Pressure-induced monotonic enhancement of Tc to over 30 K in the superconducting Pr0.82Sr0.18NiO2 thin films

The successful synthesis of superconducting infinite-layer nickelate thin films with the highest Tc ~ 15 K has reignited great enthusiasms on this family of potential analogue to high-Tc cuprates. Pursuing a higher Tc is always an imperative task in studying a new superconducting material system. Here we report high-quality Pr0.82Sr0.18NiO2 thin films with Tconset ~ 17 K synthesized by carefully tuning the amount of CaH2 in the topological chemical reduction and the effect of pressure on its superconducting properties by measuring electrical resistivity under various pressures in a cubic anvil cell apparatus. We find that the onset temperature of the superconductivity, Tconset, can be enhanced monotonically from ~ 17 K at ambient pressure to ~ 31 K at 12.1 GPa without showing signatures of saturation upon increasing pressure. This encouraging result indicates that the Tc of infinite-layer nickelates superconductors still has room to go higher and it can be further boosted by applying higher pressures or strain engineering in the heterostructure films.


Introduction
Since the discovery of the high-Tc superconductivity in cuprates (1), numerous experimental and theoretical investigations have been carried out aiming at finding more superconductors with higher Tc and unveiling the mysteries mechanisms. After over 30 years of endeavor, the highest Tc in cuprates, ~135 K at ambient (2) and ~164 K under pressure (3), remains to be lower than room temperature, and the mechanism is still an enigma. As the nearest neighbor to copper in the periodic table, the infinitelayer nickelates showing the great similarities in crystal structures and electronic configurations to cuprates have been considered as potential high-Tc superconductors ever since the early 1990s (4)(5)(6)(7)(8)(9)(10)(11)(12)(13). Unfortunately, superconductivity was not observed in the synthesized powder and thin film nickelates until very recently.
In 2019, Li et al. reported the experimental observation of the superconductivity with Tc = 9-15 K in the hole-doped infinite-layer Nd1-xSrxNiO2 thin films obtained by softchemistry topotactic reduction from the corresponding perovskite phase (14). From the experimentally constructed superconducting phase diagram, the observed Tc(x) has a non-monotonic evolution with doping x, similar to the hole-doped cuprates (15)(16)(17). This discovery has reignited the enthusiasms on the nickelates and immediately attracted extensive investigations recently (for a review, see Ref. (18)). For the parent LaNiO2 and NdNiO2, X-ray absorption spectroscopy (XAS) and resonant inelastic Xray scattering (RIXS) confirmed the nominal 3d 9 electronic configuration but revealed a reduced hybridization between Ni 3d and O 2p orbitals, and an enhanced coupling between Ni 3d and La/Nd 5d states (19). Notably, the electron energy loss spectroscopy (EELS), high-resolution XAS and RIXS experiments further revealed that the doped holes reside on the Ni sites, forming the low-spin d 8 state (20,21).
These observations are different from those in cuprates (22,23). Recent STM experiments uncovered a mixed s-and d-wave superconducting gap feature on the rough surface of Nd1-xSrxNiO2 thin films (24), and these results were reproduced by employing ab initio treatment on different terminated surfaces (25,26). From the theoretical point of view, three main perspectives on nickelates have been proposed, including the cuprate-like correlated single-Ni-orbital dx 2 −y 2 band (23,25,(27)(28)(29)(30)(31)(32), the Ni-3d-multiorbital effects (33)(34)(35)(36)(37), and the Kondo physics between Ni-3d and Nd-5d orbitals (38)(39)(40). So far, consensus has not yet been reached about the superconducting mechanism of nickelates. This is partially attributed to the great challenges in the materials' synthesis, the relatively poor quality of these infinite-layer nickelates, and the limited techniques for regulating their physical properties. In contrast to the superconducting thin-film samples, the bulk samples exhibit an insulating ground state, and no indication of superconductivity was observed even under pressures up to 50 GPa (41). It has raised the question whether the observed superconductivity correlates intimately with the heterostructure or epitaxy strain between the thin films and the substrate.
