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Roton pair density wave in a strong-coupling kagome superconductor

Abstract

The transition metal kagome lattice materials host frustrated, correlated and topological quantum states of matter1,2,3,4,5,6,7,8,9. Recently, a new family of vanadium-based kagome metals, AV3Sb5 (A = K, Rb or Cs), with topological band structures has been discovered10,11. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures11,12,13,14,15,16,17,18,19. Here we report the observation of unconventional superconductivity and a pair density wave (PDW) in CsV3Sb5 using scanning tunnelling microscope/spectroscopy and Josephson scanning tunnelling spectroscopy. We find that CsV3Sb5 exhibits a V-shaped pairing gap Δ ~ 0.5 meV and is a strong-coupling superconductor (2Δ/kBTc ~ 5) that coexists with 4a0 unidirectional and 2a0 × 2a0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a0/3 spatial modulations of the superconducting gap, coherence peak and gap depth in the tunnelling conductance. We term this novel quantum state a roton PDW associated with an underlying vortex–antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong field that suppresses superconductivity and in zero field above Tc, reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-Tc cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

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Fig. 1: Atomic structures and the surface identification of the CsV3Sb5.
Fig. 2: V-shaped pairing gap and the Josephson effect observed using a SC STM tip on the Cs and Sb surfaces.
Fig. 3: STM topography, dI/dV map and linecut at 300 mK revealing CDW, PDW and spatial modulations of superconductivity on Sb surfaces.
Fig. 4: PDW and pseudogap in CsV3Sb5 in magnetic fields at 300 mK and in zero field at 4.2 K.

Data availability

Data measured or analysed during this study are available from the corresponding author on reasonable request.

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Acknowledgements

We thank I. Zeljkovic, S. Wilson, J. Yin and Z.-X. Zhao for helpful discussions. The work is supported by grants from the National Natural Science Foundation of China (61888102, 52022105, 11974422, 51771224 and 11974394), the National Key Research and Development Projects of China (2016YFA0202300, 2017YFA0206303, 2018YFA0305800 and 2019YFA0308500) and the Chinese Academy of Sciences (XDB28000000, XDB30000000, XDB33030100 and 112111KYSB20160061). Z.W. is supported by the US DOE, Basic Energy Sciences grant no. DE-FG02-99ER45747. 

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H.-J.G. designed the experiments. H.C., B.H., Y.X., G.Q., Z.H., Y.Y., C.S. and G.L. performed STM experiments with guidance from H.-J.G. and H.Y. Z.Z. and H.L.prepared samples. Q.Y., C.G. and Z.T. also participated in sample preparation. X.D., J.Y., H.Y., S.M., H.Z. and S.N. performed the transport experiments. Z.W., S.Z., H.T. and B.Y. carried out theoretical work. All of the authors participated in analysing experimental data, plotting figures and writing the manuscript. H.-J.G. and Z.W. supervised the project.

Corresponding authors

Correspondence to Ziqiang Wang or Hong-Jun Gao.

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Extended data figures and tables

Extended Data Fig. 1 Detailed STM characterization of the Sb and Cs surfaces.

a, Top panel: a typical STM image showing a step edge of Cs surface. Bottom panel: line profile along the white dotted arrow in a, indicating that the height of the step edge is ~0.95 nm, which is consistent with the calculated interlayer distance (Vs = -1 V, It = 0.1 nA). b, Atomically-resolved STM image of Cs surface, showing a hexagonal lattice with a period of 1.0 nm, which is \(\surd 3\) times larger than the lattice constant (\(a=b=\,\)0.55 nm, see Fig. S1a). (Vs = -500 mV, It  = 0.5 nA). c, Atomically-resolved STM image of Sb surface, showing a honeycomb lattice. The periodicity of the honeycomb lattice is about 0.56 nm, which agrees with the bulk lattice constant (\(a=b=\,\)0.55 nm, see Fig. S1a). (Vs  = -500 mV, It  = 0.5 nA). d, Atomically-resolved STM image of an interface between the top Cs and bottom Sb surfaces (same as in Fig. 1d). The atomic model is overlaid on the image, showing that each Cs atom sits on top of the Sb honeycomb center (Vs = -500 mV, It  = 0.5 nA). e, FFT of d showing the Cs √3 × √3R30o reconstruction relative to the Sb 1 × 1 lattice. f, g Top panels: schematics showing STM manipulations to expose the bottom Sb surface. Bottom panels: STM images of Cs surface before (f) and after (g) STM manipulation, respectively, showing the freshly-obtained bottom Sb surface highlighted by the white dotted square (Vs = -500 mV, It  = 0.5 nA).

