Nodal superconductivity and superconducting domes in the topological Kagome metal CsV3Sb5

Recently superconductivity was discovered in the Kagome metal AV3Sb5 (A = K, Rb, and Cs), which has an ideal Kagome lattice of vanadium. These V-based superconductors also host charge density wave (CDW) and topological nontrivial band structure. Here we report the ultralow-temperature thermal conductivity and high pressure resistance measurements on CsV3Sb5 with Tc = 2.5 K, the highest among AV3Sb5. A finite residual linear term of thermal conductivity at zero magnetic field and its rapid increase in fields suggest nodal superconductivity. By applying pressure, the Tc of CsV3Sb5 increases first, then decreases to lower than 0.3 K at 11.4 GPa, showing a clear first superconducting dome peaked around 0.8 GPa. Above 11.4 GPa, superconductivity re-emerges, suggesting a second superconducting dome. Both nodal superconductivity and superconducting domes point to unconventional superconductivity in this V-based superconductor. While our finding of nodal superconductivity puts a strong constrain on the pairing state of the first dome, which should be related to the CDW instability, the superconductivity of the second dome may present another exotic pairing state in this ideal Kagome lattice of vanadium.


Introduction
Finding unconventional superconductors and understanding their superconducting mechanism is the frontier of condensed matter physics, e.g., the heavy-fermion superconductors, Cu-based and Fe-based high-temperature superconductors 1 , and recent Ni-based superconductors 2 .Unlike the conventional swave superconductors, the wave function of Cooper pairs for unconventional superconductors is usually not s-wave.Symmetry imposed nodes (gap zeros) are often observed, such as in d-wave cuprate superconductors and heavy-fermion superconductor CeCoIn5 (ref. 3,4).Note that the Fe-based superconductors are exceptions, in which both multiple s-wave gaps and nodal gaps are found 5 .
Furthermore, the superconducting pairing mechanism of unconventional superconductors is not phonon-mediated.This usually manifests as a superconducting dome neighbouring a magnetic order or density-wave order in the phase diagram, and spin or density-wave fluctuations are considered as the major pairing glue 1 .The superconducting gap structure and superconducting dome nearby an ordered state provide important clues to the underlying pairing mechanism.
Recently, superconductivity was discovered in a new family of V-based compounds AV3Sb5 (A = K, Rb, and Cs) [6][7][8][9] .These compounds have the ideal Kagome lattice of vanadium coordinated by antimony, with the A atoms intercalated between the layers, as seen in Fig. 1a and 1b.The superconducting transition temperature Tc is 0.93, 0.92, and 2.5 K for A = K, Rb, and Cs, respectively [7][8][9] .While there are no local magnetic moments 10 , these V-based superconductors manifest a charge density wave (CDW) order at 78, 103, and 94 K, respectively [6][7][8][9] .Interestingly, for KV3Sb5, high-resolution scanning tunneling microscopy (STM) study demonstrated that such charge order in the frustrated Kagome lattice is topological 11 , which leads to a giant anomalous Hall effect 12 , and can also be a strong precursor of unconventional superconductivity 11 .Moreover, topological nontrivial band structures, including multiple Dirac points and possible surface state, were revealed by angle-resolved photoemission spectroscopy (ARPES) measurements combined with density-functional theory (DFT) calculations 7,12 .In this context, the Kagome metal AV3Sb5 provides a great platform to study the interplay of superconductivity, CDW, frustration, and topology.It will be very important to understand the superconducting state first.
In this paper, we present ultralow-temperature thermal conductivity measurements of CsV3Sb5 single crystal to investigate its superconducting gap structure.The data in zero and magnetic fields clearly demonstrate that there are nodes in the superconducting gap.Furthermore, two superconducting domes in the temperature-pressure phase diagram are revealed by resistance measurement under pressures up to 47.0 GPa.These results suggest unconventional superconductivity in CsV3Sb5.We discuss the possible novel superconducting states in these V-based superconductors.

