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[Ryo Matsumoto](https://orcid.org/0000-0001-6294-5403), Akitoshi Nakano, Takafumi D. Yamamoto, [Kensei Terashima](https://orcid.org/0000-0003-0375-3043), [Kazuki Yamane](https://orcid.org/0000-0002-0162-5411), [Masahiro Ohkuma](https://orcid.org/0000-0002-3861-592X), Ichiro Terasaki, [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928)
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[Pressure-induced anomalous enhancement in the superconducting critical temperature of the transition metal chalcogenides and ](https://mdr.nims.go.jp/datasets/48560ee7-06e4-46fa-baf5-9f55f01981a6)
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1 Pressure-induced anomalous enhancement in superconducting critical temperature of transition-metal chalcogenide Ta2PdS6 and Ta2PdSe6 *Ryo Matsumoto1, Akitoshi Nakano3, Takafumi D Yamamoto4, Kensei Terashima1, Kazuki Yamane1,2, Masahiro Ohkuma1, Ichiro Terasaki3, Yoshihiko Takano1,2 1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 2Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan 3Department of Physics, Nagoya University, Nagoya 464-8602, Japan 4 Department of Material Science and Technology, Tokyo University of Science, Tokyo 125-8585, Japan *Corresponding author; Email: MATSUMOTO.Ryo@nims.go.jp Abstract The emergence of a second dome in the superconducting phase through pressure-driven manipulation of crystal structures in materials has attracted considerable attention. Transition metal chalcogenides (TMCs) represent a highly promising platform, as the second dome has been observed in several binary compounds. Recently, ternary TMCs such as Ta2PdS6 and Ta2PdSe6 have exhibited pressure-induced superconducting domes. In this study, we perform electrical transport measurements of Ta2PdS6 and Ta2PdSe6 under extremely high pressures exceeding 100 GPa, namely uninvestigated regions in previous reports, to reveal the emergence of the second dome. The superconducting critical temperatures (Tc) in both Ta2PdS6 and Ta2PdSe6 initially decrease with increasing pressure. Subsequently, the Tcs tend to enhance drastically above 100 GPa. Notably, the maximum Tc in Ta2PdS6 is 11.2 K at 130.0 GPa, which is a relatively high record among the TMCs. The emergence of the second dome in Ta2PdS6 and Ta2PdSe6 opens further motivation for the investigation under extreme conditions beyond the first dome to find hidden ordered phases. 2 1. Introduction Application of high pressure is an effective method to tune the structural and electronic properties of materials. In particular, the effects of pressure on the emergence and suppression of ordered phases, such as charge density wave (CDW), spin density wave (SDW), and superconductivity (SC), have attracted significant research attention in recent decades [1–6]. The transition temperatures of these ordered phases typically exhibit a dome-like behavior under applied pressure. Interestingly, the emergence of a second SC phase is observed in several materials following the suppression of the first SC dome [7]. Although most second SC domes show a lower or comparable Tc than that of the first SC dome, certain compounds, such as the ion-based superconductors, exhibit higher Tc in the second dome [8,9]. The reemergent superconductivity with a higher Tc in the second dome of other material families has become a focused research area, as theoretical calculations have predicted in high-Tc materials [10]. Transition metal chalcogenides (TMCs) have been focused as the platform for studying dome-like behavior in ordered phases under high pressure, particularly in binary systems, such as a pressure-driven suppression of the CDW phase and the emergence of SC phase [11–13]. Recently, ternary TMCs of Ta2PdS6 and Ta2PdSe6, which crystallize in a monoclinic quasi-1D structure with space group C2/m, as shown in Fig. S1, have been studied actively due to their anomalous electrical properties at ambient pressure. For instance, Ta2PdS6 exhibits semiconducting behavior with an electron carrier density of 4.6×1018 cm−3 at 100 K [14], despite band calculations predicting a metallic state in the electronic structure. The transport measurements of the semimetal Ta2PdSe6 reveal a non-Fermi liquid-like