⇦Chinese Physics Letters, 2021, Vol. 38, No. 5, Article code 057402Express Letter Highly Robust Reentrant Superconductivity in CsV$_{3}$Sb$_{5}$ under Pressure Xu Chen (陈旭)1†, Xinhui Zhan (战鑫慧)2†, Xiaojun Wang (王晓郡)2, Jun Deng (邓俊)1, Xiao-Bing Liu (刘晓兵)2*, Xin Chen (陈欣)2, Jian-Gang Guo (郭建刚)1,3*, and Xiaolong Chen (陈小龙)1,3* Affiliations 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2Laboratory of High Pressure Physics and Material Science (HPPMS), School of Physics and Physical Engineering, Qufu Normal University, Qufu 273100, China 3Songshan Lake Materials Laboratory, Dongguan 523808, China Received 29 March 2021; accepted 14 April 2021; published online 20 April 2021 Supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0304700, 2018YFE0202601, and 2016YFA0300600), the National Natural Science Foundation of China (Grant Nos. 51922105, 11804184, 11974208, and 51772322), the Chinese Academy of Sciences (Grant No. QYZDJ-SSW-SLH013), the Beijing Natural Science Foundation (Grant No. Z200005), and the Shandong Provincial Natural Science Foundation (Grant Nos. ZR2020YQ05, ZR2019MA054, and 2019KJJ020).
†Xu Chen and Xinhui Zhan contributed equally to this work.
*Corresponding authors. Email: xiaobing.phy@qfnu.edu.cn; jgguo@iphy.ac.cn; chenx29@iphy.ac.cn Citation Text: Chen X, Zhan X H, Wang X J, Deng J, and Liu X B et al. 2021 Chin. Phys. Lett. 38 057402    Abstract We present the superconducting (SC) property and high-robustness of structural stability of kagome CsV$_{3}$Sb$_{5}$ under in situ high pressures. For the initial SC-I phase, its $T_{\rm c}$ is quickly enhanced from 3.5 K to 7.6 K and then totally suppressed at $P \sim 10$ GPa. With further increasing pressure, an SC-II phase emerges at $P \sim 15$ GPa and persists up to 100 GPa. The $T_{\rm c}$ rapidly increases to the maximal value of 5.2 K at $P=53.6$ GPa and slowly decreases to 4.7 K at $P=100$ GPa. A two-dome-like variation of $T_{\rm c}$ in CsV$_{3}$Sb$_{5}$ is concluded here. The Raman measurements demonstrate that weakening of $E_{\rm 2g}$ mode and strengthening of $E_{\rm 1g}$ mode occur without phase transition in the SC-II phase, which is supported by the results of phonon spectra calculations. Electronic structure calculations reveal that exertion of pressure may bridge the gap of topological surface nontrivial states near $E_{\rm F}$, i.e., disappearance of $Z_{2}$ invariant. Meanwhile, the Fermi surface enlarges significantly, consistent with the increased carrier density. The findings here suggest that the change of electronic structure and strengthened electron-phonon coupling should be responsible for the pressure-induced reentrant SC. DOI:10.1088/0256-307X/38/5/057402 © 2021 Chinese Physics Society Article Text A kagome lattice, composed of atoms at the vertices of a two-dimensional network with the corner-sharing triangles, provides a fascinating playground for exploring the novel frustrated, correlated and topological electronic states of matters recently.[1–4] Due to the special geometry, the kagome lattice naturally possesses Dirac dispersion and nearly flat bands that promote topological and correlation effect.[5] Kagome systems are predicted to host too many exotic electronic states, such as spinless fermions,[6–8] Mott phase transition,[6,9,10] charge density waves (CDW),[6,11–13] and superconductivity (SC).[6,7,11,14] Up to date, exploring exotic properties, in particular, the interplay between multiple electronic orders in kagome lattices, have been of challenge. Recently, a new family of quasi-2D kagome metals $A$V$_{3}$Sb$_{5}$ ($A$ = K, Rb and Cs) have attracted considerable attention.[15] The vanadium sublattice of P6/mmm CsV$_{3}$Sb$_{5}$ is a structurally perfect kagome lattice. There are two distinct Sb sublattices. The sublattice formed by the Sb1 atom is a simple hexagonal net, centered on each kagome hexagon. All interatomic distances within the kagome layer are equal, as required by the high symmetry of the V1 (Wyckoff 3g) and Sb1 (Wyckoff 1b) sites. The Sb2 (Wyckoff 4h) sublattice creates graphite-like layers of Sb (antimonene) that encapsulate the kagome sheets. The Cs sublattice fills the space between the graphite-like sheets. The superconducting transition temperatures ($T_{\rm c}$) are 0.93, 0.92, and 2.5 K for the three compounds, respectively.[16–18] In addition, in normal state they all manifest a proposed charge density wave transitions at 78, 103, and 94 K, respectively.