Pressure‐Induced Superconductivity and Structure Phase Transition in SnAs‐Based Zintl Compound SrSn2As2

Layered SnAs‐based Zintl compounds exhibit a distinctive electronic structure, igniting extensive research efforts in areas of superconductivity, topological insulators, and quantum magnetism. In this paper, the crystal structures and electronic properties of the Zintl compound SrSn2As2 upon compression are systematically investigated. Pressure‐induced superconductivity is observed in SrSn2As2 with a nonmonotonic evolution of superconducting transition temperature Tc. Theoretical calculations together with high‐pressure synchrotron X‐ray diffraction and Raman spectroscopy have identified that SrSn2As2 undergoes a structural transformation from a rhombohedral R 3¯$\bar{3}$m phase to the monoclinic C2/m phase. Beyond 28.3 GPa, Tc is suppressed due to a reduction of the density of state (DOS) at the Fermi level. The discovery of pressure‐induced superconductivity, accompanied by structural transitions in SrSn2As2, greatly expands the physical properties of layered SnAs‐based compounds and provides new ground states upon compression.

Layered Zintl compound NaSn2As2 crystallizes in trigonal R3 � m structure, where Na + ions are separated by two honeycomb [SnAs] 2-layers.The adjacent honeycomb layers interaction is via van der Waals (vdW) forces [25,28].At ambient pressure, NaSn2As2 showed bulk superconductivity with Tc of 1.3 K [25,28].It should be noted that NaSn2As2 is a non-electron-balanced compound, containing Sn 2+ ions with lone pairs of electrons [22,29].In contrast to NaSn2As2, the isostructural compounds EuSn2As2 is electron-balanced.EuSn2As2 contains magnetic Eu 2+ ions, forming a peelable layered magnetic Zintl phase.A transition from paramagnetic (PM) to antiferromagnetic (AFM) phase in EuSn2As2 occurs around TN ~ 24 K [30][31][32].Below TN, EuSn2As2 is ferromagnetic in the  plane and antiferromagnetic between adjacent layers, forming an A-type AFM.A combination of first-principles calculations and angle-resolved photoemission spectroscopy (ARPES) experiments reveal that EuSn2As2 is a magnetic topological insulator (TI), characterizing by the absence of a detectable gap in the Dirac topological surface states (SSs).Besides, EuSn2As2 transforms from a strong TI with PM state to an axial insulator with AFM state below TN [33].TN shows a linear increase with pressure below 10 GPa, attributed to the enhanced interlayer magnetic exchange coupling among Eu 2+ ions [34].Beyond ∼14 GPa, EuSn2As2 experiences a two-step highpressure structural transformation, giving rise to a novel monoclinic configuration.The bent Sn-Sn bonds become planar and form honeycomb Sn sheets, coinciding with the emergence of superconductivity around 4 K [35,36].
SrSn2As2 is the sister compound of EuSn2As2, and SrSn2As2 remains relatively less explored.Theoretical calculations of the electronic structure propose that SrSn2As2 is a potential candidate for the novel three-dimensional Dirac semimetal due to its close proximity to the critical point [37].The ARPES results present a band reversal feature near the Γ point, indicating that SrSn2As2 may be a new topological insulator [38].Given that EuSn2As2 is superconducting accompanied with structure transition under high pressure, it is interesting to explore novel quantum phenomena in SrSn2As2 upon compression.Hence, we systematically investigate the structural and electronic properties of the SnAs-based Zintl compound SrSn2As2 under high-pressure.Interestingly, we observed the pressure-induced superconductivity in SrSn2As2, with a characteristic dome-shaped evolution of Tc.Our theoretical calculations reveal that SrSn2As2 undergoes a structural transformation from a trigonal to a monoclinic phase under high pressure, as evidenced by both Xray diffraction (XRD) and Raman data.The electronic band structure of high-pressure phase and the evolution of Tc are also discussed.

