Double superconducting dome and triple enhancement of Tc in the kagome superconductor CsV3Sb5 under high pressure
K. Y. Chen, N. N. Wang, Q. W. Yin, Z. J. Tu, C. S. Gong, J. P. Sun, H. C. Lei, Y. Uwatoko, J.-G. Cheng
11 Double superconducting dome and triple enhancement of T c in the kagome superconductor CsV Sb under high pressure K. Y. Chen , N. N. Wang , Q. W. Yin , Z. J. Tu , C. S. Gong , J. P. Sun , H. C. Lei , Y. Uwatoko , and J.-G. Cheng Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan = These authors contributed equally to this work. E-mails: [email protected], [email protected], [email protected]
Abstract
CsV Sb is a newly discovered Z topological kagome metal showing the coexistence of a charge density wave (CDW)-like order at T * = 94 K and superconductivity (SC) at T c = 2.5 K at ambient pressure. Here we study the interplay between CDW and SC in CsV Sb via measurements of resistivity and magnetic susceptibility under hydrostatic pressures. We find that the CDW transition decreases with pressure and experience a subtle modification at P c1 P c2 T c ( P ) displays an unusual M-shaped double dome character with two maxima around P c1 and P c2 , respectively, leading to a tripled enhancement of T c to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of many unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range P c1 P P c2 as evidenced by the broad superconducting transition and reduced superconducting volume fraction. This work not only demonstrates the potential to raise the T c of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electronic correlations in this novel family of topological kagome metals. Keywords: CsV Sb , high pressure, superconductivity, charge density wave The newly discovered Kagome metals AV Sb (A = K, Rb, Cs) have attracted considerable attention due to the observation of many intriguing phenomena, including superconductivity (SC), nontrivial band topology, and charge order [1-4]. At ambient conditions, these materials crystallize into a layered structure with hexagonal symmetry (space group P6/mmm ), consisting of alkali-metal A layer and V-Sb slab stacked alternatively along the c -axis [1]. The most prominent feature of this structure is the presence of quasi-two-dimensional ideal kagome layers of V ions coordinated by Sb. These compounds are found to be metallic and even enter a superconducting ground state below the transition temperatures of T c = 0.93 K, 0.92 K, and 2.5 K for A= K, Rb, and Cs [2-4], respectively. Moreover, recent measurements of thermal conductivity on CsV Sb single crystal at ultra-low temperature evidenced a finite residual linear term, pointing to an unconventional nodal SC [5]. Interestingly, proximity-induced spin-triplet SC and edge supercurrent were observed in the Nb/K V Sb devices [6]. In addition, in the normal state they all exhibit a clear anomaly at T * ~ 78-104 K in the electrical transport and magnetic properties due to the formation of charge order (CDW-like) as revealed by the X-ray diffraction and scanning tunning microscopy measurements [2-4,7]. The charge order in KV Sb has been found to display a chiral anisotropy [7], which can lead to giant anomalous Hall effect in the absence of magnetic order or local moments [8,9]. It has also been argued as a strong precursor of unconventional SC [7]. Moreover, angle-resolved photoemission spectroscopy measurements and density-functional-theory calculations have characterized their normal state as a Z topological metal with multiple Dirac nodal points near the Fermi level [1,4]. The observations of pronounced Shubnikov-de Haas quantum oscillations and small Fermi surfaces with low effective mass in RbV Sb single crystals are consistent with the existence of multiple highly dispersive Dirac band near the Fermi level [3]. In addition, similar to staggered arrangement of hexagonal graphene [10], theoretical calculations on the kagome Hubbard model with different electron fillings have shown the stabilization of many exotic phases, such as the spinless fermions [11-13], Mott transition [11,14,15], charge density waves [11,16,17], chiral spin-density-wave state [11], exotic superconducting state [11,12] and topological point defects [17]. Therefore, these V-based kagome metals AV Sb have been regarded as a novel platform to study the interplay between SC, nontrivial band topology, and electronic correlations [1-9]. At present, the topologically related phenomena and SC have been actively studied in these AV Sb compounds, but the possible rich physics related to the electronic correlation, especially the relationship between the intertwined electronic orders, has been barely revealed. In this regard, it is highly interesting