on the emergent high-pressure phase. As the counterpart of topological insulators, TCIs possess metallic boundary states protected by crystal symmetry, rather than time reversal. In consideration of topological surface states (TSSs) and helical spin texture observed in the high-pressure state of SrAs3, the superconducting state may be induced in the surface states, and is most likely topologically nontrivial, making pressurized SrAs3 a strong candidate for topological superconductor.

In recent years, topological semimetals including Dirac, Weyl, and nodal-line semimetals have been theoretically predicted and experimentally verified, opening a new field in condensed-matter physics in which novel properties and new applications can arise from spin-polarized states with unique band dispersion [1][2][3] . Unlike the discrete points in momentum space in Dirac or Weyl semimetals 2,3 , the band crossings in nodal-line semimetals can form closed loops inside the BZ 4 ; a nodal chain consisting of several connected loops 5 ; or an extended line traversing the entire BZ 6 . These one-dimensional nodal curves are topologically protected by certain discrete symmetries, for example mirror reflection, timereversal, or spin-rotation symmetries 2,3 . Upon breaking symmetries in a TNLSM, the nodal line is either fully gapped or gapped into several nodal points 4 . The nodal-line structure is expected to have several intriguing properties 3 , such as unique Landau energy levels 7 , special collective modes 8 , longrange Coulomb interactions 9 , or drumhead-like nearly-flat surface states 10,11 which can be considered a higher-dimensional analogue of the flat band on the zigzag edge of graphene 3 . These drumhead states may host interesting correlation effects, and even offer the possibility of realizing high-temperature superconductivity 12 .
In the search for nodal-line semimetals, several systems have been theoretically proposed since 2011 2,3 . However, only a few candidates including PbTaSe2 13,14 , ZrSiX (X = S, Se, Te) 15,16 , CaAgX (X = P, As) 17,18 and MB2 (M = Ti, Zr) 19 have been verified experimentally. More recently, the CaP3 family of materials (MAs3, for M = Ca, Ba, and SrX3 for X = P, As) was proposed as another potential host of TNLSMs 20 . Among these compounds, only SrAs3 shows a strongly topological nature at ambient pressure, while others need extra compressing 20 . SrAs3 displays semimetallic behavior with the hole carriers dominating 21,22 . Previously, unusual galvanomagnetic properties and a first-order longitudinal Hall effect have been found in SrAs3 23 , and quantum oscillation experiments have been applied to map out the shape of the Fermi surface, finding two asymmetric, quasi-ellipsoidal Fermi-bodies as well as light cyclotron effective mass 22 . Recent magnetotransport measurements on SrAs3 single crystals found a nontrivial Berry phase and a robust negative longitudinal magnetoresistance (MR) induced by the chiral anomaly, which indicates the presence of topological properties in SrAs3 24,25 . Subsequently, Song et al. observed the complete nodal-line feature around the Y point by means of angle-resolved photoemission spectroscopy (ARPES), demonstrating the existence of Dirac nodal-line fermions 26 . In contrast to most TNLSMs, the nodal-line structure in SrAs3 does not coexist with complex topologically trivial Fermi surfaces, which may pave an easy path to potential applications 20,26 .
Among the topological materials, intense effort has been applied to realizing topological superconductors (TSCs) 27,28 , one source of Majorana fermions, an effort which suffers from a severe lack of suitable materials to study 27,28 . Experimentally, applying chemical doping or pressure to search for superconductivity in known topological materials are two common methods to obtain new TSC candidates 27,28 . While chemical doping introduces chemical complexity and disorder, pressure is a clean and effective approach for tuning the interactions among multiple degrees of freedom, and superconductivity has been found in many materials via this route [29][30][31] . Among the CaP3 family of materials, CaAs3 was proposed to host a single nodal loop due to time reversal, spatial inversion, and accidental degeneracies 32 . Li et al. reported its transport properties under hydrostatic pressure up to 2.09 GPa, finding a decrease in the resistivity and a possible superconducting transition under pressure 33 . Since SrAs3 has already been demonstrated to be a TNLSM, the lack of any high-pressure report inspired us to explore its pressure dependence.