temperature dependence, indicating an exotic electronic state with an unconventional scattering process for charge carriers [15]. Among the investigations of fundamental physics in this system, the emergence of the SC phase through the application of pressure has been reported in both Ta2PdS6 and Ta2PdSe6, with dome-like behavior of Tc [16,17]. However, the question of reemergent SC phases beyond the first dome in this system remains an open issue. In this study, we perform electrical transport measurements on single-crystalline Ta2PdS6 and Ta2PdSe6 under extremely high pressures to investigate the SC properties beyond the first dome. Through the electrical resistance measurements on Ta2PdS6 and Ta2PdSe6 above the megabar pressure range, we reveal the existence of a second SC phase with a Tc higher than that in the first dome. Specifically, the Tc in Ta2PdS6 rises drastically above 80.4 GPa, reaching 11.2 K at 130.0 GPa. This observation of the second SC dome with a higher Tc under extreme pressure offers significant motivation to investigate the megabar pressure region in functional materials, potentially opening new aspects of materials physics. 2. Materials and methods High-quality single crystals of Ta2PdS6 and Ta2PdSe6 were grown for electrical transport 3 measurements and Raman spectroscopy under high pressure using a chemical vapor transport with a transport agent of I2 by referring to previous reports [14,18,19]. Starting materials of tantalum (99.9%), palladium (99.9%), and sulfur (99.999%) or selenium (99.9% or 99.999%) were loaded into an evacuated quartz tube with an I2 concentration of ∼3 mg cm−3. A temperature difference of 145°C between 875 and 730°C in a three-zone furnace facilitated crystal growth over four days. The compositional ratio is evaluated by energy dispersive spectrometry (EDX) using a JSM-6010LA (JEOL). Details of the characterization of the obtained sample at ambient pressure were provided elsewhere [14]. A polycrystalline sample of Ta2PdS6 was synthesized via a solid-state reaction for a structural analysis under high pressure. The same starting powders as the single crystalline sample were used. The raw powder, once heated to 550°C, was re-grounded and heated at 730°C for 48 h in a tube furnace. The obtained sample was identified as a single phase of Ta2PdS6 by powder X-ray diffraction (XRD). The crystal structure was displayed by VESTA software [20]. Electrical transport measurements under high pressure in Ta2PdS6 and Ta2PdSe6 were conducted within a diamond anvil cell (DAC), employing a diamond electrode [21–23]. The temperature (T) dependence of resistance (R) was measured in the physical property measurement system (PPMS, Quantum Design) with a superconducting magnet. Raman spectroscopy was also performed at room temperature for the sample to evaluate the vibrational modes under high pressure. The diamond anvil equipped a beveled culet with a diameter of ~100 μm. A cleaved single-crystalline sample was positioned onto the diamond anvil with the electrodes, and a SUS316 plate served as a metal gasket. The pressure-transmitting medium and insulating layer consisted of cubic BN powders. The applied pressure was estimated using fluorescence from ruby powder placed on the culet [24] and the Raman spectrum from the diamond anvil itself [25], employing an inVia Raman Microscope (RENISHAW). The crystal structure of Ta2PdS6 under high pressure was investigated through XRD measurements in the DAC. The culet of diamond anvil was 300 μm, the gasket was a tungsten plate, and the PTM was the sample itself. These measurements were carried out using synchrotron radiation at the AR-NE1A beamline of the Photon Factory (PF) located at the High Energy Accelerator Research Organization (KEK). The X-ray beam monochromatized to an energy of 30 keV (λ = 0.4175 Å), was directed to the sample in the DAC through a collimator with a diameter of 50 μm. The obtained XRD patterns were integrated into a one-dimensional profile using IPAnalyzer [26]. The applied pressure was estimated using the same procedures as those used for electrical measurements. 