to unveil the correlation between the CDW-like order and SC commonly observed in these AV Sb materials. Here we have chosen to study CsV Sb single crystal with the highest T c = 2.5 K among this series of compounds by applying the high-pressure approach, which has been widely used in disentangling the competing electronic orders of the strongly correlated metals [18]. Through detailed measurements of resistivity, DC and AC magnetic susceptibility on CsV Sb single crystals under hydrostatic pressure, we successfully uncover an M-shaped double superconducting dome associated with the modification of the CDW-like order and its complete suppression under pressure, respectively. Interestingly, the T c of CsV Sb is triply enhanced to about 8 K at 2 GPa, indicating that the T c of these V-based kagome superconductors can be raised considerably. By revealing the coexistence and competition of SC with the CDW-like order, the temperature-pressure phase diagram of CsV Sb resembles those of many unconventional superconductors, and thus offer more insights into the rich correlation-related physics pertinent to this novel family of kagome metals. Single crystals of CsV Sb were grown from Cs ingot (purity 99.9%), V powder (purity 99.9%) and Sb grains (purity 99.999%) using the self-flux method, similar to the growth of RbV Sb [3]. Temperature dependences of resistivity for two CsV Sb samples ( P (GPa) = ( T - T c )/0.365, where T = 7.20 K is the T c of Pb at ambient pressure. We also measured the temperature-dependent resistivity on sample Details about the crystal growth procedures and high-pressure measurements can be found in the Supplementary Materials (SM). Figures 1(a) and 1(b) show the temperature dependence of resistivity ( T ) and its derivative d /d T of sample T *
94 K is manifested as a kink-like anomaly in ( T ) and a corresponding peak in d /d T , respectively. With increasing pressure, T * moves to lower temperature progressively and reaches about 15 K at 1.86 GPa, above which it cannot be discerned any more in resistivity, implying a complete suppression of CDW-like order by pressure. It is noteworthy that the kink feature in ( T ) at T * become much diminished at 0.6-0.9 GPa, and changes at P T *. This is a typical character for the CDW transition due to the gap opening over part of the Fermi surfaces [21-23]. Accordingly, the anomaly in d /d T changes from a peak for P < 0.6 GPa through an intermediate crossover region 0.6-0.9 GPa to a dip for P P > 0.6-0.9 GPa. Such a change at the normal state has a profound impact on the superconducting transition as shown below. Figure 2(a) displays an enlarged view of the ( T ) data in Fig. 1(a) at T
10 K, highlighting a complex, non-monotonic variation with pressure of the superconducting transition. As marked by arrows in Fig. 2(a), the onset of superconducting transition, T conset , is determined from the cross point of two straight lines above and below the transition, while the T czero is defined as the zero-resistance temperature. The ( T ) at 0 GPa shows a relatively sharp superconducting transition with T conset T czero T conset and T czero are raised up quickly to ~ 5 K and ~ 4.3 K at 0.37 GPa, and to ~ 6.8 K and ~ 5 K at 0.61 GPa, respectively. At 0.61 GPa, there exists a small step before reaching zero resistivity, indicating the presence of two superconducting phases. This small resistivity-step feature seems to evolve into a stronger shoulder at 0.9 GPa, resulting in a significantly broad superconducting transition width T c T conset ~7.2 K and the T czero ~ 3 K. When applying pressure to 1.2 GPa, the normal-state resistivity is reduced gradually, and the two-step feature of the superconducting transition is weakened by reducing the T conset to ~ 5.7 K but leaving the T czero at ~ 2.8 K, which is close to that at 0.9 GPa. But the transition width T c T c is shifted again to higher temperatures upon further increasing pressure; the T conset and T czero at 1.86 GPa reaches ~ 8 K and ~ 6 K, respectively. In this pressure range 1.2-1.86 GPa, the superconducting transition width T c T c T conset and T czero are 7.96 and 7.63 K for 2.03 GPa, and 7.68 and 7.43 K for 2.19 GPa, respectively. It seems that T c will decrease again at higher pressures. To track the evolution of T c ( P ) in a larger pressure range, we measured ( T ) of sample ( T ) data at low temperatures are shown in Fig. 2(b), and those in the whole temperature range are given in Fig. S2. The results in CAC are highly consistent with those in PCC. As can be seen, the ( T ) of 1.9 GPa in CAC resembles that of 1.86 GPa in PCC, showing a relatively sharp onset but a long tail with T conset T czero superconducting transition becomes