In this work, we present the results of high-pressure measurements on single-crystalline SrAs3. Upon applying pressure, the topologically-protected α pocket and trivial β pocket disappear around 1 GPa, and two higher frequencies denoted as ε and ξ emerge, indicating a Lifshitz transition. More interestingly, a superconducting transition has been observed from 20.6 GPa, with a dome-like pressure dependence. High-pressure X-ray diffraction (XRD) was conducted to investigate the high-pressure structure of SrAs3, and a structural transition was found around 20 GPa. DFT calculations on the highpressure structure of SrAs3 reveal a TCI state. TCI states have previously been experimentally verified only in narrow-gap IV-VI semiconductors with a rock-salt structure, for example SnTe 34 and Pb1-xSnxM (M = Se, Te) 35,36 . Thus, the observation of a pressure-induced TCI state in SrAs3 offers an alternative route to explore this exotic state. Moreover, the finding of superconductivity in this state makes highpressure SrAs3 a candidate topological superconductor.

Results
SrAs3 crystallizes in a triclinic (space group P1 _ ) or monoclinic (space group C2/m) structure; the latter is proposed to possess topological-nodal-line states protected by time-reversal symmetry, spatialinversion symmetry, and mirror symmetry 20 . Figure 1 along the b axis 21 . The As layers form channels and the Sr cations are inserted into the channels, as shown in Fig. 1(b) 21 . The inset in Fig. 1(c) shows the x-ray diffraction (XRD) rocking curves of SrAs3 single crystals grown from both Bi flux (which we refer to as BF) and self flux (SF). From an x-ray rocking curve of the (002) Bragg peak, a full width at half maximum (FWHM) of 0.04° indicates the high quality of the SrAs3 single crystal grown from Bi flux, while a broader FWHM of 0.15° for the SF sample suggests lower quality. In resistivity measurements ( Fig. 1(c)), the SF sample exhibits semimetallic behavior, while the BF sample exhibits metallic behavior with a residual resistivity ratio RRR = ρ(300 K)/ρ0 of 5, and a residual resistivity ρ0 of 72.7 μ cm, which are further indicative of its high quality. For magnetotransport measurements, the higher-quality BF-grown samples were chosen. GPa on a BF-grown SrAs3 single crystal. Upon increasing the pressure from 0.14 to 1.18 GPa, the lowtemperature resistivity becomes increasingly metallic. The MR, shown in Fig. 2(b), is non-monotonic in pressure. Upon increasing the pressure from 0.14 to 1.18 GPa, the MR at 9 T and 1.8 K increases from 5000% to 32500%. However, further increasing the pressure to 1.47 GPa reduces the MR to 22000%. The oscillatory component ΔRxx, plotted in Fig. 2(c), exhibits low-frequency modes for lower pressures and higher-frequency modes at higher pressures, indicating a significant change in the electronic structure at the Fermi surface. Fast Fourier transforms (FFTs) of the MR oscillations, displayed in Fig. 2(d) contain only the α (1.4 T) and β (5.5 T) pockets from 0.14 to 0.69 GPa, as previously seen at ambient pressure 25 . At 0.99 GPa, the α and β pockets abruptly disappear, replaced by a single frequency of 21.5 T which we assign to a ξ pocket. Upon increasing the pressure to 1.47 GPa, the ξ-frequency pocket is joined by an even higher frequency of 48.3 T which grows rapidly to 63.2 T, which we assign to an ε pocket. Tc 10% of 3.6 K appears, and the Tc increases to 5.8 K at 54.7 GPa. Upon further pressurization to 63.6 GPa, the Tc decreases slightly to 5.5 K. The pressure dependence of the superconducting transition, summarized in Fig. 3(c), is clearly dome-shaped. To verify that this is a superconducting transition, the effect of