EXPERIMENTAL DETAILS and CALCULATION METHODS
The single crystals of SrSn2As2 were grown by self-flux method.In order to obtain high-quality single crystals, pretreatment of starting materials (Sn, Alfa Aesar, 99.999% and As, Alfa Aesar, 99.99%) was performed to remove possible oxide layers on their surface by hydrogen reduction method and sublimation recrystallization method.High-purity starting materials of Sr, Sn, and As were loaded into an Al2O3 crucible with the atomic ratio of Sr: Sn: As = 1: 2: 2.2, and sealed into a quartz tube in a vacuum of 8×10 -4 Pa.The raw materials were reacted and homogenized at 1173 K for several hours, followed by cooling down to 773 K at a rate of 3 K/h.The crystalline phase of SrSn2As2 was checked by the X-ray diffraction (XRD, Cu Kα, λ = 1.54184Å).The chemical composition of SrSn2As2 is given by energy-dispersive x-ray spectra (EDX).Electrical transport properties were performed on a physical property measurement system (PPMS, Quantum Design).
Electrical transport measurements under higher pressures were performed in a nonmagnetic diamond anvil cell (DAC) [39][40][41].A cubic BN/epoxy mixture layer was inserted between BeCu gaskets and electrical leads.Four platinum sheet electrodes were touched to the sample for resistance measurements with the van der Pauw method [40,42,43].Pressure was determined by the ruby luminescence method [44].High-pressure in situ Raman spectroscopy investigation was performed using a Raman spectrometer (Renishaw in-Via, UK) with a laser excitation wavelength of 532 nm and a low-wavenumber filter.A symmetric DAC with anvil culet sizes of 300 μm was used, with silicon oil as pressure transmitting medium (PTM).High-pressure in situ XRD measurements were performed at beamline BL15U of Shanghai Synchrotron Radiation Facility (Xray wavelength λ = 0.6199 Å).A symmetric DAC with anvil culet sizes of 200 μm and Re gaskets were used.Silicon oil was used as the PTM.The two-dimensional diffraction images were analyzed using the FIT2D softwar [45].Rietveld refinements of crystal structure under various pressures were performed using the GSAS and the graphical user interface EXPGUI [46,47].We used the machine learning graph theory accelerated crystal structure search method (Magus) to explore the structures of SrSn2As2 under 30 GPa and 50 GPa [48,49].We performed the geometry optimization using the Vienna Ab-initio Simulation Package (VASP) based on the density functional theory [50,51].The exchange-correlation functional was treated by the generalized gradient approximation of Perdew, Burkey, and Ernzerhof [52].The calculations used projector-augmented wave (PAW) approach to describe the core electrons and their effects on valence orbitals [53].The plane-wave kinetic-energy cutoff was set to 600 eV, and the Brillouin zone was sampled by the Monkhorst-Pack scheme of 2π × 0.03 Å -1 .The convergence tolerance was 10 -6 eV for total energy and 0.003 eV/Å for all forces.The electronic structure calculations used a denser k-mesh grid of 2π × 0.02 Å -1 .The phonon spectrum were calculated by the PHONOPY program package using the finite displacement method with the supercell 2 × 2 × 2 [54].