very sharp with T c T conset and T czero are reduced to 2.82 and 2.58 K at 6.6 GPa. Since T c ( P ) exhibits a complex variation with pressure and the T c is quite wide in the pressure range 0.6-1.9 GPa where the high-temperature CDW order coexists, it is essential to further characterize the superconducting transition via detailed magnetic measurements. To this end, we measured the dc magnetization M ( T ) of sample ′ ( T ) of sample M ( T ) data collected upon warming up under an external magnetic field of H = 20 Oe after zero-field cooled from room temperature. As can be seen, the diamagnetic signal in M ( T ) appears at T c M = 2.5 K for 0 GPa, in agreement with the resistivity data, and it moves quickly to ~ 6.3 K at 0.54 GPa. In this pressure range, the bulk nature of SC is also confirmed by the large diamagnetic response of M ( T ). However, for P = 0.74 and 0.88 GPa, the diamagnetic response in M ( T ) appears at high temperature of ~ 6-7 K, but the transition is very broad and its magnitude is dramatically lowered. These observations suggest that the superconducting volume fraction is substantially reduced, consistent with the ( T ) data in the similar pressure range as shown in Fig. 2(a). At 1.06 GPa, a large diamagnetic signal emerges again below 3 K, signaling the resurgence of a new bulk superconducting phase. The ′ ( T ) results in Fig. 2(d) show one-to-one correspondence to the ( T ) data shown in Fig. 2(a), including the two-step feature of ′ ( T ) at 0.61 and 0.9 GPa (inset of Fig. 2(d)), the reduction of T c from 0.6 to 1.2 GPa followed by a resurgence of T c up to 1.86 GPa with a relatively broad transition, and a sharp superconducting transition at P T - P phase diagram of CsV Sb , Fig. 3(a, b), which depicts explicitly the evolution and correlations of T * and T c as a function of pressure. As can be seen, T *( P ) decreases monotonically with pressure and vanishes completely around P c2 T c ( P ) displays an M-shaped double-dome character with two maxima around P c1 P c2 , respectively. As shown in Figs. 3(b) and 3(c), the superconducting transition width T c in the pressure range P c1 P P c2 is significantly larger that at the lower and higher pressures. The highest T c P c2 and it is three times higher than that at ambient pressure. This observation immediately calls attention to further raise the T c of these V-based kagome superconductors. Discussions . The major finding of the present work is the observation of an M-shaped double superconducting dome that has an intimated interplay with the high-temperature CDW-like order. As shown in Fig. 1(a), the ( T ) anomaly around T * displays a subtle change from a kink-like rapid reduction at P < 0.6 GPa to a hump-like weak upturn at P > 0.9 GPa through an intermediate crossover region 0.6 - 0.9 GPa. Accordingly, the anomaly in d /d T around T * changes from a peak to a dip. To illustrate such a change, the symbols of T * in Fig. 3(a) are color-coded in terms of the sign of (d /d T ) at T * as defined in Fig. 1(b), which shows a clear crossover around P c1 . This means that, although the suppression of CDW-like order by pressure leads to an initial enhancement of T c , the modification of the CDW state around P c1 shows a stronger competition with the superconducting pairing, leading to the first extremum of T c shown in Fig. 3(b). As mentioned above, the weak upturn of ( T ) upon cooling through T * in the pressure range P c1 P P c2 is a typical character for the formation of CDW-like state that opens a gap over part of the Fermi surfaces. Although the density wave instability in this class of kagome metals is not unexpected, this pressure-induced CDW order should be distinct from the ambient-pressure one given the different responses in ( T ). At first, it seems to fulfill a better nesting condition across the in-plane two-dimensional Fermi surface, which can be finely tuned by compression [25]. As a result, the resistivity exhibits an enhancement across T *. Secondly, this new CDW order has a stronger tendency to compete for the electronic state responsible for SC [24,26], featured by a microscopic phase separation, leading to very broad superconducting transitions and substantially reduced superconducting volume fraction as observed in Figs. 2, and 3(b, c). The continuous suppression of the CDW order by pressure results in the resurgence of SC at higher pressures, leading to a second extremum of T c around P c2 where the CDW order just vanishes. However, the observed maximal T c in the vicinity of P c2 followed by a subsequent monotonic reduction of T c at higher pressure do not conform the typical behaviors of conventional two-dimensional CDW superconductors, such as transition-metal