[15,19,20] Interestingly, high-resolution scanning tunneling microscopy (STM) study reveals that such charge order displays a chiral anisotropy,[21–23] which leads to a giant anomalous Hall effect in the absence of resolvable magnetic order or local moments,[17,24–26] pointing to a precursor of unconventional SC.[21,27] Furthermore, the proximity-induced spin-triplet pairing and an edge supercurrent have been observed in Nb/KV$_{3}$Sb$_{5}$ devices.[28] More importantly, $Z_{2}$ nontrivial topological band structures, including multiple Dirac nodal points near the Fermi level ($E_{\rm F}$) and possible topological surface states, were demonstrated by angle-resolved photoemission spectroscopy (ARPES) and density-functional theory (DFT) calculations.[15,16,18] Therefore, AV$_{3}$Sb$_{5}$ is regarded as a candidate to study the interplay among SC, electron correlation and nontrivial band topology. It is known that in situ pressure tuning is a ‘clean’ way to tune basic electronic and structural properties without changing the chemical composition, and eventually benefits for elucidating mechanisms of the puzzling state in new superconducting materials.[29–34] Very recently, Zhao et al. and Chen et al. reported that the $T_{\rm c}$ of CsV$_{3}$Sb$_{5}$ first increases to 7.5 K and quickly reduces under pressure, proving the competition between SC and possible CDW.[27,35] Then, Zhao et al. and Zhang et al. updated the data of relatively high pressure, and the reemergence of SC after 15 GPa was discovered.[27,36] In this study, we performed the in situ high pressure transport measurements on the CsV$_{3}$Sb$_{5}$ sample as pressure is up to 100 GPa. Two superconducting domes in the temperature-pressure phase diagram are revealed. Interestingly, in pressure-induced superconducting state, the $T_{\rm c}$ and crystal structure are rather robust evidenced by the transport measurements, Raman spectra and phonon spectra calculations. Thus, varied electronic structure and possibly enhanced electron-phonon coupling play important roles in inducing reentrant SC. Sample Preparation. Single crystals of CsV$_{3}$Sb$_{5}$ were grown from Cs (Alfa, 99.98%), V powder (Alfa, 99.9%) and Sb grains (Alfa, 99.999%) using the self-flux growth method similar to the previous reports.[15] Cs, V and Sb were weighted as the stoichiometric ratio in an argon-filled glove box (A small excess of Cs was used to compensate for volatility of the alkali metal). Then they were packed into Al$_{2}$O$_{3}$ crucible in order and sealed into an evacuated silica tube under partial argon atmosphere. The sealed quartz ampoule was heated to 1273 K and soaked there for 24 h. Then, it was cooled down to 823 K at 2 K/h. Finally, the ampoule was taken out from the box furnace and decanted with a centrifuge to separate CsV$_{3}$Sb$_{5}$ single crystals from the flux. The shinning CsV$_{3}$Sb$_{5}$ single crystals were obtained, see Fig. S1 (in the Supporting Information). In Situ High-Pressure Measurements. High pressure resistivity of CsV$_{3}$Sb$_{5}$ single crystals was measured in a physical property measurement system (PPMS, Quantum Design) using a diamond anvil cell (DAC) at temperatures of 2–300 K. We used the van der Pauw method for electrical transport measurements on the CsV$_{3}$Sb$_{5}$ samples. Be–Cu cells were used for the resistance experiments. The cubic boron nitride (cBN) powders (200 and 300 nm in diameter) were employed as the pressure medium and the insulating material. The pressure was measured using the ruby fluorescence method at room temperature each time before and after the measurement. In addition, in situ Raman spectra under high pressure were taken (Horiba, Lab- RAM HR revolution) to characterize their structures. Theoretical Calculations. We performed structural optimization and electronic property calculations within framework of the DFT + $U$ by the Vienna ab initio simulation package (VASP) code.[37–40] The generalized-gradient approximation (GGA) is used for the exchange-correlation term within the Perdew–Burke–Ernzerhof (PBE) approach.[41–43] The additional Hubbard-like term is used to treat the on-site Coulomb interactions on the localized $d$-states of vanadium atoms. A plane wave energy cutoff of 350 eV and the Monkhorst–Pack $k$-meshes with a maximum spacing of $2\pi \times 0.15$ Å$^{-1}$ were used to ensure that all the enthalpy calculations are well converged to better than 1 meV/atom. To examine the dynamical stability of the structure, we performed phonon calculations using the finite displacement method as implemented in the PHONOPY code.