Superconductivity emerging from a pressurized van der Waals kagome material Pd3P2S8

Kagome materials have been reported to possess abundant and peculiar physical properties, which provide an excellent platform to explore exotic quantum states. We present a discovery of superconductivity in van der Waals material Pd3P2S8 composed of Pd kagome lattice under pressure. Pd3P2S8 displays superconductivity for those pressures where the semiconducting-like temperature dependence of the resistivity turns into a metallic one. Moreover, it is found that the increased pressure results in a gradual enhancement of superconducting transition temperature, which finally reaches 6.83 K at 79.5 GPa. Combining high-pressure x-ray diffraction, Raman spectroscopy and theoretical calculations, our results demonstrate that the observed superconductivity induced by high pressure in Pd3P2S8 is closely related to the formation of amorphous phase, which results from the structural instability due to the enhanced coupling between interlayer Pd and S atoms upon compression.

diffraction (XRD), Raman spectroscopy and theoretical calculations, our results suggest that the appearance of superconductivity could be related to the amorphous transition as a result of structural instability arising from the increased coupling of Pd and S atoms between adjacent layers under high pressure.
Single crystals of Pd 3 P 2 S 8 were grown by chemical vapor transport technique [18] with a molar ratio of Pd:P:S = 3:2:8 in a two-zone furnace. Both the powder and single crystal XRD patterns of Pd 3 P 2 S 8 at ambient pressure were measured in x-ray diffractometer (Bruker D8 Advance) with Cu K α radiation of wavelength λ = 0.15418 nm. In situ high-pressure electrical transport property was performed in Physical Property Measurement System (PPMS-9T). The resistivity of Pd 3 P 2 S 8 samples was measured by van der Pauw method using Pt wires. The single crystal was cut into plenty of small pieces, then loaded and pressed in diamond anvil cell (DAC) with 200 µm anvil culet. In order to make sure the electrical insulation in DAC, a cubic boron nitride and epoxy mixture layer was employed above the BeCu gasket. The applied magnetic field was parallel to c-axis direction. In situ high-pressure XRD experiments were carried out on the beamline BL15U of Shanghai Synchrotron Radiation Facility using x-ray (λ = 0.6199 Å). In situ high-pressure Raman spectroscopy experiments were performed in a Renishaw Raman spectrometer (laser excitation wavelength λ = 532 nm). Ruby luminescence method [26] was used for determining the pressure in all of high-pressure experiments.
The phonon spectra of Pd 3 P 2 S 8 under pressure were investigated with the density functional perturbation theory [27] calculations as implemented in the Quantum ESPRESSO package [28]. The kinetic energy cutoffs of the wave functions and the charge densities were chosen to be 60 and 600 Ry, respectively. The Fermi surface was broadened by the Gaussian smearing method with a width of 0.0037 Ry (0.05 eV). In the structural optimization, both lattice constants and internal atomic positions were fully relaxed until the forces on atoms were smaller than 0.0001 Ry/Bohr. For the BZ sampling of the primitive cell, the 7 × 7 × 7, 12 × 12 × 12 k-point mesh and the 4 × 4 × 4 q-point mesh were used for the structural optimization, the self-consistent and phonon spectra calculations, respectively. The DFT-D2 method [29,30] was used to account for the vdW interaction between Pd 3 P 2 S 8 layers. Pd 3 P 2 S 8 is crystalized in hexagonal layered structure with P-3m1 space group (No. 164) [31] at ambient pressure. Pd atoms form perfect two-dimensional kagome lattice ( figure 1(a)). In the S-Pd-S slabs marked with dashed rectangular in figure 1(a), each Pd atom is surrounded by four S atoms, forming a coplanar tetragon. Moreover, there are partial S atoms exactly lying below and above P atoms. Pd 3 P 2 S 8 single crystal is partially transparent with red (inset of figure 1(b)). The powder XRD pattern of Pd 3 P 2 S 8 single crystal ( figure 1(b)) shows that all of peaks can be well refined with the P-3m1 space group, yielding lattice parameters a = 6.8534(3) Å, c = 7.2453(5) Å. The values are consistent with those reported in previous literature [31]. There is no impurity phase in Pd 3 P 2 S 8 single crystal. Moreover, as shown in figure 1(c), the (00l) peaks observed in the single crystal XRD spectra implies that the plane of Pd 3 P 2 S 8 single crystal is perpendicular to the [00l] direction.