Results and discussion
Figure 1c plots the XRD pattern of CsV3Sb5 single crystal, showing that the largest natural face is (00l) plane.In Fig. 1d, the magnetization measured in 1 T with zero-field and field cooling modes displays a sharp drop at 94 K, which is the CDW transition reported previously 7 .The low-temperature magnetic susceptibility measured at 10 Oe with zero-field and field cooling modes is plotted in Fig. 2a.The onset of the superconductivity is at 2.5 K, which is also consistent with previous report 7 .
In Fig. 2b, we present the temperature dependence of in-plane resistivity for CsV3Sb5 single crystal in magnetic fields up to 2 T. In zero field, the Tc defined at 10% drop of normal-state resistivity (Tc 10% ) and zero resistivity Tc zero ) are 3.6 K and 2.7 K, respectively.The Tc zero is slightly higher than the onset Tc from magnetic susceptibility measurement.The normal-state resistivity shows a very weak temperature dependence below 6 K.A simple extrapolation gives residual resistivity ρ0(0T) = 4.75 µΩ cm and ρ0(0.2T)= 4.82 µΩ cm, respectively.The temperature dependence of Hc2, determined by the Tc zero values in Fig. 2b, is plotted in Fig. 2c.The red line is a linear fit to µ0Hc2(T), and µ0Hc2(0) ≈ 0.47 T is roughly estimated.
The ultralow-temperature heat transport measurement is an established bulk technique to probe the superconducting gap structure 13 .Figure 3 presents the in-plane thermal conductivity results of CsV3Sb5 single crystal.At very low temperatures, the thermal conductivity can usually be fitted to κ/T = a + bT α−1 (ref. 14,15), in which the two terms aT and bT α represent contributions from electrons and phonons, respectively.The power a is typically between 2 and 3, due to specular reflections of phonons at the boundary 14,15 .In zero field, the fitting of the data below 0.5 K gives a finite residual linear term κ0/T ≡ a = 0.22 ± 0.04 mW K -2 cm -1 and α = 2.70 ± 0.12. Figure 3a is plotted as κ/T vs T 1.70 to show the data more clearly.
Further information on the superconducting gap structure can be obtained by examining the behavior of field-dependent κ0/T (ref. 13).In Fig. 3b, the thermal conductivity of CsV3Sb5 in magnetic fields up to 0.25 T are plotted.By applying a very small field 0.01 T, one can see a large enhancement of thermal conductivity.Since all the curves in magnetic fields are roughly linear, we fix α to 2, thus fit the data to κ/T = a + bT and obtain the κ0/T for each magnetic field.For µ0H = 0.16 T, the fitting gives κ0/T = 4.15 ± 0.13 mW K -2 cm -1 .Further increasing field to 0.25 T does not increase the thermal conductivity, therefore we take 0.16 T as the bulk Hc2(0).Note that this value is lower than that obtained from resistivity measurements.Interestingly, there is about 20% violation of Wiedemann-Franz law in the normal state, when we compare the κ0/T at 0.16 T to its Wiedemann-Franz law expectation L0/ρ0 (0.16T) ≈ 5.08 mW K -2 cm -1 , with the Lorenz number L0 = 2.45 × 10 −8 W Ω K −2 and ρ0(0.16T)≈ ρ0(0.20T)= 4.82 μΩ cm.The origin of this violation is not clear to us at this stage.It may come from the topological nontrivial band structure, i.e., either the Dirac quasiparticles violate the Wiedemann-Franz law, or the surface state conducts electrical current much better than the heat current.We leave this issue for future investigation.
The normalized values of [κ0/T]/[κN0/T] as a function of H/Hc2 for CsV3Sb5 is plotted in Fig. 3c, with κN0/T = 4.15 mW K -2 cm -1 and Hc2 = 0.16 T. For comparison, similar data of the clean s-wave superconductor Nb (ref. 22), the dirty s-wave superconducting alloy InBi (ref. 16), the multiband s-wave superconductor NbSe2 (ref. 17), and an overdoped d-wave cuprate superconductor Tl-2201 (ref. 18), are also plotted.For CsV3Sb5, the field dependence of κ0/T clearly mimics the behaviour of Tl-2201.The rapid increase of κ0/T in magnetic field should come from the Volovik effect of nodal quasiparticles, thus provides further evidence for nodes in the superconducting gap 13 .To our knowledge, so far all nodal superconductors have unconventional pairing mechanism 1 .In this regard, the nodal gap we demonstrate from thermal conductivity results suggests unconventional superconductivity in CsV3Sb5.
To get further clue to the pairing mechanism in CsV3Sb5, we map out its temperature-pressure phase diagram by resistance measurement under pressures.Figure 4a presents the low-temperature resistance of CsV3Sb5 single crystal under various pressures up to 11.4 GPa.At ambient pressure, the Tc 10% is 3.6 K.With increasing pressure, the Tc 10% first increases sharply to 5.6 K at 0.8 GPa, enhanced by 56%.
Under this pressure, applying magnetic field gradually suppresses the superconducting transition, as shown in Fig. 4b.With further increasing pressure, Tc 10% decreases slowly to below 0.3 K at 11.4 GPa.
The non-monotonic pressure dependence of Tc 10% is plotted in Fig. 4c, which shows a clear superconducting dome.Since the CDW usually competes with superconductivity, it is expected that the CDW order may be suppressed near the optimal pressure pc ~ 0.8 GPa of the superconducting dome.This needs to be examined by high pressure magnetization measurements.More interestingly, as the pressure further increases, superconductivity re-emerges, and the Tc keeps increasing up to 47.0 GPa, as shown in Fig. 4d.The effect of field on the resistance transition under 29.3 GPa in Fig. 4e demonstrates it is a superconducting transition.In Fig. 4f, we plot the full temperature -pressure phase diagram, which includes two superconducting domes.
A temperature -pressure (Tc vs p) or temperature -doping (Tc vs x) superconducting dome has been commonly observed in many unconventional superconductors, including heavy-fermion superconductors, cuprate superconductors, iron-based superconductors, and quasi-two-dimensional organic superconductors 1 .For example, the heavy-fermion superconductor CeCoIn5 manifests a Tc vs p superconducting dome, and the unconventional superconductivity with  symmetry may result from the antiferromagnetic spin fluctuations 23 .Theoretically, it has been shown that unconventional superconductivity with dxy symmetry can also appear in close proximity to a chargeordered phase, and the superconductivity is mediated by charge fluctuations 24,25 .This may be the case of the pressure-induced superconductivity in 1T-TiSe2, with the superconducting dome appearing around the critical pressure related to the charge-density wave (CDW) meltdown 26 .For Kagome lattice at van Hove filling, previous theoretical calculations found competing electronic orders, including CDW and chiral  +  superconductivity 27,28 .However, proximity-induced spin-triplet superconductivity was claimed in Nb-K1-xV3Sb5 devices 29 .Nevertheless, our finding of nodal superconductivity put a strong constrain on the pairing state of the first dome of CsV3Sb5, which should be related to the CDW instability.A second superconducting dome is rare, including the heavy-fermion CeCu2(Si1-xGex)2 (ref. 30) and the iron chalcogenides 31 .Since the second dome is away from the CDW order, more experimental and theoretical works are needed to understand the superconductivity of the second dome in CsV3Sb5.
In summary, we investigate the superconducting gap structure of the new V-based superconductor CsV3Sb5 by ultralow-temperature thermal conductivity measurements.The finite κ0/T in zero magnetic field and its rapid field dependence give strong evidences for nodes in the superconducting gap.Further measurements of resistance under pressure reveal two superconducting domes in the temperaturepressure phase diagram.These results suggest unconventional superconductivity in CsV3Sb5.While our finding of nodal superconductivity puts a strong constrain on the pairing state of the first dome, which should be related to the CDW instability, the superconductivity of the second dome may present another exotic pairing state in this ideal Kagome lattice of vanadium.

