Experimental Investigation of Superconductivity in PdSSe Under High Pressure

Analysis of the superconducting properties of transition metal dichalcogenides (TMDs) under high pressures offers valuable insights to guide the design and synthesis of high‐performance superconducting materials. Herein, the effect of pressure is investigated on the superconductivity of a typical van der Waals layered TMDs material, PdSSe, by measuring its transport properties. After initially increased pressure, superconductivity emerges at 10.2 GPa, with a critical superconducting temperature (Tc) of ≈5.1 K, accompanied by the diminishing charge density wave (CDW) that is originally strengthening. Then, the Tc gradually increases with increasing pressure, reaching 12.1 K at the maximum pressure. The study provides experimental evidence for the superconductivity of PdSSe, and to the best of the knowledge, this is the first report on the observation of amplified CDW phenomena under increasing pressure in nonmagnetic TMDs. The abnormal enhancement of CDW transition temperature at low pressure is consistent with the upward trend of resistance, which is related to the electron–electron interaction. Moreover, synchrotron X‐ray diffraction experiments reveal two additional structural phase transitions.


Introduction
Since the successful exfoliation of graphene, [1] 2D materials have undergone rapid development and have been applied in diverse fields, including condensed matter physics, materials DOI: 10.1002/aelm.202300707science, nanotechnology, and other disciplines.For instance, the large specific surface areas of 2D materials promote their utilization in surface active catalysis. [2]Furthermore, owing to their pronounced structural anisotropy, 2D materials can be used in electrical devices. [3]As a prominent branch of 2D materials, transition-metal dichalcogenides (TMDs) have garnered significant interest owing to their unique properties, including a strongly correlated electron effect, [4] quantum spin Hall effect, [5] and superconductivity. [6]ressure application is an efficient technique for clean and precise modification of the crystal and band structures of crystalline materials, [7][8][9] without introducing chemical perturbations.To date, several high-performance superconducting TMD materials, such as 1T-MoS 2 , [10] 1T ' -MoS 2 , [11] 2H-NbS 2 , [12] 1T-NbS 2 , [13] and WTe 2 , [14] have been developed via pressure tuning.Identifying the correlation between superconductivity and other electronic orders is crucial to gaining insights into the mechanics of superconductivity and for developing novel superconductors.Unlike copper-and iron-based superconductors, [15] which exhibit rich electron ordering states (such as nematic phases, [16] stripes, [17] and magnetism [18] ), the most common electron ordering state in TMDs superconductors is CDW.Because CDW and superconductivity in TMDs originate from Fermi surface instability and electron-phonon coupling, examining the correlation between the CDW and superconductivity of TMDs systems is essential for exploring the origin of superconductivity.
Under high pressures, PdS 2 [21] and PdSe 2 [22] undergo the transition from a layered 2O phase to a 3D cubic pyrite-type structure, after which these two NMDCs exhibit metallization, superconductivity, nodal and Dirac topological state development. [23]High-pressure measurements reveal that cubic pyrite PdS 2 and PdSe 2 exhibit a dome-shaped pressure-superconducting temperature (T c ) correlation curve.PdSSe with an orthorhombic P212121 structure serves as an isomorphic intermediate between PdS 2 and PdSe 2 .According to theoretical predictions, PdSSe undergoes a phase transition from a 2O phase to a 3D pyrite structure. [24]Firstprinciples calculations of its energy band at high pressures reveal the existence of Wyel points close to the Fermi surface and a superconducting transition temperature higher than those of PdS 2 and PdSe 2 .Despite extensive research on the effect of pressure on superconductivity in TMDs, the influence of pressure on superconducting properties in NMDCs remains largely unexplored.After its successful synthesis in 1965, [25] there has been absence of experimental reports on PdSSe. [26]The superconductivity of PdSSe under high pressure still poses an unresolved question, awaiting further experimental investigation.
Herein, we evaluated the effect of high pressures on the superconducting properties of PdSSe.As pressure was increased, superconductivity appeared at 10.2 GPa with T c = 5.1 K; simultaneously, the associated CDW diminished, and the observed enhancement of CDW weakened, accompanied by a reduction in the upward shift of the low-temperature resistance.The emergence of superconductivity in PdSSe is related to the enhancement of the electron-phonon coupling under pressure.

