RESULTS

High-pressure structural evolution of ReO3

Figure 1 shows the pressure-induced evolution of the crystal structure of ReO3, which is particularly intriguing, especially when viewed from the perspective of the oxygen sublattice. The R-I phase emerges from the C-I phase through coupled rotations of ReO6 octahedra along the ⟨111⟩ direction [20]. As illustrated in the bottom panel of Fig. 1a, the oxygen atoms progressively evolve from a perfect kagome lattice in the C-I phase into a distorted triangular lattice in the R-I phase. With further increasing pressure, this lattice becomes more uniform and eventually attains a hexagonal close-packed configuration at a rotation angle of 30° above 30 GPa. Under higher pressures, volume reduction can no longer be accommodated solely by octahedral rotations, leading to an additional structural transition into the R-II phase above 39 GPa [20,21]. Notably, such close-packed oxygen layers in the R-I phase are rarely observed in other oxide materials.

These sequential structural phase transitions were confirmed by our high-pressure synchrotron X-ray diffraction (SXRD) measurements on ReO3. As displayed in Fig. S1a, the SXRD patterns can be indexed by using the C-I, C-II, mixed C-II/R-I, and R-I phase in different pressure ranges up to 30 GPa, respectively. Moreover, some new diffraction peaks emerge at 36.1 GPa, Fig. S1b, which indicates the occurrence of structure phase transition to R-II phase. We refined the structure parameters of single-phase regions for C-II and R-I, and the obtained pressure-volume (P-V) relations were displayed in Fig. 1b. As shown in Fig. 1c, the coupled rotations of ReO6 octahedra exhibit a significant anisotropic compression, i.e. the a-axis shrinks by more than 6% while c-axis is only reduced by 0.6% at 40 GPa. By assuming rigid rotations of the octahedra, the rotation angle can be estimated by the ratio of a/c. We can see that the rotation angle gradually increases from 25° to 30° in the R-I phase, Fig. 1d. With further increasing pressure, the octahedra rotates inward by nearly 2°, which destabilizes the R-I phase at ∼ 39 GPa and leads to a new structure phase transition to R-II phase. The above results provide a quantitative description of octahedral rotations by involving the structural phase transitions associated with the R-I phase.

Experimental characterization of superconductivity in ReO3

Then we performed high-pressure transport measurements on ReO3 single crystals by employing cubic anvil cell (CAC) and diamond anvil cell (DAC). The samples were labeled as s1 for CAC and s2 to s3 for DAC, and more details can be found in Table S3. As shown in Fig. S2a and b, the resistance and Hall resistance measured at AP are consistent with previous reports [24]. As we can see in Figs 2a–c, S2c and S3a–c, the normal-state resistance increases gradually both in C-II and R-I phases under high pressures. Surprisingly, an obvious drop gradually emerges in resistance below 2 K above 12 GPa and the zero resistance can be observed at 13 GPa, which indicates the emergence of superconductivity in the R-I phase, inset of Fig. S2c. More detailed evolution of superconducting transition can be clearly tracked from normalized resistance R(T)/R(20 K) in Fig. 2d and e. Here, we define the temperature of deviation from normal-state resistance as _T_conset and the zero resistance as _T_czero. With increasing pressure gradually, the superconducting _T_c exhibits continuous enhancement for both s2 and s3. Moreover, the maximum _T_conset and _T_czero can reach about 17.8 K and 16.3 K at 35 GPa. To the best of our knowledge, the observed maximum _T_conset and _T_czero of ReO3 produces the record of the highest T_c among 5_d transition-metal oxides.

Figure 2.: Electrical transport properties measured under high pressure. Temperature dependence of resistance of ReO3 (DAC s2) measured at various pressures: (a) from 1.7 to 10.7 GPa, (b) from 12.0 to 37.0 GPa, and (c) from 41.7 GPa to 65.1 GPa. (d and e) Normalized resistance R/R20 K of ReO3 (DAC s2 and s3) under various pressures up to 35 GPa. (f) Temperature dependence of resistance (DAC s2) under various magnetic fields at 27.6 GPa. (g) Temperature dependence of the upper critical field μ0Hc2(T) at 27.6 GPa (DAC s2). The dashed line represents the fitting results by using WHH two-band model.

To further characterize superconducting properties, we measured R(T) under various magnetic fields at each pressure. As displayed in Figs 2f and S4, the superconducting transition gradually shifts to lower temperatures with increasing magnetic field. Here, we define _T_c as the temperature where the resistance drops to half of normal state resistance Rn. In Figs 2g and S5, _μ_0_H_c2(T) exhibits obvious upward curvature at low fields, which indicates multi-band feature of ReO3. The _μ_0_H_c2(T) can be well fitted by the Werthamer-Helfand-Hohenberg (WHH) two-band model [25], and the obtained μ_0_H_c2(0) ∼ 14.6 T at 27.6 GPa is smaller than Pauli limit μ_0_H_pBCS = 1.84_T_c = 28.3 T, Fig. 2g. The analysis of upper critical field indicates that the emergent superconductivity in ReO3 has multiband features that may originate from the hybridization between Re-5_d and O-2_p orbitals.

In addition, we performed magnetic susceptibility measurements to confirm the bulk nature of pressure-induced superconductivity in ReO3. As shown in Fig. S6, systematic pressure-dependent ZFC/FC and field-dependent M-T measurements confirm the bulk superconductivity. The superconducting volume fraction exceeds 78% at 23 GPa for s4 and approaches or even slightly exceeds 100% at 25 and 30 GPa for s5 after properly corrected for demagnetization effects. The detailed calculations can be seen in the Methods section.