Extended Data Fig. 2 STM topography and dI/dV maps over a 40 nm × 40 nm region at 300 mK.

a, Topography, dI/dV maps and the intensity of the drift-corrected Fourier transforms at the sample bias from -2 mV to 0 mV, respectively. Each map consists of 500 pixels  ×  500 pixels. b, Energy dependence of the Fourier line cuts along the three directions of the hexagonal zone. (Vs = -5 mV, It = 2 nA, Vmod = 0.5 mV).

Extended Data Fig. 3 Absence of 4a0/3 in high energy dI/dV maps at 300 mK.

a, Large-scale STM image (60 nm  ×  60 nm) of the Sb surface obtained at the temperature below Tc (300 mK), where a unidirectional charge order is visible (Vs = -20 mV, It = 2 nA). b, The magnitude of drift-corrected Fourier transform of a, showing clearly the Q3q-2a CDW and Q1q-4a stripe CDW peaks. c, d dI/dV mapping (1024 pixels  ×  1024 pixels) over the same region at -20 mV and the corresponding magnitude of drift-corrected Fourier transform (Vs = -20 mV, It = 2 nA, Vmod = 0.2 mV). d, f dI/dV mapping (1024 pixels  ×  1024 pixels) over the same region at -30 mV and the corresponding magnitude of drift-corrected Fourier transform (Vs = -30 mV, It = 2 nA, Vmod = 0.2 mV).

Extended Data Fig. 4 Schematic illustration of the roton-PDW.

Top panel: the roton dispersion and roton minimum at Qroton =  Q3q-4a/3 in the reciprocal lattice. Bottom panel: the 3Q roton-PDW at Qpdw  =  Qroton forming a commensurate vortex-antivortex lattice (red, blue and yellow circles) that spatially modulates the tunneling conductance spectra along a line cut.

Extended Data Fig. 5 Spatial map of pseudogap and Q3q-4a/3 modulations.

a, Spatially-averaged dI/dV spectrum obtained below Tc, exhibiting several peaks in the energy range between 1 mV and 6 mV (Vs = -10 mV, It = 1 nA, Vmod = 0.05 mV). The PDW pseudogap peak located near 5 mV is labelled as P. b, Waterfall and color plot of a dI/dV line cut, showing spatial modulations of the peak P (Vs = -3.7 mV, It = 1 nA, Vmod = 0.05 mV). c, Spatial gap map of *(r), showing the spatial modulations of the pseudogap (Vs = -3.7 mV, It = 1 nA, Vmod = 0.05 mV). d, Fourier transform of the pseudogap map showing peaks at the PDW vectors Q3q-4a/3 circled in magenta.

Extended Data Fig. 6 Charge ordered normal state in CsV3Sb5 above Tc.

a,b Large-scale STM topography of Sb surface obtained at 4.2 K and the magnitude of drift-corrected Fourier transform, showing 2a0 × 2a0 and 4a0 striped CDW peaks at wave vectors Q3q-2a and Q1q-4a (Vs = -90 mV, It = 2 nA). c,d dI/dV mapping of a at 20 mV and the magnitude of drift-corrected Fourier transform, respectively (Vs = -90 mV, It = 2 nA, Vmod = 0.5 mV). e. Energy dependence of the Fourier line cuts along qa directions, showing that peaks at Q3q-2a and Q1q-4a at 4 K are non-dispersive (Vs = -90 mV, It = 2 nA, Vmod = 0.5 mV).

Extended Data Fig. 7 Normal state angular-dependent magnetoresistance.

a, Schematic of the in-plane resistance measurement under a 5 T magnetic field by rotating the sample along c axis of the single crystal. b, Angular plot of the normalized anisotropic magnetoresistance \((\varDelta R/\,{R}_{min},\varDelta R=R(\theta )-{R}_{min})\), showing two-fold symmetry at the temperature below ~50 K. \(\theta \) is defined in a. c, Temperature dependence of the angular-dependent of at \(\varDelta R/\,{R}_{min}\) the angle of 28°, showing the onset of two-fold rotational symmetry below T* 50 ± 10 K.

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Chen, H., Yang, H., Hu, B. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222–228 (2021). https://doi.org/10.1038/s41586-021-03983-5

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