[44] The Brillouin zone was sampled with a $3 \times 3 \times 2$ supercell. Crystal orbital Hamilton population (COHP) analysis was performed using the LOBSTER package[45,46] in conjunction with VASP. Results and Discussion. In the inset of Fig. 1(a), one can see that the temperature-dependent resistivity of CsV$_{3}$Sb$_{5}$ under ambient pressure, in which the kinks due to proposed charge density wave of 90 K and SC of 3.5 K coexist. The residual resistivity ratio value is about 25, indicating good quality of our sample. In a typical in situ high pressure measurement (run 1), two clear features emerge as shown in the main panel of Fig. 1(a). Firstly, the $T_{\rm c}^{\rm onset}$ of SC-I phase increases to 7.6 K at 0.7 GPa and then decreases to below 2 K at 9.0 GPa, leading to a dome-like $T_{\rm c}$. This pressure-dependent $T_{\rm c}$ is consistent with the recent reports.[27,35] The $H$-dependent resistivity at 1.5 GPa are plotted in Fig. 1(b). It is found that the $H$ of 3.0 T can totally suppress the superconducting transition. The upper critical field $\mu_{0}H_{c2}$, 4.2 T, is obtained based on the linear fitting. Another feature is that the magnitude of resistivity and the slops of the $\rho $–$T$ curve continuously decrease. The former is due to the pressure-induced compact of crystal, and the latter may relate to the variation of electron-phonon coupling under pressure. In Fig. 1(c), we can find that the sample is normal metal without any signature of SC in the pressure range of 12.0–14.9 GPa. The total magnitude of resistivity and residual resistivity increases with $P$. As $P>19.5$ GPa, a new superconducting phase appears. The $T_{\rm c}^{\rm onset}$ of reentrant SC is 2.8 K, which slowly increases to $T_{\rm c}$ of $\sim $5.1 K at $\sim $57.1 GPa. It should be noted is that the SC phase survives after the pressure is released, indicating a reversible structure even the pressure is squeezed up to 57.1 GPa, see Fig. S2. In run 2, we further increase the pressure to 100 GPa. In Fig. 1(d), it is found that the second SC reenters as $P>20$ GPa, exhibits peak $T_{\rm c}^{\rm onset}$ of 5.2 K at 53.6 GPa and then gradually decreases. The $T_{\rm c}$ is rather robust against pressure. At 100 GPa, the $T_{\rm c}^{\rm onset}$ is 4.7 K. We measured the $H$-dependent superconducting transition under $P=53.6$ GPa, and plotted the curves in Fig. 1(e). The SC is suppressed as $H>2$ T. The calculated $\mu_{0}H_{c2}$(0) is about 3.5 T. We show the temperature-dependent $\mu_{0}H_{c2}$ of CsV$_{3}$Sb$_{5}$ under selected pressure. The pressure dependence of $\mu_{0}H_{c2}$ are plotted in Fig. 1(f) and Fig. S3, and the values are smaller than the Pauli limit of $1.84 T_{\rm c}$.
cpl-38-5-057402-fig1.png
Fig. 1. Transport properties of CsV$_{3}$Sb$_{5}$ at various pressures. (a) The $\rho$–$T$ curves in the temperature range 2–300 K for 0.7–9.0 GPa. The inset of (a) is the $\rho$–$T$ curve for 0 GPa. (b) The $\rho / \rho_{_{\scriptstyle \rm 8K}}$ around $T_{\rm c}$ under external magnetic field at 1.5 GPa. (c) The $\rho$–$T$ curves in the temperature range 2–300 K for 12.0–57.1 GPa. The inset of (c) is the $\rho$–$T$ curves in the temperature range 2–6 K. (d) The $\rho$–$T$ curves in the temperature range 2–300 K for 1.3–100 GPa. The inset of (d) is the $\rho$–$T$ curve in the temperature range 2–6 K. (e) Behavior of $\rho / \rho_{_{\scriptstyle \rm 8K}}$ around $T_{\rm c}$ under external magnetic field at 53.6 GPa. (f) Temperature dependence of the upper critical field $\mu_{0} H_{c2}$ at different pressures. The broken lines represent the linear fitting curves.
cpl-38-5-057402-fig2.png
Fig. 2. Pressure dependence of (a) $T_{\rm c}$ and related physical parameters of CsV$_{3}$Sb$_{5}$: (b) index $\alpha$, (c) prefactor $A$, (d) Debye temperature $\varTheta_{\rm D}$, and (e) carrier density $n$.
The pressure-dependent $T_{\rm c}$ and related physical parameters are summarized in Fig. 2. There are two dome-like superconducting states under pressure as shown in Fig. 2(a). In the first SC range (SC-I), applying pressure rapidly enhances the $T_{\rm c}$ to $\sim $7.6 K and then suppresses the $T_{\rm c}$ below 2 K as $P \sim 10$ GPa. In the second SC range (SC-II), as $P>15$ GPa, the $T_{\rm c}$ continuously increases to the highest $T_{\rm c}$ of 5.2 K, which is slightly lower than that in the SC-I region. The two SC ranges are separated by $\sim $10 GPa. As previously reported, the highest $T_{\rm c}$ of reentrant SC is higher than that in SC-I phase such as FeSe-based superconductors. In $K_{x}$Fe$_{2}$Se$_{2}$ and (Li$_{1- x}$Fe$_{x}$)OHFe$_{1- y}$Se superconductors, the SC-I phases of 30 K and 41 K are rapidly suppressed at $P=10$ GPa and 4 GPa, respectively. Then pressure-induced SC-II phases emerge with the maximum $T_{\rm c}$ of 48.7 K and 50 K.