Results
To determine the electronic structure under high pressure, we conducted high-pressure resistance measurements on PdSSe up to 85 GPa.Initially, we examined the temperature dependence of the sample's resistance R(T) at 1.7-300 K under atmospheric pressure.Theoretical predictions [24] suggested that the material should exhibit semiconductor properties, but the experimental synthesized sample turned out to be metallic in nature from our R (T) curve in Figure S1 (Supporting Information).This distinction arises from our high-pressure and high-temperature synthesis method, which differs from the previous synthesis [27] of PdSSe as a semiconductor.Figure 1 shows the measured resistance as a function of temperature at high pressures.The resistance steadily decreases with increasing pressure, and upon compression up to 10.2 GPa, the sample's resistance abruptly drops at 5.1 K, indicating the onset of superconductivity as presented in the inset of Figure 1a.However, the zero resistance remained elusive.As the pressure steadily increased, T c exhibited a gradual rise and a zero resistance appeared under a pressure of 26.5 GPa and persisted up to the highest pressure reached in our experiment, as shown in Figure 1b,c.In order to demonstrate that the drop in resistance was attributed to superconductivity, measurements of the low-temperature resistance were conducted under the presence of an external magnetic field at 13.1 and 50 GPa, respectively, as depicted in Figure 2a,b.Evidently, T c gradually decreases as the strength of the magnetic field applied at the two pressure points increases, and this result confirms the existence of superconductivity in the PdSSe.Figure 2c depicts the relationship between the upper critical magnetic field strength and superconducting transition temperature.By fitting the Ginzburg-Landau [28] and conventional single-band Werthamer-Helfand-Hohenberg [29] isotropic s-wave superconductor equations, we determined the upper critical field strength at 0 K (μ 0 H c2 (0)) as 9.8 and 8.4 T, respectively.Both the μ 0 H c2 (0) values were lower than the Bardeen-Cooper-Schrieffer (BCS) weak coupling Pauli paramagnetic limit of μ 0 H p = 1.84 T c .In the framework of the traditional BCS theory, the Pauli order limit shows that PdSSe is a conventional phonon-mediated superconductor.T c gradually increases with pressure, reaching 12.1 K at the highest pressure of 85 GPa.
There are two striking trends in the R (T) curve obtained from both atmospheric and low-pressure conditions.First, a distinct hump appears at ≈200 K in the R(T) curve recorded from ambient pressure to 10.2 GPa in Figures S1 (Supporting Information) and 1a.Such a hump pattern typically appears in the R(T) curves of topological low-dimensional and 3D systems and is different for topological semimetals and topological insulators.The resistance humps exhibited by the R(T) curves of topological semimetals can be attributed to intrinsic chiral fermions, which represent a distinctive electronic state characterized by energy band intersections exhibiting chirality.Temperature variations or external pressure application can induce scattering among these chiral fermions, resulting in an increasing resistance profile characterized by humps; for instance, such behavior is exhibited by materials such as Cd 3 As 2 [30] and SnSe. [31]Meanwhile, the bandgaps of topological insulators exhibit protected boundary states, whose energy levels are not affected by external impurities or defects.At high temperatures or under pressure, the scattering interactions between these boundary states and the bulk state result in an increasing resistance profile characterized by humps; this behavior can be observed in materials such as Bi 2 Te 3 [32] and Bi 2 Se 3 . [33]Alternatively, the emergence of the hump in the R(T) curve can be attributed to the CDW features of the sample; owing to the CDW, the bandgap of the sample opens up at the Fermi level, causing an abnormal decrease in the conductivity, which manifests as a hump in the R(T) curve, and this mechanism is observed materials such as TaS 2 , [34] CuS 2 , [35] and LaAuSb 2 . [36]Early theoretical calculations indicate that the PdSSe compound in the orthorhombic crystal structure phase P212121 does not possess topological properties at ambient pressure. [24]Our first-principles calculations reveal the absence of topologically related Weyl points near the Fermi level in the band structure of PdSSe at ambient pressure in Figure 3. Therefore, after excluding the possibility of the sample having topological attributes, we believe that the reason for the appearance of a hump in the R(T) curve is due to the sample having the CDW property.However, because of the lack of direct experimental evidence of CDW, we refer to this peak as a CDW-like feature (in the following description, for the sake of simplicity, we will refer to all CDW-like phenomena as CDW).To determine the transition temperature (T CDW ), we used the commonly used method of taking the first derivative to plot the dR/dT-T curve.Our investigation reveals a distinctive trend wherein T CDW exhibits a gradual increment with increasing pressure.This observation deviates from the majority of prior studies that report a suppression of the charge density wave under elevated pressure conditions.