RESULTS AND DISCUSISION
Prior to high-pressure measurements, we first check the sample quality by single-crystal and powder XRD diffractions.The single-crystal XRD patterns on the flat surface of the sample shows sharp (00l) diffraction peaks [Figure 1(a)].The calculated lattice parameter is c = 26.66Å, in agreement with the previous report [20].The inset of Fig. 1(b) is the chemical compositional analysis results using EDX, illustrating a Sr:Sn:As atomic ratio of 20.45:38.97:40.59,which is consistent with the nominal composition.In addition, we further performed the powder XRD for structure characterizing.As shown in Fig. 1(b), all the Bragg peaks can be indexed into rhombohedral symmetry with the space group R3 � m.The consistence between powder and single crystal XRD measurements guarantees the correct phase.The ambient crystal structure of SrSn2As2 is shown in Figure 1(c), which is identical to the configuration of EuSn2As2 and NaSn2As2.Then, we performed transport measurements at ambient pressure.Figure 1(d) shows the resistivity of SrSn2As2 as a function of temperature, showing typical metallic behavior with residual resistivity ratio (RRR) = 2.31.
Since NaSn2As2 showed superconductivity at ambient pressure and EuSn2As2 achieved superconductivity upon compression, it is natural to explore superconductivity in SrSn2As2 using high pressure technology.Hence, we investigated the effect of high-pressure on SrSn2As2 single crystals.Figure 2(a) shows the electrical resistivity ρ(T) of SrSn2As2 at different pressures.Increasing pressure induces a continuous suppression of the overall magnitude of ρ(T), which is typical behavior of metal under high pressure.At 14.9 GPa, the resistivity of SrSn2As2 drops abruptly at 1.8 K [Figure 2(b)].As shown in Fig. 2(b), the resistivity dropped around 3 K and becomes more pronounced upon further compressing.Above 28.3 GPa, zero resistivity is observed at low temperatures, indicating a superconducting transition.The superconducting transition temperature Tc (90% drop of the normal state resistivity) reaches 4.63 K at P = 28.3GPa.As plotted in Fig. 2(c), Tc decreases slowly beyond this pressure, and the superconductivity persists up to 53.5 GPa.The temperature dependence of transition width ΔTc (10%-90% of the normal state resistance at Tc) is in Fig. 6.The transition width ΔTc has a sharp decline from 2.07 K to 0.44 K in the pressure range from 22.9 GPa to 34.4 GPa.Transition width ΔTc reflects the superconducting stated disturbance originating from the thermodynamic fluctuations, the applied magnetic field, the presence of secondary crystalline phases, the applied pressure, etc. [55], which needs further evidence to confirm its origin.The overall behavior of Tc is a typical dome-like evolution under high pressure.Interestingly, a dome-like Tc is observed during decompression, and the superconducting transition persists until recovery to 14.9 GPa (Fig. S1 in the Supplemental Material).
To gain insight into the superconducting transition, we applied an external magnetic field of 28.3 GPa and 48.01 GPa during the rise and fall of Tc on SrSn2As2, respectively.Figure 2(d) and (e) demonstrate that the Tc is continuously suppressed with increasing magnetic field and the superconducting transition could not be observed above 1.8 K at around 2.5 T. This confirms that the sharp drop of ρ(T) around 4 K in SrSn2As2 originates from a pressure-induced superconducting transition.The upper critical field μ0Hc2 is determined from the 90% point on the resistivity transition curve，and the plot of temperature normalized Hc2(T) is shown in Fig. 2(f).By fitting the data using the Ginzburg-Landau (GL) formula ⁄ is the reduced temperature with zero-field superconducting Tc.The extrapolated upper critical fields μ0Hc2 (0) at 28.3 GPa and 48.1 GPa are 2.05 T and 2.41 T, which yields a Ginzburg-Landau coherence length  GL (0) of 12.68 nm and 11.69 nm, respectively.
The transition width ΔTc drastic changed at around 30 GPa, and the slopes of dHc2/dT are notably different: − 0.53 and − 0.69 T/K for 28.3 and 48.1 GPa, respectively.Our results suggest that the nature of the superconducting state beyond 30 GPa may differ from that of the initial superconducting one.In order to identify the structural stability of SrSn2As2 under high pressure, we have performed high-pressure in situ synchrotron XRD and Raman spectroscopy measurements, as shown in Fig. 3.The XRD patterns of SrSn2As2 collected at different pressures are shown in Fig. 3(a).As the pressure increases, all diffraction peaks move to higher angles due to lattice contraction, and no structural phase transition is observed at pressures up to 29.8 GPa.Above 33.0 GPa, additional diffraction peaks appear, indicating a structural phase transition.Fig. 3(b) presents the Raman spectra of bulk SrSn2As2 under various pressures up to 55.5GPa.With increasing pressure, the interaction force between adjacent layers increases and all four phonon modes exhibit blue-shift, which is analogous to EuSn2As2 [36].The Raman signals of the  1 2 mode become significant, while   2 mode decreases monotonically.An abrupt disappearance of Raman peaks for pressure beyond 33.6 GPa indicates the structural phase transition to a high-pressure phase.The evolution of the Raman spectra is consistent with our synchrotron XRD patterns and provides further evidence for pressure-induced structural phase transitions.