[33,47,48] According to the transport property analysis, the suppression of the first SC phase is related to a possible quantum phase transition from Fermi liquid to non-Fermi liquid behavior.[49] In some superconductors such as KMo$_{3}$As$_{3}$, the $T_{\rm c}$ of the pressure-induced SC-II phase is slightly lower than that of the initial SC-I phase.[50] In the normal state, the pressure-dependent key transport parameters are plotted in Figs. 2(b)–2(f). We fit the $\rho (T)$ curve by the equation $\rho =\rho_{0}+AT^{\alpha}$ from $T_{\rm c}$ to 50 K. Here $\rho_{0}$ is residual resistivity, and $A$ is constant. The pressure-dependent index $\alpha$ is plotted in Fig. 2(b). In the SC-I, the $\alpha$ increases from 1.69 to 1.93, then it continuously decreases to 1.50 as the reentrant SC occurs. As the $P$ goes through the optimal value, the $\alpha$ increases again to 1.87. Such behaviors imply that the electron-correlated states possibly transit from Fermi-liquid to non-Fermi-liquid state, and then back to Fermi-liquid state again.[51,52] For the $A$, in SC-I region, it quickly increases to the peak value at 0.7 GPa, and then lowers to the minimum as the $T_{\rm c}$ is totally suppressed, see Fig. 2(c). In the NSC and SC-II regions, the $A$ shows the peak value of $0.029\,µ\Omega\cdot$cm$\cdot$K$^{-\alpha}$. On the other hand, in a pressurized sample, the $\rho_{0}$ generally decreases with increasing $P$, similar to the trend in the SC-I region. However, the enhancement of $\rho_{0}$ in higher $P$ is unusual, which may be caused by disorder if there is no metal-insulator transition. Based on the Bloch–Grüneisen model of scattering of electrons by longitudinal acoustic vibrations:[53] $$ \rho (T)=\rho _{0}+B\times \frac{T^{n}}{\theta _{\rm D}^{n-1}}\int_0^{\theta _{\rm D} / T}\frac{z^{n}dz}{(e^{z}-1)(1-e^{-z})} - kT^{3}, $$ where $\rho_{0}$ is residual resistivity, the value of $n$ is typically fixed at 3, $k$ the coefficient of the cubic term, $\varTheta_{\rm D}$ the Debye temperature from the resistivity data, and $B$ a prefactor depending on the material. We fitted the $\rho (T)$ data above $T_{\rm c}$ at each $P$, and obtained the $\varTheta_{\rm D}$ as shown in Fig. 2(d). It can be found that the $\varTheta_{\rm D}$ firstly rapidly increases to the maximal 344 K in the SC-I range, and then slowly decreases to a constant value of 150 K as entering the SC-II range, implying reduction of average frequency of phonon vibration. In addition, we measure the pressure-dependent carrier density $n$ as shown in Fig. 2(e), and find that it gradually increases from $1.6\times 10^{22}$ cm$^{-3}$ to $2.9\times 10^{22}$ cm$^{-3}$. The magnitude of $n$ is consistent with the reported values in analogous compounds.[24,25] It is instructive to check the structural stability at high pressure, thus we calculated phonon dispersions and projected phonon density of states at $P=0$ GPa, 10 GPa, 20 GPa, 40 GPa, and 60 GPa, see Figs. S4 and S5. The optimized crystallographic parameters are summarized in Table S1. The phonon dispersions at $P=0$ GPa exhibit large negative frequency at multiple directions in the Brillouin zone, indicating the structural instability. A $2 \times 2$ CDW ground state due to Peierls instability is proposed in the kagome lattice.[54] However, no imaginary frequencies are observed at higher pressure, suggesting that the dynamical stability enhances under pressure. Moreover, the contributions of phonon dispersions mainly come from the vibration of V and Sb atoms. The heavier Sb atoms dominate the low-frequency branches, while the relatively light V atoms contribute significantly to the high-frequency modes. Cs vibration has a smaller contribution over the whole frequency range due to the negligible chemical bonding with Sb atoms. More interestingly, it is found from Fig. S5 that the low-energy acoustic phonons soften around the $M$ point with increasing pressure up to 40 GPa.
cpl-38-5-057402-fig3.png
Fig. 3. (a) Three Raman-active modes of CsV$_{3}$Sb$_{5}$ as $A_{\rm 1g}$, $E_{\rm 2g}$ and $E_{\rm 1g}$. (b) Pressure-induced Raman intensity and position change of CsV$_{3}$Sb$_{5}$ in the pressure range of 1–53 GPa. (c) Intensity ratio of $A_{\rm 1g}/E_{\rm 2g}$ taken from (b).
