The recent discovery of superconductivity in LaH₁₀ at high pressure with record-high superconducting transition temperatures T_c ∼ 260 K has fueled the search for room-temperature superconductivity in compressed superhydrides.1–3 The three-dimensional clathrate-like structure of H with La atoms filling the clathrate cavities has been described as an extended metallic hydrogen host structure stabilized by the La as a guest electron donor. The introduction of electrons into H₂ molecules by the guest atom leads to a significant contribution of H to the electronic density of states at the Fermi level. As a result, substantial coupling of electrons on the Fermi surface with high-frequency phonons in response to the motion of the H atoms is crucial for promoting superconductivity.4–7 Actually, clathrate-like superhydrides with alkaline-earth or other rare-earth atoms have also been proposed as potential high-T_c superconductors.8,9 Following their theoretical prediction, experimental progress on the synthesis of these clathrate superhydrides has been remarkable: YH₆,10,11 YH₉,10,12 ThH₉,13 ThH₁₀,13 CeH₉,14,15 CeH₁₀,16 (LaY)H₆,17 (LaY)H₁₀,17,18 and CaH₆,19 with high T_c values in the range of 146–253 K, have been synthesized. Thus, a new class of high-temperature superconductors with clathrate-like structure has been born.

The creation of a distinctive H clathrate structure incorporating metal inside the voids is the key to the unusually high-T_c superconductivity. Aside from hydrogen clathrate cages, the host–guest and interframework interactions are also significant in influencing superhydride superconductivity. Until now, the experimentally obtained high-temperature superconducting clathrate superhydrides have only existed above megabar pressures. The ultrahigh pressure required to synthesize and maintain these clathrate superhydrides impedes their experimental investigation. Alternatively, several clathrate or caged compounds exhibit a superconducting transition at ambient pressure, which provides a platform to examine the relationship between guest atom and cage unit under comparatively benign conditions.20–27 In this work, we utilize an in situ high-pressure method to systematically investigate the evolution of superconductivity for two Ba-filled cage compounds BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆. We discover that the first superconducting phase in both caged compounds is gradually suppressed under pressure. At a higher pressure, a pressure-induced superconducting phase dome emerges. No structural phase transition is revealed by high-pressure synchrotron x-ray diffraction (XRD). The pressure-induced reemergence of superconductivity in BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆ can be attributed to phonon softening, which is related to shrinkage of the cage.

Polycrystalline BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆ were prepared from stoichiometric amounts of high-purity elements by argon arc melting and subsequent annealing in evacuated quartz capsules at 1000 °C for 20 h.23 The superconducting transition was confirmed by magnetization measurements using a Magnetic Property Measurement System (MPMS). In situ high-pressure resistivity measurements were conducted on a nonmagnetic diamond anvil cell (DAC) as described elsewhere.28–32 A piece of nonmagnetic BeCu was used as the gasket. A cubic boron nitride (BN)/epoxy mixture layer was inserted between the BeCu gasket and the electrical leads as an insulator layer. Four Pt foils were arranged according to the van der Pauw method. In situ high-pressure XRD measurements were performed at beamline BL15U of the Shanghai Synchrotron Radiation Facility with an x-ray wavelength λ = 0.6199 Å. A symmetric DAC with 200 µm culet was used with a rhenium gasket. Silicone oil was used as the pressure-transmitting medium (PTM), and the pressure was determined by the ruby luminescence method.33 Two-dimensional diffraction images were analyzed using FIT2D software.34 Rietveld refinements of crystal structures under high pressure were performed using the General Structure Analysis System (GSAS) and the graphical user interface EXPGUI.35,36 An in situ high-pressure Raman spectroscopy investigation of BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆ was performed using a Raman spectrometer (Renishaw in-Via, UK) with a laser excitation wavelength of 532 nm and a low-wavenumber filter.

For BaIr₂Ge₇, we carried out high-pressure in situ synchrotron XRD, Raman, and transport measurements. To confirm the emergence of a second superconducting state under high pressure, we repeated the measurements with new samples for a second run. For Ba₃Ir₄Ge₁₆, we carried out high-pressure in situ Raman measurements and transport measurements in two runs.