dichalcogenides Ta(Se,S) , in which the T c ( P ) shows a plateau or broad spectrum even after the CDW is suppressed by doping or pressure [27-29]. Instead, the T - P phase diagram of CsV Sb shown in Fig. 3(a, b) resembles those of many unconventional superconducting systems, such as heavy-fermion [30], cuprates [31], iron-based superconductors [18,32-34] and Lu(Pt x Pd x ) In [35], which are characterized by the presence of quantum criticality. To examine such a possibility, we probe the evolution of the electronic states by evaluating the upper critical field H c2 of the superconducting state. Figure S3 shows all the ( T ) data under various magnetic fields at different pressures for sample However, the critical field required to eliminate the superconducting transition exhibits a strong dependence as a function of pressure. In order to quantify this evolution, here we determined T c as the middle-point temperature of superconducting transition and plotted μ H c2 versus T c in Fig. 4. Then, we can estimate the zero-temperature upper critical field μ H c2 (0) by fitting the μ H c2 ( T ) with the empirical Ginzburg–Landau (GL) equation, viz . μ H c2 ( T ) = μ H c2 (0) (1 − t )/(1 + t ), where μ H c2 (0) is zero-temperature upper critical field and t is the reduced temperature T / T c . The fitting curves are shown as the broken lines in Fig. 4 and the extracted μ H c2 (0) values are plotted in Fig. 3(d) as a function of pressure. Interestingly, the μ H c2 (0) also displays two pronounced peaks around P c1 and P c2 , respectively. The corresponding μ H c2 (0) values are larger than 3 T, which is about one order of magnitude higher than that at ambient pressure. Similar double-peak features are also observed in the pressure dependence of the initial slope μ H c2 ( T ), i.e., -d H c2 /d T | T c , which is proportional to the effective mass of charge carriers [36]. As shown in Fig. S4, the divergence behaviors of -d H c2 /d T | T c around P c1 and P c2 , especially the latter, signal the dramatic enhancement of effective mass, which has been regarded as a hallmark of quantum criticality [37]. The presence of quantum criticality around P c2 is conceivable due to complete suppression of the CDW order, in line with many unconventional superconductors [38-43]. However, whether there is a buried quantum critical point around P c1 deserves further investigations. To unveil the nature of the subtle change of the CDW-like order around P c1 should be key to understand these peculiar behaviors. Conclusion
In summary, we performed a comprehensive high-pressure study on the electrical transport and magnetic properties of the CsV Sb single crystal, which is a newly discovered Z topological kagome metal showing the coexistence of a CDW-like order at T * = 94 K and SC at T c = 2.5 K at ambient pressure. Our results uncover a hitherto unknown pressure-induced modification of the CDW order around P c1 P c2 T c ( P ) exhibits an unusual M-shaped double superconducting dome with two maxima occurring right at P c1 and P c2 , respectively, thus revealing an intimated interplay between the CDW and SC. The competition between these two electronic orders is particularly strong for the intermediate pressure range P c1 P P c2 as evidenced by the strong reduction of superconducting volume fraction and the broad transition width. The T c of CsV Sb can be triply enhanced to ~ 8 K at a moderate pressure of 2 GPa, implying that the T c of these V-based kagome superconductors still has a room to go higher. In addition, the double-peak character has also been observed in the H c2 (0), and characteristics of quantum criticality around P c1 and P c2 has also been indicated. The determined T - P phase diagram with a quantum criticality around P c2 resemble those of many unconventional superconductors, thus providing more ingredients related to the strong electron correlations into the rich physics of this novel family of topological kagome metals. Several open issues still need to be addressed in the future studies, such as the nature of the CDW-like order in the intermediate pressure range, and the plausible buried quantum critical point around P c1 . Acknowledgements
This work is supported by the National Natural Science Foundation of China (12025408, 11904391, 11921004, 11888101, 11834016, 11822412 and 11774423), the Beijing Natural Science Foundation (Z190008 and Z200005), the National Key R&D Program of China (2018YFA0305700, 2018YFE0202600 and 2016YFA0300504), the Strategic Priority Research Program and Key Research Program of Frontier Sciences of the Chinese Academy of Sciences (XDB25000000, XDB33000000 and QYZDB-SSW-SLH013), and the CAS Interdisciplinary Innovation Team.