Another striking trend in the R(T) curve is the upward curvature in the low-temperature, which can be primarily attributed to electron-electron interactions.We compared the extracted minimum temperature point (T min ), where the low-temperature resis-tivity increases with pressure, with the T CDW shown in Figure 5 (further information is provided in the supporting information).Below 10.2 GPa, T CDW and T min exhibit a strong correlation, whereas above 10.2GPa, T min decreases significantly, and the characteristic peak of the CDW state disappears.Notably, similar pressure-dependent CDW enhancement has also been observed in the antiferromagnetic material 1T-VSe 2 , [37,38] whose low-temperature resistivity increases owing to the Kondo effect.These results suggest that the observed CDW enhancement in PdSSe with increasing pressure can be ascribed to the increase in resistance at low temperatures.
We performed high-pressure synchrotron X-ray diffraction (XRD) measurements at pressures up to 43.2 GPa to elucidate the underlying structural development.Figure 4a displays the typical XRD patterns of the powdered PdSSe crystals recorded at various pressures.As the pressure increases, all the diffraction peaks shift to high angles, consistent with the lattice's continual contraction.The relative intensities of the two peaks at 12.7 and 13.5 °change significantly at 19.9 GPa, and a new peak appears at the position of the asterisk at 22.6 GPa.These results can be attributed to the structural phase transition induced by interlayer sliding in typical 2D materials.For example, in MoS 2 , [42,43] the 2H c -2H a structural phase transition caused by an interlayer slip phase occurs at above 19.9GPa, and this transition coincides with the emergence of metallization and superconductivity.Conversely, in MoSSe, [44] interlayer sliding from the ambientpressure 2H c ' phase into a 2H a ' structure is observed under high pressures.Thus, we can infer that PdSSe experiences interlayer sliding above 19.9GPa, resulting in the emergence of a new highpressure phase (HP-I).Furthermore, another new peak appears at 14.2 °under a pressure of 31.7 GPa, indicating a potential highpressure phase transition (HP-II) in PdSSe.By integrating these findings with the results of synchrotron XRD experiments, we postulate that the fluctuations in residual resistance are closely related to the occurrence of two structural phase transitions in   4b.The variation in the unit cell volume V with pressure can be fitted using the third-order Birch-Murnaghan equation [45] of state, as shown by the solid purple line in Figure 4c.The fitting results yield V 0 = 241.5 ± 3.6 Å 3 , B 0 = 18.4 ± 1.2 GPa, and the first derivative of the bulk modulus B 0 ' = 3.8 ± 0.4.Although our study presents empirical evidence of structural phase transition and offers a more plausible explanation for the high-pressure phase, the definitive high-pressure phase remains undetermined.
In order to further study the mechanism of superconductivity under pressure, the contribution of different atomic pairs to the band structure and Fermi level at different pressures was analyzed using first-principles calculations.It can be observed that at ambient pressure, the closure of the valence and conduction  bands indicates a metallic behavior, which is attributed to the major contribution of the Pd -d orbitals at the Fermi level in Figure S2 (Supporting Information).With increasing pressure, the overlap between the valence and conduction bands increases, resulting in enhancement of the metallic properties of the sample.At 12 GPa, a new hole pocket appears between the Y-X highsymmetry points, indicating a drastically altered Fermi surface in Figure 3, which possibly strengthens the electron-phonon coupling interactions, resulting in the emergence of superconductivity at 10.2 GPa.In addition, the calculated density of states (DOS) reveals that within the pressure range where superconductivity occurs, there is a significant increase in the contribution of the S -p and Se -p orbitals near the Fermi level, while the contribution of the Pd -d orbitals decreases significantly in Figures S5 and  S6 (Supporting Information).41] Further investigations are required to determine its highpressure phases.The phase diagram of compressed PdSSe is illustrated in Figure 5, which demonstrates the relationship between CDW and superconductivity as a function of pressure.Evidently, T c increases with pressure, reaching a maximum value of 12.1 K at a pressure of 85 GPa.T CDW first increases with increasing pressure, consistent with T min , and disappear at 10.2 GPa with the weakening of electron-electron interaction.Our test results indicate that the T c of PdSSe lies between those of PdS 2 and PdSe 2 at comparable pressures.These findings suggest that the majority of intermediate materials with isomorphic relationships exhibit features that are similar to those of the two initial components.