magnetic field at 39.4 GPa was studied, as plotted in Fig. 3(b) -the transition is gradually suppressed by magnetic field, as expected for superconductivity. Figure 3  At ambient conditions, SrP3 and SrAs3 have the same crystal structure (C2/m), while SrBi3 forms in the cubic Cu3Au-type structure (space group: Pm-3m, No. 221) 43 . Thus the corresponding static principle suggests the Cu3Au structure type as a strong candidate for the high-pressure structure. The crystal structure model for high-pressure SrAs3 was deduced by testing several candidates, and was ultimately refined with a SrBi3-like structure (space group: Pm-3m, No. 221) 43 . The schematic crystal structure of the high-pressure phase is depicted in Fig. 4(d). Sr and As atoms occupy 1a (0, 0, 0) and 3c (0, 0.5, 0.5) Wyckoff positions, respectively, and the CN for Sr has increased to 12. Figure 4(e) shows the Rietveld refinement of SrAs3 under 49.8 GPa, yielding 70% and 30% for the ambient and high-pressure phases, respectively. The coexistence of high and ambient-pressure phases up to 51.9 GPa indicates that the pressure-induced structural phase transition in SrAs3 is first order and that the two phases have only a minute difference in Gibbs free energy.
Since the pressure-induced superconductivity appears long after the topologically-protected α pocket is eliminated, it is important to check whether the high-pressure band structure of SrAs3 is topologically nontrivial, which is a necessary condition for topological superconductivity. To obtain more electronic structure information on the high-pressure phase of SrAs3, we performed DFT calculations for pressurized SrAs3 at 34 GPa, as summarized in Owing to the cubic symmetry of this material, there are twelve band crossing points at symmetricallyequivalent points in the full BZ. Upon turning on SOC, a gap will be opened at these crossing points, resulting in a continuous SOC gap with a curved chemical potential between valence and conduction bands at each k point, as shown in Fig. 5(b).
To identify the topological nature of this material, the Fu-Kane parity criterion 44,45 at eight timereversal invariant momenta (TRIM) was utilized to determine the Z2 index. We obtain a trivial Z2 of (0;000) from the production of the parities of all occupied bands at the eight TRIM points, as shown in Fig. 5(c). However, the surface states on the (001)-projected surface contain two surface Dirac cones located at X ̅ points, as seen in Fig. 5(d). Because of SOC, these Dirac states host a helical spin texture as shown in Fig. 5(f). The Wilson loop method was employed to determine the mirror Chern number (MCN), and get MCN = 1, in agreement with the surface state behavior observed on the (001) surface [44][45][46] . The continuous SOC gap, topologically-trivial Z2 index, nontrivial mirror Chern number and even number of surface Dirac points indicate that this material is a topological crystalline insulator [44][45][46] . As a counterpart of topological insulators in which crystalline symmetry replaces time-reversal symmetry to enforce topological protection, TCIs possess topological surface states (TSSs) with an even number of gapless Dirac cones on the surface BZ and host a variety of exotic phenomena 46 , for example, large-Chern-number quantum anomalous Hall effect 47 or strain-induced superconductivity 48 . The superconductivity in high-pressure SrAs3 may exist in or be induced in these surface states. Owing to their helical spin texture, any superconducting phase in these surface states would most likely be topologically nontrivial [34][35][36][46][47][48] , making high-pressure SrAs3 a strong candidate for topological superconductor.