On the other hand, according to the structural symmetry, three Raman-active models assigned as $A_{\rm 1g}$, $E_{\rm 2g}$ and $E_{\rm 1g}$ due to vibration of Sb are drawn in Fig. 3(a). The peak positions of three modes can be theoretically estimated from the phonon spectra at 10 GPa, 20 GPa, 40 GPa and 60 GPa. One can find that the three peaks are blue-shifted under applied pressure as shown in Fig. S6. We measured the pressure-dependent Raman spectra of CsV$_{3}$Sb$_{5}$ from 1 to 53 GPa and plotted them in Figs. 3(b), S7 and S8. At low $P$, two peaks of 119.5 cm$^{-1}$ and 135.3 cm$^{-1}$ are observed, which belong to $E_{\rm 2g}$ and $A_{\rm 1g}$ modes associated with longitudinal and transversal vibrations of Sb atoms. As $P>20$ GPa, a small peak at $\sim $100 cm$^{-1}$ emerges, which is $E_{\rm 1g}$ mode associated with in-plane relative vibration of upper Sb and lower Sb atoms. With increasing $P$, the peaks of $E_{\rm 2g}$ and $A_{\rm 1g}$ move to higher wave numbers like the observations in MnBi$_{2}$Te$_{4}$.[55] Simultaneously, the intensity of $E_{\rm 2g}$ slowly decreases while that of $A_{\rm 1g}$ increases. This anomalous change leads to the fact that the intensity ratio of $A_{\rm 1g}$/$E_{\rm 2g}$ starts to increase as $P>20$ GPa, then reaches the peak value at $P=30$ GPa, see Fig. 3(c). At the same time, from the $P$-dependent Raman spectra in the right panel of Fig. S7, we can see that the $E_{\rm 1g}$ mode emerges at 20.5 GPa. From the above lattice dynamic information, we can deduce that the initial structure of CsV$_{3}$Sb$_{5}$ with space group of P6/mmm is very robust, and no structural transition happens as $P=53$ GPa. Intuitively, the reentrant SC may relate to enhanced vibration of the low frequency $E_{\rm 1g}$ and weakened vibration of the high frequency $E_{\rm 2g}$, which may partially strengthen electron-phonon coupling.
cpl-38-5-057402-fig4.png
Fig. 4. Electronic band structures and partial density of states (PDOS) for CsV$_{3}$Sb$_{5}$ at (a) 0 GPa, (b) 5 GPa, (c) 20 GPa and (d) 40 GPa. Three bands crossing the $E_{\rm F}$ are plotted with different colors (light blue, blue and purple). The Fermi surface of each band crossing the Fermi energy at (e) 0 GPa, (f) 5 GPa, (g) 20 GPa and (h) 40 GPa. The blue arrows in Fig. 4(h) denote the nesting vector along $\varGamma$–$A$ and $L$–$M$ directions.
We calculated the electronic band structures at various pressures, as shown in Fig. 4. It can be seen that the electronic states of CsV$_{3}$Sb$_{5}$ near the $E_{\rm F}$ are mainly attributed by the V $d$ and the Sb $p$ orbitals. With the increase of pressure, the density of states (DOS) near $E_{\rm F}$ decreases from 5 to 3 states/eV per formula, see the right panels of Figs. 4(a)–4(d) and Fig. S9. Meanwhile, applying of pressure lifts the energy of middle band (blue color), closing the continuous direct gap in partial Brillouin zone. This implies that the $Z_{2}$ topological invariant may disappear at $P>20$ GPa.[56,57] The Dirac-cone at the $M$ point moves away from this high symmetry point at $P>20$ GPa, and some more Dirac-like cones appear near Fermi surface at $P=40$ GPa, see Figs. 4(c) and 4(d). In addition, the broadening of the band structure leads to more bands crossing through the $E_{\rm F}$ especially along $\varGamma$–$A$–$L$ direction. From the pressure-dependent topology of Fermi surface [Figs. 4(e)–4(h)], it can be found that the scale of Fermi surface increases, consistent with the enhanced carrier density shown in Fig. 2(e). Interestingly, there are extra Fermi surface rings at $P=20$ GPa and 40 GPa in Figs. 4(g) and 4(h), which supports the emergence of Lifshitz transition.