Conclusion
We successfully synthesized PdSSe with a 2O configuration under high-temperature and high-pressure conditions.Theoretical calculations indicate that the emergence of superconductivity at 10.2 GPa is closely related to the enhanced electron-phonon coupling.The observed anomalous enhancement in the CDW with increasing pressure was attributed to electron-electron interactions, and in the pressure range of 10.2-85 GPa, T c increased from 5.1 to 12.1 K. Our work enriches the study of the physical properties of NMDCs family under high pressure and provides ideas for designing more ternary superconducting compounds.

Experimental Section
The powder PdSSe compounds were synthesized by a sophisticated highpressure, high-temperature method inside an SPD 6 × 27 000 cubic anvil device.A mixture of 1:1:1 ration of 99.99% pure selenium, 99.99% pure sulfur, and 99.99% pure palladium was prepared in the anvil apparatus at 5 GPa and 1700 K for 30 min.XRD measurements were conducted at ambient pressure to confirm the purity and structure of the orthorhombic P212121 PdSSe sample in Figure S4 (Supporting Information).
High-pressure electrical transport measurements were conducted in a nonmagnetic Be-Cu diamond anvil cell, equipped with a pair of 200-μm anvil culets, using tungsten as the gasket material, and aluminum oxide and an epoxy resin adhesive were used to insulate the gasket.The standard four-electrode method was used to measure the resistance.
The high-pressure powder XRD experiments were conducted at the BL15U1 beamline of the Shanghai Synchrotron Radiation Facility ( = 0.6199 Å).The collected images were first processed using the DOIP-TAS program [46] to convert them into data outputs, which were then subjected to data refinement and analyzed by fitting using the Materials Studio software. [47]

Figure 1 .
Figure 1.Temperature dependence of electrical resistance in the PdSSe sample under high pressure a) between 1.7 and 10.2 GPa and illustration highlights the emergence of superconductivity.b) Between 13.1 and 31.0GPa and the illustration highlights the emergence of zero resistance of superconductivity.c) Between 36.9 and 85 GPa.

Figure 2 .
Figure 2. Determination of the critical magnetic field μ 0 H c2 (0) at zero-temperature of PdSSe.The R (T) curve a) at 13.1 GPa under an external magnetic field of 0-3 T. b) At 50 GPa under an external magnetic field of 0-4 T. c) A μ 0 H c2 -T c phase diagram.The solid lines in red and blue represent fitting by the WHH formula and GL equation, respectively.

Figure S3 (
FigureS3(Supporting Information).The pressure dependences of the lattice parameters a, b, and c and the cell volume V determined by fitting before the phase transition are shown in Figure4b.The variation in the unit cell volume V with pressure can be fitted using the third-order Birch-Murnaghan equation[45] of state, as shown by the solid purple line in Figure4c.The fitting results yield V 0 = 241.5 ± 3.6 Å 3 , B 0 = 18.4 ± 1.2 GPa, and the first derivative of the bulk modulus B 0 ' = 3.8 ± 0.4.Although our study

Figure 4 .
Figure 4. a) XRD patterns from 1.1 GPa up to 43.2 GPa at room temperature ( = 0.6199 Å) and the gray area represents the XRD peak position of tungsten.b) The variation of cell parameters with pressure.c) The B-M equation was used to fit the changes of volume with pressure.

Figure 5 .
Figure 5. Pressure-temperature (P-T) phase diagram of PdSSe.The vertical dashed line demarcates the boundary of the atmospheric structure, HP-I and HP-II.