Discussion
Searching for Majorana fermions has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation, and they can be realized as a bound state at zero energy, i.e. The superconducting phase of SrAs3 is centrosymmetric (Pm-3m), so barring the exceedingly unlikely possibility of bulk spin-triplet superconductivity, the bulk route to Majorana quasiparticles is not available. However, we propose a TCI state hosting TSSs with helical spin texture. Superconductivity in these states or induced in these states by proximity effect from the bulk could potentially be topologically nontrivial. However, unlike in other TCIs such as SnTe or Pb1-xSnxM (M = Se, Te), trivial bulk bands in pressurized SrAs3 cross the Fermi level, and we are unable to distinguish which bands participate in the superconductivity. Further work will be required to elaborate the contributions from TSSs and bulk states to the superconductivity.
In summary, at ambient pressure, SrAs3 is a TNLSM with 2D drumhead-like nearly-flat surface states, which may be strongly correlated and are often associated with the enhancement of superconductivity 54 , although pressure did not succeed in driving this material superconducting before changing the electronic structure. A Lifshitz transition has been identified below 1.0 GPa, evidencing a topological phase transition, as the quantum oscillations associated with the TNLSM state vanish.
Higher-pressure experiments on a powder sample reveal a dome-like superconducting transition accompanying a structural phase transition into a phase which we predict to host a topologicalcrystalline-insulator state with TSSs and helical spin texture. Besides its intrinsic interest as a TNLSM, SrAs3 offers an alternative route to explore the topological-crystalline-insulator state beyond IV-VI semiconductors and, as a superconducting TCI, high-pressure SrAs3 could serve as a candidate topological superconductor. Doping studies or strain may still be able to induce superconductivity in the low-pressure phase, and should be pursued, and the evolution of the drumhead-like states with pressure remains to be clarified.

Methods
Sample synthesis.
Self-flux method. Sr (99.95 %, Alfa Aesar), and As (99.999 %, PrMat) were mixed in a molar ratio of 1:3 and placed into an alumina crucible. The crucible was sealed in a quartz ampoule under vacuum and subsequently heated to 750 ℃ in 10 h. After reaction at this temperature for 300 h, the ampoule was cooled to 400 ℃ in 50 h and cooled freely to room temperature. SrAs3 single crystals with black shiny metallic lustre were obtained.
Bi-flux method. Sr (99.95%, Alfa Aesar), As (99.999%, PrMat) and Bi (99.9999%, Aladdin) blocks were mixed in a molar ratio of 1:3:26 and placed into an alumina crucible. The crucible was sealed in a quartz ampoule under vacuum and subsequently heated to 900 ℃ in 15 h. After reaction at this temperature for 20 h, the ampoule was cooled to 700 ℃ over 20 h, and then slowly cooled to 450℃ at 1 ℃/h. The excess Bi flux was then removed in a centrifuge, and SrAs3 single crystals with black shiny metallic lustre were obtained.

Pressure measurements.
Resistance measurements under pressure. For high-pressure experiments, samples were loaded in a piston-cylinder clamp cell made of Be-Cu alloy, with Daphne oil as the pressure medium. The pressure inside the cell was determined from the Tc of a tin wire. A SrAs3 single crystal was cut into a bar shape, and the standard four-probe method was used for resistivity measurements, with contacts made using silver epoxy. Higher-pressure measurements were performed on powder samples comprising crushed single crystals using a diamond anvil cell (DAC). The experimental pressures were determined by the pressure-induced fluorescence shift of ruby 55 at room temperature before and after each experiment. A direct-current van der Pauw technique was adopted. Resistance measurements were performed with a physical property measurement system (PPMS, Quantum Design).  58 . The cutoff energy for the plane-wave basis taken was 500 eV. The first Brillouin Zone was sampled, using a Γ-centered 12×12×12 k-point mesh. The energy convergence criteria were defined as 10−8 eV. The lattice constants were fully relaxed using a conjugate gradient scheme until the Hellmann-Feynman forces on the ions were less than 0.001 eV/Å . We constructed the maximally-localized Wannier functions (MLWF) 59-61 using Sr d and As s and p atomic orbitals.
The topological features of surface state spectra were calculated using the iterative Green's function technique 62