[36] Strikingly, in Fig. 4(h), the P6/mmm structure exhibits Fermi surface nesting at $P=40$ GPa along $\varGamma$–$A$ and $M$–$L$ directions, associated with highly dispersive bands in this directions as discussed above. Therefore, we suggest that the induced Fermi-surface nesting also favors the reemergence of SC-II phase. From Fig. S10(a), it is found that the lattice parameter $c$ reduces rapidly in the low-pressure region and gradually changes slowly with the increasing pressure over 40 GPa. In contrast, the lattice parameter $a$ does not change significantly, leading to the slow decrease of interatomic distances within the kagome layer. Especially after 60 GPa, the bond length of V–Sb1 (V–V) exhibits a tendency to exceed that of V–Sb2 under pressure, see Fig. S10(b). In order to further investigate the bonding character of CsV$_{3}$Sb$_{5}$, we calculated projected crystal orbital Hamiltonian population (pCOHP) and plotted them in Fig. S11. It can evaluate the weighted population of wave functions on two atomic orbitals of a pair of selected atoms. It is noted that the occupied bonding states in CsV$_{3}$Sb$_{5}$ at 40 GPa move to deeper energy below the $E_{\rm F}$, indicating higher stability of P6/mmm CsV$_{3}$Sb$_{5}$ at 40 GPa. Moreover, in Fig. S12, we use the integrated COHP (ICOHP) to quantitatively estimate the bonding strength. It is noted that the V–Sb1 covalent bonding in kagome net of vanadium is the strongest, and with increasing pressure, the V–Sb1 bond strengthens non-significantly as that of V–Sb2 and V–V bonds, suggesting the stable kagome layer upon compression as verified above. In summary, we have investigated the SC, transport property and structural stability of CsV$_{3}$Sb$_{5}$ under high pressure up to 100 GPa. Initial SC phase-I is rapidly suppressed at $P \sim 10$ GPa, and then a second SC phase-II emerges for $P>15$ GPa. Interestingly, the SC-II exhibits a dome-like $T_{\rm c}$, in which the $T_{\rm c}$ quickly increases to peak $T_{\rm c}^{\rm onset}$ of 5.2 K and then slowly decreases to 4.7 K at $P=100$ GPa. Theoretical calculations and Raman measurements demonstrate that the initial crystal structure can persist in the whole pressure range. The reentrant SC should relate to variation of electronic structure and enhanced electron-phonon coupling due to partial phonon softening. The findings here suggest that the highly stable SC and structure in such kagome lattice deserve further investigation. References Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnetKagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinonsQuantum spin liquid statesDisordered flat bands on the kagome latticeTheoretical prediction of a strongly correlated Dirac metalCompeting electronic orders on kagome lattices at van Hove fillingDoped kagome system as exotic superconductorStrongly correlated fermions on a kagome latticeHard-Core Bosons on the Kagome Lattice: Valence-Bond Solids and Their Quantum MeltingSpin-Liquid Ground State of the S = 1/2 Kagome Heisenberg AntiferromagnetUnconventional Fermi Surface Instabilities in the Kagome Hubbard ModelTopological insulator on the kagome latticeFractionally charged topological point defects on the kagome latticeChiral superconducting phase and chiral spin-density-wave phase in a Hubbard model on the kagome latticeNew kagome prototype materials: discovery of KV 3 Sb 5 , RbV 3 Sb 5 , and CsV 3 Sb 5 Superconductivity in the $\mathbb{Z}_2$ kagome metal KV$_3$Sb$_5$Superconductivity and Normal-State Properties of Kagome Metal RbV 3 Sb 5 Single Crystals Cs V 3 Sb 5 : A Z 2 Topological Kagome Metal with a Superconducting Ground StateCascade of correlated electron states in a kagome superconductor CsV3Sb5Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metalDiscovery of topological charge order in kagome superconductor KV3Sb5Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors AV3Sb5 (A=Rb,Cs)Three-dimensional charge density wave and robust zero-bias conductance peak inside the superconducting vortex core of a kagome superconductor CsV$_3$Sb$_5$Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV 3 Sb 5Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metalAbsence of local moments in the kagome metal KV 3 Sb 5 as determined by muon spin spectroscopyNodal superconductivity and superconducting domes in the topological Kagome metal CsV3Sb5Proximity-induced spin-triplet superconductivity and edge supercurrent in the topological Kagome metal, $\mathrm{K_{1-x}V_3Sb_5}$Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressureCompressibility of the HgBa 2 Ca n − 1 Cu n O 2 n + 2 + δ ( n =1,2,3) high-temperature superconductorsMott Transition and Superconductivity in Quantum Spin Liquid Candidate NaYbSe 2Superconductivity at 43 K in an iron-based layered compound LaO1-xFxFeAsRe-emerging superconductivity at 48 kelvin in iron chalcogenidesPressure-Induced