We carried out high pressure experiments on Pd 3 P 2 S 8 single crystals to study the effect of pressure on electrical transport. The temperature dependence of resistivity ρ(T) between 14.3 and 63.2 GPa for Run 1 is depicted in figure 2(a). When the applied pressure is around 14.3 GPa, the resistivity shows significant semiconducting behavior, i.e. the ρ(T) curve increases with decreasing temperature. The value of the resistivity initially reaches 0.85 Ω cm at 10 K and 14.3 GPa and then declines rapidly with further applying pressures. Surprisingly, at 25.2 GPa, the resistivity featured semiconducting behavior begins to drop sharply in the low temperature region (figure 2(b)). The downward tendency continued until 31.1 GPa. At the pressure of 34.4 GPa, the ρ(T) curve shows metallic behavior at normal state, and the resistivity drops to zero at low temperature, strongly suggesting the emergence of superconducting state. The T c,onset determined by the linear extrapolations of ρ(T) before and after the drop in resistivity at low temperature is about 2.82 K, and T c,zero where the resistivity reaches zero is 1.84 K. It is clear that the T c increases monotonously with increasing pressure, and the resistivity at 10 K changes weakly in the metallic state. There is no saturated tendency up to 63.2 GPa and the maximum T c we measured is about 6 K. Moreover, ρ(T) curves measured on another Pd 3 P 2 S 8 single crystal under compression for Run 2 are presented in figures S1(a) and (b) of supplementary material [32]. It suggests that all these results including semiconductor-metal transition and emergent superconductivity during high pressure are reproducible and credible. Furthermore, we also measured the ρ(T) curves under decompression (figures 2(c) and (d)). During the release of pressure, the superconducting state in Pd 3 P 2 S 8 still exists and shows different values of T c compared with those under compression, indicating the superconducting transition induced by high pressure is non-reversible. Moreover, the ρ(T) curves as a function of temperature from 0 T to 5 T for 70.1 GPa in Run 2 is shown in figure 2(e). As the magnetic field increases, the superconductivity is progressively suppressed, accompanied by the monotonous reduction in the values of T c . The temperature dependent upper critical field µ 0 H c2 (T) is shown in figure 2(f). Here, the value of temperature T is derived from the half of normal state resistivity.
To determine the upper critical field   used to fit the µ 0 H c2 (T) curves [14]. The obtained µ 0 H c2 (0) for 59.5, 70.1 and 79.5 GPa are 5.6, 6.0 and 6.6 T respectively. These values are all less than the Pauli limiting field 1.84T c .
Then we measured high pressure XRD on Pd 3 P 2 S 8 single crystal so as to certify whether the pressure-induced superconductivity is associated with structural phase transition ( figure 3(a)). Most of peaks can be refined by means of the initial Pd 3 P 2 S 8 structure with P-3m1 space group until 26.5 GPa. The small peaks marked with asterisks represent the signals of rhenium gasket, which are attributed to the trailing of x-ray spot. When increasing the pressure, all of peaks slowly shift to higher angles. Interestingly, when the pressure is above 30.8 GPa, the strength of the Pd 3 P 2 S 8 peaks almost vanish except for that of the peaks of rhenium gasket around 15 • -18 • , which is a non-reversible process upon decompression. It demonstrates that Pd 3 P 2 S 8 exists no structural phase transition in the pressures below 26.5 GPa and may go through an irreversible amorphous phase transition from 30.8 to 77.1 GPa. Moreover, the lattice parameters a and c determined by means of the structural refinements below 26.5 GPa both gradually reduce under pressure, as presented in figure 3(b). Accordingly, the calculated volume declines with increasing pressure (figure 3(c)). Meanwhile, the Raman spectroscopy experiments were also carried out ( figure 3(d)). There is no anomaly below 25.2 GPa, further suggesting the absence of structural phase transition. However, above 26.0 GPa, the Raman peaks appreciably weakened, which is very analogous to the phenomenon observed in high-pressure XRD.