Methods
Sample preparation.Single crystals of CsV3Sb5 were grown from Cs ingot (purity 99.9%), V powder (purity 99.9%) and Sb grains (purity 99.999%) using the self-flux method 7 .The eutectic mixture of CsSb and CsSb2 is mixed with VSb2 to form a composition with 50 at.%CsxSby and 50 at.%VSb2 approximately.The mixture was put into an alumina crucible and sealed in a quartz ampoule under partial argon atmosphere.The sealed quartz ampoule was heated to 1273 K for 12 h and soaked there for 24 h.Then it was cooled down to 1173 K at 50 K/h and further to 923 K at a slowly rate.Finally, the ampoule was taken out from the furnace and decanted with a centrifuge to separate CsV3Sb5 single crystals from the flux.CsV3Sb5 single crystals are stable in the air.The X-ray diffraction (XRD) measurement was performed on a typical CsV3Sb5 sample by using an X-ray diffractometer (D8 Advance, Bruker), and determined the largest surface to be the (00l) plane.
DC magnetization measurement.The DC magnetization measurement was performed down to 1.8 K using a magnetic property measurement system (MPMS, Quantum Design).
Resistivity and thermal transport measurements.The sample with dimensions of 1.96 × 0.27 mm 2 in the ab plane and a thickness of 57 μm along the c axis was used for both resistivity and thermal transport measurements at ambient pressure.Four silver wires were attached to the sample with silver paint, which were used for both resistivity and thermal conductivity measurements under ambient pressure, with electrical and heat currents in the ab plane.The inplane resistivity was measured in a 3 He cryostat.The in-plane thermal conductivity was measured in a dilution refrigerator by using a standard four-wire steady-state method with two RuO2 chip thermometers, calibrated in situ against a reference RuO2 thermometer.Magnetic fields were applied perpendicular to the ab plane in all measurements.To ensure a homogeneous field distribution in the sample, all fields for resistivity and thermal conductivity measurements were applied at a temperature above Tc.
High pressure measurements.High pressure resistance of CsV3Sb5 powder sample (ground from single crystals) was measured in a physical property measurement system (PPMS, Quantum Design) and a 3 He cryostat by using a diamond anvil cell (DAC).The pressures inside of the DAC were scaled by ruby fluorescence method at room temperature each time before and after the measurement.H/Hc2, with bulk Hc2 = 0.16 T. Similar data of the clean s-wave superconductor Nb (ref. 22), the dirty s-wave superconducting alloy InBi (ref. 16), the multiband s-wave superconductor NbSe2 (ref. 17), and an overdoped d-wave cuprate superconductor Tl-2201 (ref. 18) are shown for comparison.