At ambient pressure, both BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆ exhibit typically metallic behavior and show superconducting transitions at 2.7 and 5.9 K, respectively (Fig. S1, supplementary material).23–25 Hence, we measured the electrical resistivity ρ(T) for both compounds at various pressures. Figures 1(a)–1(c) present the temperature dependence of the resistivity of BaIr₂Ge₇ at various pressure up to 44.9 GPa. The resistivity of BaIr₂Ge₇ exhibits a nonmonotonic evolution with increasing pressure. Over the whole temperature range, the resistivity is first suppressed with applied pressure, reaching a minimum value at about 15 GPa, and then displays the opposite trend with further increasing pressure. In the lower-pressure region, the superconducting transition temperature T_c is suppressed to a minimum of 2.1 K at 16.7 GPa. Surprisingly, T_c starts to increase rapidly with further increases in pressure above 20 GPa, reaching a maximum value of 4.4 K at 39.7 GPa. With still further increases in pressure, T_c slowly decreases to form a complete dome shape. Compared with the value of 2.7 K at ambient pressure, T_c in the high-pressure region is much enhanced. The measurements on different samples of BaIr₂Ge₇ for independent runs gave consistent and reproducible results (Fig. S2, supplementary material), confirming the intrinsic superconductivity under pressure. The pressure-induced reentrant superconductivity resembles the situation in a variety of compounds, including K_xFe_2−ySe₂,37 (Li_1−xFe_x)OHFe_1−ySe,38 K₂Mo₃As₃,39 Sr_0.065Bi₂Se₃,40 and CsV₃Sb₅.30,41–4330,41–43 In addition, we performed transport measurements on Ba₃Ir₄Ge₁₆ under high pressure, and a similar evolution of ρ(T) was observed, as shown in Figs. 2(a), 2(b), and S3 (supplementary material). In the first superconducting region (SC-I), the application of pressure rapidly suppresses T_c below 2 K at ∼20 GPa. In the second superconducting region (SC-II), T_c continuously increases to its highest value of 4.0 K at around 30 GPa, which is slightly lower than that in the SC-I region. Beyond this pressure, T_c decreases very slowly and exhibits a typical dome-like feature. The details are summarized in Table I.

To confirm whether the new resistance drop observed in BaIr₂Ge₇ is related to a superconducting transition, we applied a magnetic field to samples subjected to 3.8 and 44.9 GPa, respectively [Figs. 1(d) and 1(e)]. As can be seen in Fig. 1(e), this new drop in resistance shifts to a lower temperature with increasing magnetic field and is fully suppressed under a magnetic field of 2.25 T at 44.9 GPa. These results indicate that the sharp drop in resistance is a superconducting transition. We also measured the H-dependent superconducting transition under P = 3.8 GPa, and the curves are plotted in Fig. 1(d). We extract the field (H) dependence of T_c for BaIr₂Ge₇ at 3.8 and 44.9 GPa and plot H(T_c) in Fig. 1(f). The experimental data are fitted using the Ginzburg–Landau (G-L) formula44,45Hc2T=Hc201−t21+t2, where t = T/T_c is the normalized temperature, which allows us to estimate critical fields μ₀H_c2 ∼ 2.3 and 2.2 T for 3.8 and 44.9 GPa, respectively. Although the μ₀H_c2 obtained here is lower than its corresponding Pauli paramagnetic limit μ₀H_P = 1.84T_c, the slopes of dH_c2/dT are notably different: −1.08 and −0.61 T/K for 3.8 and 44.9 GPa, respectively. Our results suggest that the nature of the pressure-induced reentrant superconducting state may differ from that of the initial superconducting state. A similar evolution of μ₀H_c2 is obtained for Ba₃Ir₄Ge₁₆ under various pressures and is shown in Figs. 2(c), 2(d), and S3 (supplementary material).

To investigate whether the observed reemergence of superconductivity in pressurized BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆ is associated with a pressure-induced crystal structure phase transition, we performed in situ high-pressure XRD measurements. At ambient pressure, BaIr₂Ge₇ possesses an orthorhombic structure belonging to the space group, Ammm, while Ba₃Ir₄Ge₁₆ crystallizes into a tetragonal lattice with space group I4/mmm [Fig. 3(a)]. Both compounds are composed of two-dimensional networks of cage units, where [Ir₈Ge₁₆]²⁻ cages are connected by [Ir₂Ge₁₆]²⁻ cages encapsulating barium atoms. The XRD patterns of BaIr₂Ge₇ collected at different pressures are shown in Fig. 3(b). A representative refinement at 0.3 GPa is displayed in Fig. S4 (supplementary material). All the diffraction peaks can be indexed well to the ambient structure. With increasing pressure, all peaks shift to a higher angle owing to shrinkage of the lattice, and no structural phase transition is observed under pressures up to 60.5 GPa. Structural refinements have been carried out by Rietveld analysis using synchrotron XRD patterns, and the unit-cell lattice parameters as functions of pressure have been extracted as depicted in Fig. S5(c) (supplementary material). It is found that the lattice constants shrink obviously at the beginning, while decreasing slowly at high pressure.