In addition to Nd1-xSrxNiO2 thin films, superconductivity has also been achieved in other doped rare-earth nickelates, such as La1-x(Ca/Sr)xNiO2 (42,43) and Pr1-xSrxNiO2 (44). The phase diagrams of (La/Pr/Nd)1-xSrxNiO2 and La1-xCaxNiO2 thin films are all featured by the superconducting phase adjacent to the weakly insulating state in the underdoped and over-doped regimes (16,17,(42)(43)(44). In addition, the dopingdependent generalized superconducting dome was found to shift upon changing the rare-earth cations. However, a local Tc valley structure of the superconducting phase was not observed in the Pr1 −x SrxNiO2 (44), which is different from the situations in Nd1 −x SrxNiO2 and La1-x(Ca/Sr)xNiO2 (16,17,42,43). These comparisons highlight the important role of rare-earth cations played in addition to the lattice strain applied by the SrTiO3 substrate in regulating the superconducting state of the nickelates. Despite of much recent effort, the reported highest Tc onset of the infinite-layer nickelates remains lower than 15 K (14,16,17,(42)(43)(44)(45)(46)(47)(48); it thus becomes an important issue to further enhance the Tc of the superconducting nickelates to higher temperatures. In this regard, the application of high pressure which has been widely employed to raise Tc of cuprates (3) and iron-based unconventional superconductors (49)(50)(51)(52) should be a primary choice. To the best of our knowledge, however, this approach has not been applied to the superconducting nickelate thin films so far. We are thus motivated to investigate the effect of pressure on the superconducting properties of the infinitelayer nickelates.
In this work, we first synthesized high-quality Pr0.82Sr0.18NiO2 thin films with a high Tc onset  17 K, and then performed transport measurements by using the palm-type cubic anvil cell (CAC) apparatus under various pressures up to 12.1 GPa. We observe a positive pressure effect on the superconducting transition temperature, Tc(P), which increases monotonically from ~ 17 K at ambient pressure to ~ 31 K at 12.1 GPa without leveling off. This result is quite encouraging and should promote further endeavors to raise the Tc of this new class of superconductors.

Results and Discussions
The single-crystalline infinite-layer Pr0.82Sr0.18NiO2 thin films were synthesized by two steps. First, the precursor perovskite phase Pr0.82Sr0.18NiO3 films were deposited on TiO2-terminated SrTiO3 (001) substrates and then capped with the SrTiO3 epitaxial layer by using the pulsed laser deposition system (53,54). Subsequently, the thin films were vacuum-sealed with CaH2 in a glass tube for the ex-situ topotactic reduction process to obtain the infinite-layer films. Details about the sample syntheses can be found in the Supplementary Materials (SM). As we can see, Fig. 1(a) shows the X-ray diffraction (XRD) θ-2θ symmetric scans of thin-film samples for perovskite Pr0.82Sr0.18NiO3 (blue) and infinite-layer Pr0.82Sr0.18NiO2 (red), showing only (001) and (002) peaks for both phases. After reduction, the rightward shift of the (001) and (002) peaks in the infinite-layer phase corresponds to a compression of the out-of-plane lattice constant, which is calculated to be 3.36 Å. As seen from the reciprocal space mappings in Fig. 1  Pr0.82Sr0.18NiO3 and infinite-layer Pr0.82Sr0.18NiO2 thin films. For Pr0.82Sr0.18NiO3, the ρ(T) shows a metallic behavior but a weak temperature dependence over the whole temperature range. Pr0.82Sr0.18NiO2 also displays a typical metallic behavior upon cooling down and exhibits a pronounced superconducting transition below Tc onset  17 K, which is defined as the temperature where the resistivity deviates from the linear extrapolation of normal-state resistivity, inset of Fig. 1(e). Zero resistance is achieved at Tc zero  11 K, which is in good agreement with previous reports (44).
To further raise Tc and tune the physical properties of this new superconducting family, we studied the pressure effect on the Pr0.82Sr0.18NiO2 films by measuring resistivity under various hydrostatic pressures. The experimental details can be found in the SM.  Fig. 2(a), the magnitude of normal-state resistivity shows complex and non-monotonic evolutions with increasing pressure. At P > 1.7 GPa, a broad hump feature appears in ρ(T) between 100 and 300 K, which is similar to the situation seen in the Fe-based superconductors due to the incoherent-to-coherent crossover of the 3d electrons (55)(56)(57)(58). When we further increase pressure to 6.6 GPa, an obvious upturn in ρ(T) appears below ~ 50 K, and the superconducting transition emerges at Tc onset  26 K. Moreover, we can see that the residual resistivity at 1.5 K exhibits a prominent enhancement with increasing pressure above 2.4 GPa; it increases to the value that is about half of the normal-state value at 6.6 GPa. Such a large enhancement should be induced by the solidification of the Daphne 7373 at high pressures and low temperatures as discussed below. For the sample No. 2 in the glycerol PTM, the normal-state ρ(T) and the residual resistivity show similar evolutions with pressure as sample No. 1; it first decreases considerably from 0 to 2.5 GPa, increases gradually until 6.8 GPa, and then decreases again at higher pressures. These high-pressure results resemble the observations in the Sr/Ca-doped infinite-layer nickelate thin films (14,16,17,(42)(43)(44), in which the defects or cation-site disorders dominate the scattering processes in resistivity. As discussed below, the delicate thin films are partially deteriorated upon compression, which produces more disorders and defects that enhance the carrier scatterings. In the presence of liquid PTM, the superconducting transition remains visible up to at least 12.1 GPa, the highest pressure in the present study.