Metallization and Structural Phase Transition in the Quasi-One-Dimensional TlFeSe 2Double superconducting dome and triple enhancement of Tc in the kagome superconductor CsV3Sb5 under high pressurePressure-induced Reemergence of Superconductivity in Topological Kagome Metal CsV3Sb5Self-Consistent Equations Including Exchange and Correlation EffectsTwo theorems on the Hubbard modelBand theory and Mott insulators: Hubbard U instead of Stoner IEfficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis setTheory of the crystal structures of selenium and tellurium: The effect of generalized-gradient corrections to the local-density approximationIterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradientsGeneralized Gradient Approximation Made SimpleFirst-Principles Determination of the Soft Mode in Cubic ZrO 2 Crystal Orbital Hamilton Population (COHP) Analysis As Projected from Plane-Wave Basis SetsLOBSTER: A tool to extract chemical bonding from plane-wave based DFTReemergence of high-Tc superconductivity in the (Li1-xFex)OHFe1-ySe under high pressureHigh- T c superconductivity up to 55 K under high pressure in a heavily electron doped L i 0 . 36 ( N H 3 ) y F e 2 S e 2 single crystalPressure-Driven Quantum Criticality in Iron-Selenide SuperconductorsReemergence of superconductivity in pressurized quasi-one-dimensional superconductor K 2 Mo 3 As 3 Superconductivity and quantum criticality in the heavy-fermion system β-YbAlB4Heavy-fermion quantum criticality and destruction of the Kondo effect in a nickel oxypnictideNoncentrosymmetric superconductor BeAuCharge density waves and electronic properties of superconducting kagome metalsPressure-Induced Topological and Structural Phase Transitions in an Antiferromagnetic Topological InsulatorDirac metal to topological metal transition at a structural phase change in Au 2 Pb and prediction of Z 2 topology for the superconductorMultiple Dirac cones at the surface of the topological metal LaBi
[1] Han T H, Helton J S, Chu S, Nocera D G, Rodriguez-Rivera J A, Broholm C, and Lee Y S 2012 Nature 492 406
[2] Sachdev S 1992 Phys. Rev. B 45 12377
[3] Zhou Y, Kanoda K, and Ng T K 2017 Rev. Mod. Phys. 89 025003
[4] Bilitewski T and Moessner R 2018 Phys. Rev. B 98 235109
[5] Mazin I I, Jeschke H O, Lechermann F, Lee H, Fink M, Thomale R, and Valent R 2014 Nat. Commun. 5 4261
[6] Wang W S, Li Z Z, Xiang Y Y, and Wang Q H 2013 Phys. Rev. B 87 115135
[7] Ko W H, Lee P A, and Wen X G 2009 Phys. Rev. B 79 214502
[8] O'Brien A, Pollmann F, and Fulde P 2010 Phys. Rev. B 81 235115
[9] Isakov S V, Wessel S, Melko R G, Sengupta K, and Kim Y B 2006 Phys. Rev. Lett. 97 147202
[10] Yan S M, Huse D A, and White S R 2011 Science 332 1173
[11] Kiesel M L, Platt C, and Thomale R 2013 Phys. Rev. Lett. 110 126405
[12] Guo H M and Franz M 2009 Phys. Rev. B 80 113102
[13] Rüegg A and Fiete G A 2011 Phys. Rev. B 83 165118
[14] Yu S L and Li J X 2012 Phys. Rev. B 85 144402
[15] Ortiz B R, Gomes L C, Morey J R, Winiarski M, Bordelon M, Mangum J S, Oswald I W H, Rodriguez-Rivera J A, Neilson J R, Wilson S D, Ertekin E, McQueen T M, and Toberer E S 2019 Phys. Rev. Mater. 3 094407
[16] Ortiz B R and Sarte P M 2020 arXiv:2012.09097 [cond-mat.supr-con]
[17] Yin Q W, Tu Z J, Gong C S, Fu Y, Yan S H, and Lei H C 2021 Chin. Phys. Lett. 38 037403
[18] Ortiz B R, Teicher S M L, Hu Y, Zuo J L, Sarte P M, Schueller E C, Abeykoon A M M, Krogstad M J, Rosenkranz S, Osborn R, Seshadri R, Balents L, He J F, and Wilson S D 2020 Phys. Rev. Lett. 125 247002
[19] Zhao H, Li H, Ortiz B R, Teicher S M L, Park T, Ye M, Wang Z, Balents L, Wilson S D, and Zeljkovic I 2021 arXiv:2103.03118 [cond-mat.supr-con]
[20] Chen H, Yang H T, Hu B, Zhao Z, Yuan J, Xing Y Q, Qian G J, Huang Z H, Li G, Ye Y H, Yin Q W, Gong C S, Tu Z J, Lei H C, Ma S, Zhang H, Ni S L, Tan H X, Shen C M, Dong X L, Yan B H, Wang Z Q, and Gao H J 2021 arXiv:2103.09188 [cond-mat.supr-con]
[21] Jiang Y X, Yin J X, Denner M M, Shumiya N, Ortiz B R, He J, Liu X, Zhang S S, Chang G, Belopolski I, Zhang Q, Hossain M S, Cochran T A, Multer D, Litskevich M, Cheng Z J, Yang X P, Guguchia Z, Xu G, Wang Z, Neupert T, Wilson S D, and Hasan M Z 2020 arXiv:2012.15709 [cond-mat.supr-con]
[22] Li H X, Zhang T T, Pai Y Y, Marvinney C, Said A, Yilmaz T, Yin Q, Gong C, Tu Z, Vescovo E, Moore R G, Murakami S, Lei H C, Lee H N, Lawrie B, and Miao H 2021 arXiv:2103.09769 [cond-mat.supr-con]