Figure captions Fig. 1 |
Figure captionsFig.1 | Characterization of CsV3Sb5.a Crystal structure of CsV3Sb5.The Cs, V, Sb atoms are presented as green, red and orange balls, respectively.b Top-down view of the crystal structure.The two-dimensional Kagome lattice of vanadium can be clearly seen.c Room-temperature X-ray diffraction pattern of the CsV3Sb5 single crystal, showing that the largest natural face is (00l) plane.d Temperature dependence of the magnetization for CsV3Sb5 single crystal.The arrow denotes a charge density wave order at 94 K.

Fig. 2 |
Fig. 2 | Superconductivity of CsV3Sb5.a Low-temperature magnetization of CsV3Sb5 single crystal at H = 10 Oe, with zero-field and field cooling modes, respectively.b Low-temperature in-plane resistivity of CsV3Sb5 single crystal in magnetic fields up to 2 T. c Temperature dependence of the upper critical field µ0Hc2, extracted from the Tc zero values in panel b.The red line is a linear fit to µ0Hc2(T), and µ0Hc2(0) ≈ 0.47 T is roughly estimated.

Fig. 3 |
Fig. 3 | Thermal conductivity of CsV3Sb5.a Temperature dependence of the in-plane thermal conductivity for CsV3Sb5 single crystal in zero field.The solid line represents a fit to κ/T = a + bT α−1 below 0.5 K, which gives the residual linear term κ0/T ≡ a = 0.22 ± 0.04 mW K -2 cm -1 and α = 2.70 ± 0.12.b The thermal conductivity of CsV3Sb5 in magnetic fields up to 0.25 T. The dashed line is the normal-state Wiedemann-Franz law expectation L0/ρ0 (0.2T), with the Lorenz number 2.45 × 10 −8 W Ω K −2 and ρ0(0.2T)= 4.82 µΩ cm.c Normalized residual linear term κ0/T of CsV3Sb5 as a function of

Fig. 4 |
Fig. 4 | Resistance under pressure and temperature -pressure phase diagram for CsV3Sb5.a Temperature dependence of resistance for CsV3Sb5 under various pressures up to 11.4 GPa.The curve of 0 GPa is from the CsV3Sb5 single crystal in Fig. 2b.b Temperature dependence of resistance for CsV3Sb5 under different magnetic fields at 0.8 GPa.Increasing the magnetic field gradually suppresses the superconducting transition.c Temperature -pressure phase diagram up to 11.4 GPa for CsV3Sb5.Tc is determined at the 10% drop of the normal-state resistance.It shows a clear superconducting dome.