References [1] B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, I. W. H. Oswald, J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wilson, E. Ertekin, T. M. McQueen, and E. S. Toberer, New kagome prototype materials: discovery of KV Sb ,RbV Sb , and CsV Sb . Phys. Rev. Mater. , 094407 (2019). [2] B. R. Ortiz, E. Kenney, P. M. Sarte, S. M. L. Teicher, R. Seshadri, M. J. Graf, and S. D. Wilson, Superconductivity in the Z kagome metal KV Sb . arXiv: 2012.09097 (2020). [3] Q. W. Yin, Z. J. Tu, C. S. Gong, Y. Fu, S. H. Yan, and H. C. Lei, Superconductivity and normal-state properties of kagome metal RbV Sb single crystals. Chin. Phys. Lett. , accepted (2021). [4] B. R. Ortiz, S. M. L. Teicher, Y. Hu, J. L. Zuo, P. M. Sarte, E. C. Schueller, A. M. M. Abeykoon, M. J. Krogstad, S. Rosenkranz, R. Osborn, R. Seshadri, L. Balents, J. He, and S. D. Wilson, CsV Sb : A Z topological kagome metal with a superconducting ground state. Phys. Rev. Lett. , 247002 (2020). [5] C. C. Zhao, L. S. Wang, W. Xia, Q. W. Yin, J. M. Ni, Y. Y. Huang, C. P. Tu, Z. C. Tao, Z. J. Tu, C. S. Gong, H. C. Lei, Y. F. Guo, X. F. Yang, and S. Y. Li, Nodal superconductivity and superconducting dome in the topological Kagome metal CsV Sb . arXiv: 2102.08356 (2021). [6] Y. J. Wang, S. Y. Yang, P. K. Sivakumar, B. R. Ortiz, S. M. L. Teicher, H. Wu, A. K. Srivastava, C. Garg, D. F. Liu, S. S. P. Parkin, E. S. Toberer, T. McQueen, S. D. Wilson, and M. N. Ali, Proximity-induced spin-triplet superconductivity and edge supercurrent in the topological Kagome metal, K V Sb . arXiv: 2012.05898 (2020). [7] Y. X. Jiang, J. X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz, J. Y. He, X. X. Liu, S. S. Zhang, G. Q. Chang, I. Belopolski, Q. Zhang, M. Shafayat Hossain, T. A. Cochran, D. Multer, M. Litskevich, Z. J. Cheng, X. P. Yang, Z. Guguchia, G. Xu, Z. Q. Wang, T. Neupert, S. D. Wilson, and M. Z. Hasan, Discovery of topological charge order in kagome superconductor KV Sb . arXiv: 2012.15709 (2020). [8] S. Y. Yang, Y. J. Wang, B. R. Ortiz, D. F. Liu, J. Gayles, E. Derunova, R. Gonzalez-Hernandez, L. Šmejkal, Y. L. Chen, S. S. P. Parkin, S. D. Wilson, E. S. Toberer, T. McQueen, and M. N. Ali, Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV Sb . Sci. Adv. , eabb6003 (2020). [9] E. M. Kenney, B. R. Ortiz, C. N. Wang, S. D. Wilson, and M. J. Graf, Absence of local moments in the kagome metal KV Sb as determined by muon spin spectroscopy. arXiv: 2012.04737 (2020). [10] R. Nandkishore, L. S. Levitov, and A. V. Chubukov, Chiral superconductivity from repulsive interactions in doped graphene. Nat. Phys. , 158 (2012). [11] W. S. Wang, Z. Z. Li, Y. Y. Xiang, and Q. H. Wang, Competing electronic orders on kagome lattices at van Hove filling. Phys. Rev. B , 115135 (2013). [12] W. H. Ko, P. A. Lee, and X. G. Wen, Doped kagome system as exotic superconductor. Phys. Rev. B , 214502 (2009). [13] A. O’Brien, F. Pollmann, and P. Fulde, Strongly correlated fermions on a kagome lattice. Phys. Rev. B , 235115 (2010). [14] S. V. Isakov, S. Wessel, R. G. Melko, K. Sengupta, and Y. B. Kim, Hard-core bosons on the kagome lattice: valence-bond solids and their quantum melting. Phys. Rev. Lett. , 147202 (2006). [15] S. M. Yan, D. A. Huse, and S. R. White, Spin-liquid ground state of the S =1/2 kagome Heisenberg antiferromagnet. Science , 1173 (2011). [16] H. M. Guo and M. Franz, Topological