We summarize the transport results for BaIr₂Ge₇ in a pressure–temperature phase diagram [Fig. 4(a)]. To confirm the emergence of a second superconducting state under high pressure, we repeated the measurements with new samples for a second run and proved that all the results are reproducible. The superconducting T_c shows a similar trend to the normal resistivity. The P–T_c phase diagram reveals two distinct superconducting regions: the initial superconducting state (SC-I) and the pressure-induced superconducting state (SC-II). In the SC-I region between 1 bar and 16 GPa, T_c is monotonically suppressed with external pressure, and T_c can be suppressed to 2 K at around 16 GPa. In the SC-II region, T_c increases with pressure and shows a dome shape with the maximum T_c ∼ 4.4 K at 40 GPa.

The pressure dependence of volume is shown in Fig. 4(b). With increasing pressure, one can see that the volume decreases, but with different slopes below and above a critical pressure P_c ∼ 16 GPa. A Birch–Murnaghan equation of state was used to fit the measured pressure–volume (P–V) data for BaIr₂Ge₇.46 The obtained bulk modulus K₀ is 116(2) GPa with V₀ = 1545(1) ų and K0′ = 4. However, the structure becomes less compressible, with a higher bulk modulus of 238(3) GPa, when the pressure is higher than P_c. It should be noted that a pressure-induced reentrant superconducting state was observed above the critical pressure P_c. The in situ high-pressure XRD results indicate that the reemergence of superconductivity in BaIr₂Ge₇ is not associated with a crystal structure phase transition.

Although pressure-induced reemergence of superconductivity has been reported in various materials, the origin of the second SC dome is still an enigma. A structural phase transition is usually responsible for two-dome superconductivity. However, since no structural transition was observed from our synchrotron XRD up to 60 GPa, this mechanism can be ruled out for BaIr₂Ge₇. Another explanation is associated with the competition or coexistence of some order parameters (e.g., charge-density waves, spin-density waves, or antiferromagnetic order) with superconductivity. Since no charge or magnetic orders have been reported in this caged family, charge or antiferromagnetic fluctuations turn out to be irrelevant to the two-dome superconductivity in BaIr₂Ge₇. Considering the caged structure, local vibration due to rattling of the Ba atom coupled with low-frequency phonons and conductive electrons may be responsible for superconductivity. Typically, the low-lying excitation state from the rattling guest atom in the cage can be systemically tuned by external pressure. To gain a more detailed understanding of reemergent superconducting behavior, we performed high-pressure in situ Raman spectroscopy measurements on BaIr₂Ge₇. With increasing pressure, the profile of the spectra remains similar to that at ambient pressure, and the observed modes exhibit a blue shift, which is typical behavior under high pressure [Fig. 3(c)]. Interestingly, some typical vibrational modes (e.g., 105.6 and 115.8 cm⁻¹ under ambient condition) display the opposite trend and show redshift behavior when the pressure is raised to P_c. As summarized in Fig. 4, the suppression of superconductivity in SC-I is accompanied by blue shifting of the Raman peaks, reaching a minimum T_c and maximum Raman shifts at a turning point of 12 GPa. As the pressure is further increased, both modes of the Raman shift steadily decline with increasing T_c in SC-II. We call for theoretical investigations to determine the origin of these specific vibrational modes. Similar behavior is also observed in Ba₃Ir₄Ge₁₆ (Fig. S6, supplementary material). Calculations such as electron–phonon coupling (EPC) analysis are very tempting to decipher this anomalous phenomenon. Nevertheless, the present results signify an intimate relationship between the Raman shift and superconductivity, and pressure-induced phonon softening may be responsible for the reemergence of superconductivity in BaIr₂Ge₇.

In conclusion, pressure-induced reemergence of superconductivity has been observed in the caged superconductors BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆. The SC-I state is initially suppressed by pressure, and then a second SC dome (SC-II) emerges, with maximum T_c ∼ 4.4 and 4.0 K for BaIr₂Ge₇ and Ba₃Ir₄Ge₁₆, respectively. Synchrotron XRD measurements demonstrate that the reemergence of superconductivity is not associated with any crystal structure phase transition. In combination with in situ Raman measurements, our findings suggest that the development of the SC-II state in both caged compounds is a consequence of pressure-induced phonon softening caused by cage shrinkage.

Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. U1932217, 11974246, and 12004252), the National Key R&D Program of China (Grant No. 2018YFA0704300), the Natural Science Foundation of Shanghai (Grant No. 19ZR1477300), the Science and Technology Commission of Shanghai Municipality (Grant No. 19JC1413900), and the Shanghai Science and Technology Plan (Grant No. 21DZ2260400). The authors are grateful for support from the Analytical Instrumentation Center (Grant No. SPST-AIC10112914), SPST, ShanghaiTech University. The authors thank the staff from BL15U1 at the Shanghai Synchrotron Radiation Facility for assistance during data collection.