To explore the lattice dynamics of Pd 3 P 2 S 8 under pressure, we calculated its phonon dispersions at three typical pressure points 10, 20, and 30 GPa, as shown in figures 4(a)-(c), respectively. Under 10 GPa, the absence of imaginary frequency in the phonon dispersion across the whole BZ indicates the dynamical stability of Pd 3 P 2 S 8 . When the pressure increases up to 20 GPa, two of the acoustic branches display imaginary modes around the A point, which means that Pd 3 P 2 S 8 tends to become unstable at this pressure. As the pressure further rises to 30 GPa, almost all symmetry paths in the BZ demonstrate imaginary phonon modes, which corresponds to a large structural distortion of Pd 3 P 2 S 8 . The pressure dependence of structural instability derived from our calculations agrees well with our XRD and Raman measurements. To simulate the amorphous process theoretically, we performed ab initio molecules dynamic simulations of Pd 3 P 2 S 8 under 0 GPa and 30 GPa at 300 K by using a large 3 × 3 × 2 supercell containing 234 atoms (figure S2). As shown in figure S2(b), the crystal structure of Pd 3 P 2 S 8 remains intact under 0 GPa at 300 K. In contrast, under 30 GPa, a snapshot of the atomic structure at 10 ps becomes disordered and there is no periodicity at all ( figure S2(d)). This suggests the emergence of amorphous transition in Pd 3 P 2 S 8 , which is not a structural phase transition as in charge-density-wave materials. If we assume that the lattice framework of Pd 3 P 2 S 8 does not change under pressure, we find that the pressure can induce a gradual reduction of the lattice constants ( figure 4(d)), especially the one along the c direction with the weak interlayer vdW interaction. In contrast to the almost unchanged intralayer Pd-S bond length (d Pd-S ), the atomic distance between Pd and S atoms from the neighboring layers (d) follows exactly the tendency of lattice constant c and it even becomes comparable to the intralayer Pd-S bond length at high pressure. The drastic reduction of d under high pressure significantly enhances the coupling between Pd and S atoms from the neighboring layers. Due to the special protruding structure of each Pd-P-S layer (figure 4(e)), the two-dimensional Pd 3 P 2 S 8 can easily transform to a three-dimensional system under high pressure, which leads to the structural instability as evidenced by the imaginary phonon modes in the BZ. Figure 5 illustrates the phase diagram for the pressure dependence of both resistivity at 10 K and T c for Pd 3 P 2 S 8 single crystal in different runs. The T c increases monotonously upon compression for both Run1 and Run2, and reaches a maximum value of 6.83 K at 79.5 GPa during the transport measurements. The stable crystal structure enters into an amorphous phase above ∼26 GPa, where the pressure-induced superconducting state is observed. Hence, it indicates the appearance of superconductivity in Pd 3 P 2 S 8 has relation to the amorphous transition. In addition, there are two other similar works appeared [33,34]. For the former [33], the pressures where the superconductivity emerges are similar to the values in our work. It should be noted that the hydrostatic pressure conditions could result in the difference in the determined pressures. Due to the smaller size of anvil culet in our measurements, the pressure is increased up to ∼80 GPa. The amorphs phase transition was also certified by the high pressure XRD and Raman spectroscopy experiments in the latter work [34], reaching a similar result compared with our work. Moreover, we further analyze that the calculated imaginary modes in phonon spectra of Pd 3 P 2 S 8 above 20 GPa are possibly the main reason of the formation of amorphous transition. Similar superconducting phenomena in the amorphous phases were also observed in other materials, such as Bi 4 I 4 , (NbSe 4 ) 2 I, and MnBi 2 Te 4 [24,35,36]. Moreover, with further releasing pressure, the sample exhibits a non-reversible superconducting state, which is in agreement with the high-pressure XRD under decompression.
In summary, the vdW compound Pd 3 P 2 S 8 single crystal exhibits superconductivity induced by high pressure, where the temperature dependent resistivity undergoes a semiconducting-metallic behavior transition. With increasing pressure, the T c is monotonously enhanced up to 6.83 K at 79.5 GPa. The combined high-pressure XRD, Raman spectroscopy and phonon spectra calculation consistently evidence that the emergence of superconductivity is accompanied with an amorphization, which originates from the instability of structure. The discovery of the superconductivity in Pd 3 P 2 S 8 induced by high pressure not only enriches the studies of superconductivity in kagome system, but also encourages us to further explore novel kagome materials which host superconductivity.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).