3. Results and discussion Figure 1 shows the R-T characteristics of Ta2PdS6 under various pressures up to (a) 25.6 GPa, (b) 130.0 GPa, and (c) enlarged plots at low temperatures. The behavior of Ta2PdS6 under pressure is divided into three regions: (i) suppression of semiconducting behavior and transition to metallic 4 property below 21.5 GPa, (ii) emergence of SC phase at 25.6 GPa with a gradual change in Tc up to 70.0 GPa, and (iii) a drastic enhancement in Tc above 80.4 GPa. In region (i), Ta2PdS6 exhibits semiconducting characteristics, with a negative dR/dT at low temperatures under the lowest pressure of 1.4 GPa. This semiconducting curve is gradually suppressed with increasing pressure up to 18.6 GPa. Conversely, the R-T properties show metallic behavior across the measured temperature range at 21.5 GPa, indicating a semiconductor-to-metal transition. According to in-situ XRD analysis and Raman spectroscopy under pressure (Fig. S2), this metallization is due to a pressure-induced isosymmetric structural transition in Ta2PdS6 [17]. In region (ii), a sharp decrease in R, corresponding to the emergence of SC phase, appears above 25.6 GPa. The R starts to drop from 6.5 K, defined as Tconset, and gradually decreases to zero with several kinks, indicating inhomogeneous superconductivity. At 58.9 GPa, R reaches zero at Tczero of 2.5 K, with only slight changes in Tc as pressure increases up to 70.0 GPa. In this SC region, a sign reversal in Hall resistivity is reported in both Ta2PdSe6 [16] and Ta2PdS6 [17]. However, in our observation for Ta2PdS6, a negative slope in Hall resistance, due to electron carriers, is dominant even at the lowest pressure and maintained up to SC region, as indicated in Fig. S3. Notably, Tc increases sharply under further compression above 80.4 GPa, corresponding to region (iii). Although the rate of increase in Tc slows above 100.3 GPa, the enhancement does not fully saturate even at the highest pressure, reaching maximum values of 11.2 K for Tconset and 8.5 K for Tczero at 130.0 GPa, marking a relatively high Tc among TMCs. Fig. 1. (a) Temperature dependence of resistance under various pressures from 1.4 to 25.6 GPa and (b) 25.6 to 130.0 GPa in Ta2PdS6. (c) Enlarged plots around superconducting transition. Figure 2 presents the R-T properties of Ta2PdSe6 under pressures up to (a) 60.5 GPa, (b) 118.8 GPa, and (c) enlarged plots at low temperatures. The behavior of Ta2PdSe6 under pressure is also divided into two regions: (i) emergence of pressure-induced SC at 16.9 GPa and gradual change in Tc up to 92.1 GPa, and (ii) drastic enhancement in Tc above 102.1 GPa. In contrast to Ta2PdS6, Ta2PdSe6 exhibits metallic behavior even at low pressures, and its SC phase appears at a lower pressure of 16.9 GPa. The SC transition is initially broad at 16.9 GPa due to pressure inhomogeneity. With applying 5 pressure, Tconset decreases gradually, and the SC transition becomes sharp, with zero resistance achieved above 60.5 GPa. With further compression, Tconset shows a slight increase up to 102.1 GPa. A drastic rise in Tconset above 102.1 GPa indicates the emergence of a second dome of pressure-induced SC in Ta2PdSe6. Fig. 2. (a) Temperature dependence of resistance under various pressures from 4.7 to 60.5 GPa and (b) 71.4 to 118.8 GPa in Ta2PdSe6. (c) Enlarged plots around superconducting transition. Figure 3 presents the pressure-dependent Tconset in Ta2PdS6 and Ta2PdSe6 up to the megabar region, with comparisons to previous reports. In the unexplored pressure range beyond previous studies on Ta2PdS6 and Ta2PdSe6, specifically above the megabar region, our samples show a significant enhancement of Tc, revealing the existence of the second SC dome. Even at the maximum pressures in this study, the increases in Tc are not fully saturated. In contrast to most two-dome SC systems, where the second dome exhibits a lower or comparable Tc (e.g., CsV3Sb5 [7]), Ta2PdS6 shows double Tc of 11.2 K at 130.0 GPa than that observed at 70.0 GPa. Similarly, Tc in Ta2PdSe6 at 118.8 GPa is comparable to that at 16.9 GPa and continues to enhance steeply with applying pressure. The observed higher Tcs in the second SC domes are unique features in these materials. Although the behavior of Ta2PdS6 in low-pressure region differs from the previous report [17], a possible reason is slight changes in the composition. In the previous report, the composition was