insulator on the kagome lattice. Phys. Rev. B , 113102 (2009). [17] A. Rüegg and G. A. Fiete, Fractionally charged topological point defects on the kagome lattice. Phys. Rev. B , 165118 (2011). [18] J. P. Sun, K. Matsuura, G. Z. Ye, Y. Mizukami, M. Shimozawa, K. Matsubayashi, M. Yamashita, T. Watashige, S. Kasahara, Y. Matsuda, J. Q. Yan, B. C. Sales, Y. Uwatoko, J. G. Cheng, and T. Shibauchi, Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe. Nat. Commun. , 12146 (2016). [19] Y. Uwatoko, S. Todo, K. Ueda, A. Uchida, M. Kosaka, N. Mori, and T. Matsumoto, Material properties of Ni–Cr–Al alloy and design of a 4 GPa class non-magnetic high-pressure cell. J. Phys.: Condens. Matter , 11291 (2002). [20] J. G. Cheng, K. Matsubayashi, S. Nagasaki, A. Hisada, T. Hirayama, M. Hedo, H. Kagi, and Y. Uwatoko, Integrated-fin gasket for palm cubic-anvil high pressure apparatus. Rev. Sci. Instrum. , 093907 (2014). [21] P. Monçeau, N. P. Ong, A. M. Portis, A. Meerschaut, and J. Rouxel, Electric field breakdown of charge-density-wave-induced anomalies in NbSe . Phys. Rev. Lett. , 602 (1976). [22] J. Chaussy, P. Haen, J. C. Lasjaunias, P. Monceau, G. Waysand, A. Waintal, A. Meerschaut, P. Molinié, and J. Rouxel, Phase transitions in NbSe . Solid State Communications , 759 (1976). [23] A. F. Kusmartseva, B. Sipos, H. Berger, L. Forró, and E. Tutiš, Pressure induced superconductivity in pristine 1 T -TiSe . Phys. Rev. Lett. , 236401 (2009). [24] O. Moulding, I. Osmond, F. Flicker, T. Muramatsu, and S. Friedemann, Absence of superconducting dome at the charge-density-wave quantum phase transition in 2 H -NbSe . Phys. Rev. Research , 043392 (2020). [25] M. Hoesch, G. Garbarino, C. Battaglia, P. Aebi, and H. Berger, Evolution of the charge density wave superstructure in ZrTe under pressure. Phys. Rev. B , 125102 (2016). [26] T. Wu, H. Mayaffre, S. Krämer, M. Horvatić, C. Berthier, W. N. Hardy, R. X. Liang, D. A. Bonn, and M. H. Julien, Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa Cu Oy. Nature , 191 (2011). [27] B. S. Wang, Y. Liu, K. Ishigaki, K. Matsubayashi, J. G. Cheng, W. J. Lu, Y. P. Sun, and Y. Uwatoko, Pressure-induced bulk superconductivity in a layered transition-metal dichalcogenide 1 T -tantalum selenium. Phys. Rev. B , 220501 (2017). [28] B. S. Wang, Y. Liu, X. Luo, K. Ishigaki, K. Matsubayashi, W. J. Lu, Y. P. Sun, J. G. Cheng, and Y. Uwatoko, Universal phase diagram of superconductivity and charge density wave versus high hydrostatic pressure in pure and Se-doped 1 T -TaS . Phys. Rev. B , 220504 (2018). [29] S. X. Xu, Z. Y. Liu, P. T. Yang, K. Y. Chen, J. P. Sun, J. H. Dai, Y. Y. Yin, F. Hong, X. H. Yu, M. Q. Xue, J. Gouchi, Y. Uwatoko, B. S. Wang, and J. G. Cheng, Superconducting phase diagrams of S-doped 2 H -TaSe under hydrostatic pressure. Phys. Rev. B , 184511 (2020). [30] H. Q. Yuan, F. M. Grosche, M. Deppe, C. Geibel, G. Sparn, and F. Steglich, Observation of two distinct superconducting phases in CeCu Si . Science , 2104 (2003). [31] B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides. Nature , 179 (2015). [32] P. Shahi, J. P. Sun, S. H. Wang, Y. Y. Jiao, K. Y. Chen, S. S. Sun, H. C. Lei, Y. Uwatoko, B. S. Wang, and J. G. Cheng, High- T c superconductivity up to 55 K under high pressure in a heavily electron doped Li (NH ) y Fe Se single crystal. Phys. Rev. B , 