[23] Liang Z W, Hou X Y, Ma W R, Zhang F, Wu P, Zhang Z Y, Yu F H, Ying J J, Jiang K, Shan L, Wang Z Y, and Chen X H 2021 arXiv:2103.04760 [cond-mat.supr-con]
[24] Yang S Y, Wang Y J, Ortiz B R et al. 2020 Sci. Adv. 6 eabb6003
[25] Yu F H, Wu T, Wang Z Y, Lei B, Zhuo W Z, Ying J J, and Chen X H 2021 arXiv:2102.10987 [cond-mat.supr-con]
[26] Kenney E M, Ortiz B R, Wang C, Wilson S D, and Graf M J 2021 J. Phys.: Condens. Matter (in press)
[27] Zhao C C, Wang L S, Xia W, Yin Q W, Ni J M, Huang Y Y, Tu C P, Tao Z C, Tu Z J, Gong C S, Lei H C, Guo Y F, Yang X F, and Li S Y 2021 arXiv:2102.08356 [cond-mat.supr-con]
[28] Wang Y, Yang S, Sivakumar P K, Ortiz B R, Teicher S M L, Wu H, Srivastava A K, Garg C, Liu D, Parkin S S P, Toberer E S, McQueen T, Wilson S D, and Ali M N 2020 arXiv:2012.05898 [cond-mat.supr-con]
[29] Wu M K, Ashburn J R, Torng C J, Hor P H, Meng R L, Gao L, Huang Z J, Wang Y Q, and Chu C W 1987 Phys. Rev. Lett. 58 908
[30] Eggert J H, Hu J Z, Mao H K, Beauvais L, Meng R L, and Chu C W 1994 Phys. Rev. B 49 15299
[31] Jia Y T, Gong C S, Liu Y X et al. 2020 Chin. Phys. Lett. 37 097404
[32] Takahashi H, Igawa K, Arii K, Kamihara Y, Hirano M, and Hosono H 2008 Nature 453 376
[33] Sun L L, Chen X J, Guo J, Gao P W, Huang Q Z, Wang H D, Fang M H, Chen X L, Chen G F, Wu Q, Zhang C, Gu D C, Dong X L, Wang L, Yang K, Li A G, Dai X, Mao H K, and Zhao Z X 2012 Nature 483 67
[34] Liu Z Y, Dong Q X, Shan P F et al. 2020 Chin. Phys. Lett. 37 047102
[35] Chen K Y, Wang N N, Yin Q W, Tu Z J, Gong C S, Sun J P, Lei H C, Uwatoko Y, and Cheng J G 2021 arXiv:2102.09328 [cond-mat.supr-con]
[36] Zhang Z Y, Chen Z, Zhou Y, Yuan Y F, Wang S Y, Zhang L L, Zhu X D, Zhou Y H, Chen X L, Zhou J H, and Yang Z R 2021 arXiv:2103.12507 [cond-mat.supr-con]
[37] Kohn W and Sham L J 1965 Phys. Rev. 140 A1133
[38] Lich H L 1989 Phys. Rev. Lett. 62 1201
[39] Vladimir I, Anisimov J Z, and Ole K 1991 Phys. Rev. B 44 943
[40] Kresse G and Furthmüller J 1996 Comput. Mater. Sci. 6 15
[41] Kresse G, Furthmüller J, and Hafner J 1994 Phys. Rev. B 50 13181
[42] Payne M C, Teter M P, Allan D C, Arias T, and Joannopoulos A J 1992 Rev. Mod. Phys. 64 1045
[43] Perdew J P, Burke K, and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[44] Parlinski K, Li Z Q, and Kawazoe Y 1997 Phys. Rev. Lett. 78 4063
[45] Deringer V L, Tchougréeff A L, and Dronskowski R 2011 J. Phys. Chem. A 115 5461
[46] Maintz S, Deringer V L, Tchougreeff A L, and Dronskowski R 2016 J. Comput. Chem. 7 1030
[47] Sun J P, Shahi P, Zhou H X, Huang Y L, Chen K Y, Wang B S, Ni S L, Li N N, Zhang K, Yang W G, Uwatoko Y, Xing G, Sun J, Singh D J, Jin K, Zhou F, Zhang G M, Dong X L, Zhao Z X, and Cheng J G 2018 Nat. Commun. 9 380
[48] Shahi P, Sun J P, Wang S H, Jiao Y Y, Chen K Y, Sun S S, Lei H C, Uwatoko Y, Wang B S, and Cheng J G 2018 Phys. Rev. B 97 020508(R)
[49] Guo J, Chen X J, Dai J H, Zhang C, Guo J G, Chen X L, Wu Q, Gu D C, Gao P W, Yang L H, Yang K, Dai X, Mao H K, Sun L L, and Zhao Z X 2012 Phys. Rev. Lett. 108 197001
[50] Huang C, Guo J, Zhao K, Cui F, Qin S S, Mu Q G, Zhou Y Z, Cai S, Yang C L, Long S J, Yang K, Li A G, Wu Q, Ren Z A, Hu J P, and Sun L L 2021 Phys. Rev. Mater. 5 L021801
[51] Nakatsuji S, Kuga K, Machida Y, Tayama T, Sakakibara T, Karaki Y, Ishimoto H, Yonezawa S, Maeno Y, Pearson E, Lonzarich G G, Balicas L, Lee H, and Fisk Z 2008 Nat. Phys. 4 603
[52] Luo Y, Pourovskii L, Rowley S E, Li Y, Feng C, Georges A, Dai J, Cao G, Xu Z, Si Q, and Ong N P 2014 Nat. Mater. 13 777
[53] Amon A, Svanidze E, Cardoso-Gil R, Wilson M N, Rosner H, Bobnar M, Schnelle W, Lynn J W, Gumeniuk R, Hennig C, Luke G M, Borrmann H, Leithe-Jasper A, and Grin Y 2018 Phys. Rev. B 97 014501
[54] Tan H, Liu Y Z, Wang Z Q, and Yan B H 2021 arXiv:2103.06325 [cond-mat.supr-con]
[55] Pei C Y, Xia Y Y Y, Wu J Z et al. 2020 Chin. Phys. Lett. 37 066401
[56] Schoop L M, Xie L S, Chen R, Gibson Q D, Lapidus S H, Kimchi I, Hirschberger M, Haldolaarachchige N, Ali M N, Belvin C A, Liang T, Neaton J B, Ong N P, Vishwanath A, and Cava R J 2015 Phys. Rev. B 91 214517
[57] Nayak J, Wu S C, Kumar N, Shekhar C, Singh S, Fink J, Rienks E E, Fecher G H, Parkin S S, Yan B H, and Felser C 2017 Nat. Commun. 8 13942