Ta:Pd:S = 1.9 : 1 : 5.7 with a p-type carrier [17], whereas our sample is Ta:Pd:S = 2.0 : 1 : 5.7 with an n-type carrier as shown by Hall measurement (Fig. S3). The slight difference may induce the distinct behavior at lower pressures, as metal vacancies introduce p-type doping in several TMCs [32,33]. This drastic enhancement of Tc under high pressure is unusual, as the application of pressure typically decreases Tc due to phonon hardening and a reduction in the electronic density of state (DOS) at Fermi energy, based on Bardeen–Cooper–Schrieffer (BCS) theory [27,28]. Two-dome behavior of Tc is typically associated with structural phase transitions, as seen in FeS [29], LaFeAsO1−xFx [30], and other compounds [31]. However, a recently discovered SC phase in the topological kagome metal CsV3Sb5 shows two-dome Tc attributed to a pressure-induced Lifshitz transition, resulting from a 6 reconstruction of the Fermi surface without structural phase transition [7]. The elevated Tc in Ta2PdS6 and Ta2PdSe6 likely relate to a modification of electronic structure rather than a structural phase transition, as discussed later. Fig. 3 Pressure-dependent Tc in Ta2PdS6 and Ta2PdSe6 up to megabar region with a comparison of previously reported data of Ta2PdS6 [17] and Ta2PdSe6 [16]. The dashed lines are the guide for the eyes. To discuss the origin of anomalous enhancements, the pressure dependence of R at 300 K (R300K) in both compounds is plotted in Fig. 4 (a). In Ta2PdS6, R300K decreases monotonically with increasing pressure and reduces discretely at 21.5 GPa near Pc, suggesting a first-order transition. R300K gradually decreases further above 25.6 GPa until the maximum pressure of 130.0 GPa, without any additional discrete shifts. Similar gradual changes in R300K are observed in Ta2PdSe6. Figure 4 (b) plots the pressure dependence of the upper critical field μ0Hc2(0) and coherence length at zero temperature ξ(0) in Ta2PdS6 and Ta2PdSe6. To estimate these parameters, R-T curves under various magnetic fields were fitted with the Werthamer-Helfand-Hohenberg (WHH) model [34,35] using a Tc criterion at 95% of the normal resistance (Fig. S4). The maximum μ0Hc2(0) is 11.3 T at 130.0 GPa in Ta2PdS6 and 3.5 T at 109.35 GPa in Ta2PdSe6. These values are lower than the weak-coupling Pauli limit (1.84Tc), suggesting the absence of the Pauli paramagnetic pair-breaking effect. The ξ(0) was derived from the Ginzburg-Landau (GL) formula μ0Hc2(0) = Φ0/2πξ(0)2, where Φ0 is the fluxoid. The smooth changes in R300K, μ0Hc2(0), and ξ(0) as pressure increases beyond Pc suggest that the origin of the second SC dome is linked to modifications in electronic structures, such as a Lifshitz transition, as seen in kagome metal [7]. First-principles calculations on Ta2PdS6 indicate that enhanced DOS at Fermi energy plays a crucial role in the emergence of SC phase [17]. The observed Tc enhancement is possibly associated 7 with DOS peaks near Fermi energy, which is a favorable condition for superconductivity, as seen in high-Tc hydrides [36]. Our finding of the hidden SC phase in Ta2PdS6 and Ta2PdSe6 reveals the importance of exploring extreme conditions to accelerate further development of materials physics. Fig. 4 (a) Pressure-dependent resistance at 300 K, (b) μ0Hc2(0), and ξ(0) in Ta2PdS6 and Ta2PdSe6. 4. Conclusion In this study, we conduct the electrical transport measurements under high pressure up to 130.0 GPa in Ta2PdS6 and 118.8 GPa in Ta2PdSe6 to investigate SC properties beyond the first dome. The Tc in Ta2PdS6 exhibits a drastic enhancement above 80.4 GPa and reaches 11.2 K at 130.0 GPa, which is almost twice the Tc observed in the first dome. In Ta2PdSe6, the emergence of the second dome is also observed above 102.1 GPa. The observed higher Tc in the second dome is motivative for further investigation of fundamental physics in this materials system. Although we consider that the drastic enhancements of Tc in these compounds likely originate from modifications in the electronic structures, challenges remain in conducting structural analysis at the corresponding pressure. ACKNOWLEDGMENTS This work was partly supported by JSPS KAKENHI Grant Numbers 23H01835, 23K13549, and 23KK0088. 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