It should be emphasized that by only relying on the experimental data, the structural solution of high-pressure phases is not possible, because the XRD peaks are rather weak and broad.Hence, we performed the structure predictions at 30 GPa and 50 GPa.In each searching, structures were evaluated within 25 generations with 30 structures per generation, and the ambient stable structure R3 � m was treated as seed structure.We found one stable candidate C2/m phase under high pressure, as shown in the inset of Fig. 4(a).The buckled Sn-Sn bonds become planar and form honeycomblike Sn sheets, meanwhile the SnAs layers further connect to each other via the As-As bonds across the Sr layers to form zigzag As chains between the Sn sheets.This three-dimensional monoclinic structure comprising honeycomblike Sn sheets and zigzag As chains resembles the situation in EuSn2As2 identified under high pressure [35].As the enthalpy difference relative to R3 � m structure in Fig. 4(a), the enthalpy of C2/m structure is below that of R3 � m above 22 GPa, suggesting that C2/m structure is more energetically stable under high pressure.Then we calculated the phonon spectrum of C2/m structure under high pressure, as plotted in Fig. 4(b) and (c).There are no imaginary frequencies in the phonon dispersion of C2/m above 25 GPa, illustrating its dynamical stability.In summary, our theoretical and experimental results suggest that there is a structural phase transition from R3 � m phase to C2/m phase under high pressure.
Next, we calculated the electronic structures of C2/m structure under high pressure.As depicted in Fig. 5 (a) and (c), the valence bands and conduction bands cross the Fermi energy in the band structures of C2/m phase, exhibiting typical metal characteristics.We can observe steep conduction bands crossing the Fermi energy, which is beneficial for superconductivity.The corresponding partial density of states (PDOS) are in Fig. 5 (b) and (d).The Sn atoms make main contribution at the Fermi energy, and the total density of states (DOS) at Fermi energy N(Ef) decrease from 5.2 states/formula at 25 GPa to 4.1 states/formula at 50 GPa, which agrees with the slow decreasing of Tc from 28.3 GPa to 53.5 GPa.
Based on the aforementioned results, we can establish a Tc-P phase diagram for SrSn2As2 as shown in Fig. 6.Superconductivity was observed at around 20.8 GPa.A domelike evolution is observed with a maximum Tc of 4.63 K at 28.3 GPa for SrSn2As2.The high pressure in-situ synchrotron XRD and Raman spectroscopy reveal the evidence of structural transition around 28.3 GPa, which is in line with the theoretical predictions that the ambient R3 � m phase transforms to the high-pressure C2/m phase.Combining the transition width results and theoretical calculations, the Tc-P phase diagram reveals two distinct superconducting regions: SC-I R3 � m phase and SC-II C2/m phase.In the SC-I region, Tc increases with pressure with a broaden superconducting transition width.In the SC-I region between 25 and 60 GPa, Tc is monotonically suppressed with external pressure.The suppression of Tc in SrSn2As2 under pressure can be attributed to a decline in electronic density of states at the Fermi level.

CONCLUSION
In summary, we have synthesized SrSn2As2 single crystal and explored the structure and electronic transport properties under high pressure.Our results demonstrate a pressure-induced superconductivity in SrSn2As2.The pressure dependent Tc follows a dome-like evolution with a maximum Tc value of 4.63 K at 28.3 GPa.Our theoretical calculations, together with high-pressure in-situ X-ray diffraction, Raman spectroscopy measurements, indicate that SrSn2As2 transforms from the ambient phase R3 � m to the monoclinic C2/m phase above 25 GPa.Our research provides valuable insights into the understanding of the superconductivity in the layered SnAs-based family.

FIG. 3 .
FIG. 3. (a) XRD patterns of SrSn2As2 under different pressures up to 53.9 GPa.(b) Raman spectra of SrSn2As2 under pressure at room temperature.

FIG. 4 .
FIG. 4. (a) The enthalpy difference relative to R3 � m structure with in 40 GPa.The calculated phonon spectrum of the predicted C2/m structure at (b) 25 GPa and (c) 50 GPa.