To highlight the evolutions with pressure of the superconducting transition, we vertically shifted the ρ(T) curves below 100 K for the samples No. 1 and No. 2, as displayed in Figs. 2(c) and 2(d). We can clearly see that the Tc increases monotonically with pressure in the studied pressure range. In addition to Tc onset (red arrow, as defined above), here we also define the Tc 90%Rn as the temperature where the resistivity drops to 90% of ρ(Tc onset ) [Tc onset and Tc 90%Rn correspond to the temperatures where the superconducting state (or Cooper pairs) just appears and grows up quickly], and Tc offset as shown in Fig. 2(c). The ρ(T) at ambient pressure (AP) shows a high Tc onset  18 K and Tc 90%Rn  17.3 K. These values are a little bit higher than those in the previous report (44), which may attribute to the different reduction conditions. For sample No. 1 at AP, a small residual resistance below Tc offset  12.2 K is noted, which should be ascribed to the inhomogeneity of the small-sized sample for high-pressure measurements. Upon application of high pressure, we observed perfect zero resistivity Fortunately, we can still monitor the onset of superconducting transition that continues to increase with pressure. The Tc onset and Tc 90%Rn are enhanced gradually from 26 K and 22.7 K at 6.8 GPa to 31 K and 27.2 K at 12.1 GPa.
To check the reproducibility of the above results, we have measured three more samples (Nos. 3, 4, and 5) with thicker SrTiO3 capping layer by using different liquid PTM: mineral oil, silicone oil and glycerol, respectively. All ρ(T) data are shown in  Here, we used the criteria of Tc 90%Rn and plotted the temperature dependences of μ0Hc2(Tc 90%Rn ) in Fig. 4(b). Then, we estimate the zero-temperature upper critical field μ0Hc2(0) by employing the empirical Ginzburg-Landau (G-L) formula, i.e., μ0Hc2(T) = μ0Hc2(0)(1−t 2 )/(1+t 2 ), where t = T/Tc represents the reduced temperature. The fitting results are indicated by the broken lines in Fig. 4(b). Unlike the monotonic enhancement of Tc(P), the μ0Hc2 GL (0) exhibits a non-monotonic evolution with pressure. As show in Fig. 4(c), the obtained μ0Hc2 GL (0) first increases quickly from ~ 100.7 T at 0 GPa to 141.5 T at 2.5 GPa with a slope of about ~ 16 T/GPa, and then it increases nearly linearly to ~ 173 T with a smaller slope of 4 T/GPa up to 10.1 GPa.
When P  10.1 GPa, the μ0Hc2(0) declines continuously, which might be correlated with the degradation of the superconducting state.
The main finding of the present study is the observation of positive pressure effect on Tc(P), which shows the potential to reach higher than 30 K in the Pr0.82Sr0.18NiO2 thin films. Below we briefly discuss the mechanism and its implications.
First, the contraction of the lattice parameter under pressure should favor a higher Tc when comparing to the effect of chemical pressure at similar optimal hole doping level. For the reported nickelate thin films, the in-plane lattice constants a ~ 3.91 Å seems to be locked by the SrTiO3 substrate (14,(42)(43)(44), but the c-axis constant shows an inverse correlation to the optimal Tc, as illustrated in Fig. 4(d), Tc = 9 K for La0.8Sr0.2NiO2 (c  3.44 Å) (42), Tc = 10 K for La0.82Ca0.18NiO2 (c  3.385 Å) (43), Tc = 11 K for Nd0.775Sr0.225NiO2 (c  3.375 Å) (14,16,17), and Tc = 14 K for Pr0.82Sr0.18NiO2 (c  3.36 Å) (44). If this trend is followed under physical pressure, the contraction of c-axis under pressure should lead to an enhancement of Tc, as indeed observed here from ~ 17 K at AP to ~ 31 K at 12.1 GPa. From a linear extrapolation in Fig. 3, a higher Tc over ~ 40 K can be achieved at about 20 GPa. The shrinkage of c-axis under pressure will enhance the hybridization between the 3d orbitals of nickel and 5d orbitals of rare-earth-layer, and thus the Kondo coupling. Following the Kondo picture, the non-monotonic evolution of normal-state resistivity under high pressures can be interpreted as the magnification of enhanced Kondo effect (39,40). Moreover, a superconducting phase diagram based on the generalized K-t-J model has been established by incorporating the Kondo coupling K to the t-J model, and an evolution from d-wave dominant phase to s-wave dominant phase can be achieved by tunning the coupling parameter K at the optimal hole-doping (40). Therefore, the enhancement of Tc may originate from this proposed picture that the gap magnitude of s-wave coming from the hybridized orbitals increases under high pressures.