020508(R) (2018). [33] J. P. Sun, P. Shahi, H. X. Zhou, Y. L. Huang, K. Y. Chen, B. S. Wang, S. L. Ni, N. N. Li, K. Zhang, W. G. Yang, Y. Uwatoko, G. Xing, J. Sun, D. J. Singh, K. Jin, F. Zhou, G. M. Zhang, X. L. Dong, Z. X. Zhao, and J. G. Cheng, Reemergence of high- T c superconductivity in the (Li x Fe x )OHFe y Se under high pressure. Nat. Commun. , 380 (2018). [34] J. P. Sun, M. Z. Shi, B. Lei, S. X. Xu, Y. Uwatoko, X. H. Chen, and J. G. Cheng, Pressure-induced second high- T c superconducting phase in the organic-ion-intercalated (CTA) FeSe single crystal. EPL , 67004 (2020). [35] T. Gruner, D. J. Jang, Z. Huesges, R. Cardoso-Gil, G. H. Fecher, M. M. Koza, O. Stockert, A. P. Mackenzie, M. Brando, and C. Geibel, Charge density wave quantum critical point with strong enhancement of superconductivity. Nat. Phys. , 967 (2017). [36] V. G. Kogan and R. Prozorov, Orbital upper critical field and its anisotropy of clean one- and two-band superconductors. Rep. Prog. Phys. , 114502 (2012). [37] J. Zaanen, Quantum critical electron systems: The uncharted sign worlds. Science , 1205 (2008). [38] J. H. Chu, H. H. Kuo, J. G. Analytis, and I. R. Fisher, Divergent nematic susceptibility in an iron arsenide superconductor. Science , 710 (2012). [39] N. Barisic, M. K. Chan, Y. Li, G. Yu, X. Zhao, M. Dressel, A. Smontara, and M. Greven, Universal sheet resistance and revised phase diagram of the cuprate high-temperature superconductors. Proc. Natl. Acad. Sci. USA , 12235 (2013). [40] J. C. Davis and D. H. Lee, Concepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivity. Proc. Natl. Acad. Sci. USA , 17623 (2013). [41] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage, and D. Hsieh, A global inversion-symmetry-broken phase inside the pseudogap region of YBa Cu O y . Nat. Phys. , 250 (2016). [42] W. C. Yu, Y. W. Cheung, P. J. Saines, M. Imai, T. Matsumoto, C. Michioka, K. Yoshimura, and S. K. Goh, Strong coupling superconductivity in the vicinity of the structural quantum critical point in (Ca x Sr ) Rh Sn . Phys. Rev. Lett. , 207003 (2015). [43] Y. Nakajima, H. Shishido, H. Nakai, T. Shibauchi, K. Behnia, K. Izawa, M. Hedo, Y. Uwatoko, T. Matsumoto, R. Settai, Y. Ōnuki, H. Kontani, and Y. Matsuda, Non-Fermi liquid behavior in the magnetotransport of Ce M In ( M : Co and Rh): Striking similarity between quasi two-dimensional heavy fermion and high- T c cuprates. J. Phys. Soc. Jpn. , 024703 (2007). Figure 1. Variation with pressure of the CDW-like transition. Temperature dependences of (a) resistivity ( T ) and (b) its derivative d /d T for the CsV Sb sample T *, are marked by the arrows in the figure. The curves in (b) have been shifted vertically for clarity. Figure 2. Variation with pressure of the superconducting transition in (a, b) resistivity and (c, d) magnetic susceptibility. The resistivity ρ ( T ) data in (a) and (b) are measured for sample Figure 3. Temperature-pressure phase diagram of CsV Sb . Pressure dependences of (a) the CDW-like transition temperature T * , (b) the superconducting transition temperatures T conset , T czero , T c χ , and T c M determined from the resistivity and magnetic measurements on several samples, (c) the superconducting transition width T c , and (d) the zero-temperature upper critical field H c2 (0) obtained from the empirical Ginzburg–Landau (GL) fitting. Figure 4. Temperature dependence of the upper critical field H c2c2