Phase diagram of superconductivity in ReO3

To further elucidate the correlation between structural phase transitions and transport properties, we extract the resistance values at 280 K and 20 K and lattice dynamics information by analyzing resistance under high pressures. As displayed in Fig. 3a, the evolution of resistance at 280 K and 20 K clearly illustrates the phase boundary of successive structure phase transitions. In addition, we can clearly see that the R(T) curves at both ambient and high pressures can be well fitted by modified Bloch-Grüneisen equation [18,26] with the fitting results shown in Fig. 3b. As can be seen, both Debye and Einstein temperatures, _Θ_D and _Θ_E, exhibit a dramatic drop above ∼ 10 GPa where the structure phase transition to R-I phase takes place. This feature is correlated with a phonon softening effect and is expected to assist the emergence of superconductivity.

Figure 3.: Electrical and superconducting properties of ReO3. Pressure dependences of (a) the resistance of ReO3 at 20 and 280 K, (b) the calculated Debye and Einstein temperatures from fitting to resistance by using modified Bloch-Grüneisen equation, (c) superconducting transition temperatures of ReO3 in different runs. The dashed line marks the phase boundaries. (d) Typical 5d transition metal oxide superconductors and their maximum superconducting transition temperatures, such as TaO (Tc = 6.2 K @ AP) [27], Rb0.26WO3 (Tc = 7.5 K @ AP) [28], K0.3ReO3 (Tc = 3.6 K @ AP) [29], HgxReO3 (Tc = 11.1 K @ 4 GPa) [30], ReO3 (Tc = 17.8 K @ 35 GPa) (our work), KOs2O6 (Tc = 9.65 K @ AP) [31], and Ti4Ir2O (Tc = 5.7 K @ AP) [32].

Based on the obtained _T_conset, _T_czero and T_c_χ of ReO3 under various high pressure, the temperature-pressure phase diagram can be constructed in Fig. 3c. The superconducting _T_c(P) is featured by a broad dome with maximum _T_c ≈ 17.8 K at 35 GPa. Combined with structural characterizations, we can see that the emergence of superconducting phase is accompanied by a structure phase transition and the maximum _T_c is achieved when the oxygen layers form a perfect hexagonal close packing. Figure 3d summarizes the reported T_c of 5_d transition-metal oxide superconductors at AP and high pressure [27–32], which highlights the highest _T_c ∼ 17.8 K of ReO3. The present work thus will inspire researchers to explore high-T_c superconductivity in 5_d transition-metal-oxides by using high-pressure and heterostructure engineering.

Theoretical insights on superconductivity of ReO3

To further explore the mechanism of pressure-induced high-T_c superconductivity in ReO3, we performed theoretical calculations at selected pressures. First, the crystal structure was fully relaxed from 0 to 45 GPa to mimic the structural evolutions of ReO3. The DFT calculations further demonstrate that the rotations of ReO6 octahedra in the C-I phase along the <111> axis gradually densifies oxygen layers and then transforms to R-I phase above 10 GPa, which is consistent with experimental results. An ideal hexagonal close packing is realized with rotation angle of 30° around 30 GPa. Figure 4a–c shows the electronic DOS at 0 GPa (cubic-I), 15 and 30 GPa (R-I) with different rotation angles. With increasing pressure gradually, the N(E_F) shows an increase at 15 GPa and is almost doubled at 30 GPa. Moreover, the Re-5_d and O-2_p orbitals are strongly hybridized, and O-2_p_ orbitals have considerable contributions to the N(_E_F) at 15 and 30 GPa in the R-I phase. Moreover, the Crystal Orbital Hamilton Population (COHP) analyses reveal the above evolution that the Re-O interactions exhibit a distinct antibonding character near the Fermi level and show continuous enhancement with pressure, Fig. S7. As displayed in Fig. S8, the integrated COHP (-ICOHP) displays significant increase. It explicitly demonstrates that the evolution of Re-O bonding directly driven the enhancement of N(_E_F). Figure 4d–f displays the calculated phonon DOS, Eliashberg spectral function α_2_F(ω) and cumulative frequency-dependent EPC constant λ(ω) at 0, 15 and 30 GPa. It can be clearly seen that both Re and O have large contributions to the lower frequency phonons (<250 cm−1), while the higher frequency phonons (>250 cm−1) were dominated by oxygen. However, the α_2_F(ω) exhibits a pronounced spectra weight shift to lower-frequency region, which indicates the clear phonon softening of Re-O bonding branches upon entering the R-I phase. Based on the Eliashberg theory, the phonon softening is consistent with a sudden drop of Debye and Einstein temperatures observed in experiments and can dramatically enhance the EPC constant. As shown in Fig. 4g and h, the λ exhibits a fourfold enhancement from ∼ 0.2 at 0 GPa to ∼ 0.9 at 34 GPa, and the _T_c emerges in the R-I phase and displays a dome shape with the maximum reaching ∼ 15 K at 34 GPa when the rotation angle approaches 30°, which is consistent with the experimental results.

Figure 4.: Electronic density of states, electron-phonon coupling and superconducting properties of ReO3 under high pressures. (a–c) Total density of states (DOS) and partial DOS for ReO3 at 0, 15, and 30 GPa. Energy zero represents the Fermi level. (d–f) Eliashberg spectral function α2F(ω), and cumulative frequency-dependent EPC constant λ(ω), total phononic density of states (PhDOS) and partial PhDOS at 0, 15, and 30 GPa. (g) Calculated λ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\omega }{{\mathrm{log}}}$\end{document} as a function of pressure. (h) Tc and rotation angle as a function of pressure. The dashed line marks the phase boundaries._