Secondly, based on the single-band model, the initial slope of μ0Hc2(T) is related to the effective mass m* of charge carriers via the relationship of -(1/Tc)[dμ0Hc2/dT]|Tc  (m*) 2 (59,60). From a linear fitting to μ0Hc2(T), we can extract the normalized slope - (1/Tc)[dμ0Hc2/dT]|Tc, which decreases from ~ 0.42 T/K 2 at 0 GPa to ~ 0.26 T/K 2 at 10.1 GPa, Fig. 4(c). Such a pressure-induced reduction of effective mass m* or the electron correlations should correlate with the changes of bandwidth under high pressures. As indicated by the theoretical calculations based on the one-band Hubbard model, the superconducting Tc can be further enhanced by fine tuning the second-and thirdnearest neighbor hopping parameters t and t″ on a square lattice other than hole-doping (32). In this sense, our high-pressure results are consistent with the theoretical predictions that high pressure can create the compressive strain which broadens the bandwidth with a slight interaction-to-bandwidth ratio (32,61). On the other hand, a continuous increase of Tc from ~ 20 to ~ 35 K is observed in calculations by reducing the onsite interaction U from 9t to 7t (32), which is in good agreement with our experimental results. Further theoretical studies on the electronic structures under pressure are needed to have a better understanding on the importance of electronic correlations, hybridization between Ni-3d and rare-earth 5d electrons.
Finally, we would like to briefly comment the influence of pressure environment on the superconducting nickelate thin films, which are found to be very sensitive to the pressure conditions or the used PTM during this study. To confirm our assumption, we performed the STEM measurements on the Pr0.82Sr0.18NiO2 thin film (No. 2) after decompression. As shown in Fig. S5(a), we can clearly see that the atomic-resolution image of infinite-layer structure of Pr0.82Sr0.18NiO2 thin film before we perform the high-pressure resistivity measurements. However, the infinite-layer structure is partially destroyed, producing considerable amount of dislocations and defects in a large scale after the high-pressure measurements, Fig. S5(b-d). Obviously, the broaden of the superconducting transition at high pressures has direct correlation with the cracked infinite-layer structure. Moreover, this can explain why the bulk materials don't show the superconducting transition at ambient pressure and high pressures. For bulk polycrystalline samples, although they have infinite-layer structure, there is no ideal infinite-layer structure in a large-scale as seen in the thin films. To further verify the above hypothesis about the influence of extrinsic disorders and/or stress, we performed comparative high-pressure resistivity measurements on the Pr0.82Sr0.18NiO2 thin film (No. 6) in CAC by using the solid h-BN as the PTM, which is expected to produce a stronger stress/strain than the liquid one. As shown in Fig. S6, the ρ(T) is immediately altered to an insulating-like behavior under pressure of 2 GPa, and the magnitude of resistivity increases significantly with further increasing pressure to 4 GPa, which reproduces the insulating behavior of the bulk polycrystalline samples.
This comparison also highlights that the liquid PTM, though solidified under pressure, remains relatively soft so that it can preserve the metallic behavior and allows us to see the evolution of the superconducting transition.

Conclusion
In summary, we have performed a high-pressure study on the superconducting Pr0.82Sr0.18NiO2 thin films by employing the cubic anvil cell apparatus. Our results reveal that its Tc increases from ~ 17 K at 0 GPa to ~ 31 K at 12.1 GPa without showing any signature of saturation. This result indicates that there is still much room for further raising the Tc of the superconducting nickelates. We have explained the positive pressure effect of Tc(P) in terms of the lattice contraction and enhanced hybridization between the Ni-3d and Pr-5d orbitals considering the theoretical calculations. This finding is encouraging and should promote more studies to explore superconducting nickelates with higher Tc. Figure 1. (a) X-ray diffraction θ-2θ symmetric scans of perovskite Pr0.82Sr0.18NiO3 thin film (blue) and infinite-layer Pr0.82Sr0.18NiO2 thin film (red). Reciprocal space mappings (RSM) of (b) perovskite Pr0.82Sr0.18NiO3 thin film and (c) infinite-layer Pr0.82Sr0.18NiO2 thin film, respectively. (d) The atomic-resolution HAADF-STEM imaging of infinite-layer samples in (a). (e) Temperature-dependent resistivity for perovskite Pr0.82Sr0.18NiO3 thin film (blue) and infinite-layer Pr0.82Sr0.18NiO2 thin film (red) which shows a high superconducting transition temperature Tc onset  17 K. Inset of (a) shows the crystal structure of PrNiO2.