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Cascade of correlated electron states in the kagome superconductor CsV3Sb5

Abstract

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene.

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Fig. 1: Surface identification.
Fig. 2: Large-scale electronic characterization.
Fig. 3: Charge ordering at low temperature.
Fig. 4: Visualizing rotational symmetry breaking in the QPI of CsV3Sb5.

Data availability

The data supporting the findings of this study are available upon request from the corresponding author. Source data are provided with this paper.

Code availability

The computer code used for data analysis is available upon request from the corresponding author.

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Acknowledgements

We thank K. Fujita and A. Pasupathy for valuable discussions. I.Z. gratefully acknowledges the support from the National Science Foundation grant no. NSF-DMR-1654041 and Boston College startup. S.D.W., B.R.O., L.B., S.M.L.T. and T.P. gratefully acknowledge support via the University of California Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i programme under award DMR-1906325. B.R.O. also acknowledges support from the California NanoSystems Institute through the Elings Fellowship programme. We acknowledge use of the shared computing facilities of the Center for Scientific Computing at University of California Santa Barbara, supported by NSF CNS-1725797, and the NSF Materials Research Science and Engineering Center at University of California Santa Barbara, NSF DMR-1720256. M.Y. is supported in part by the Gordon and Betty Moore Foundation through Grant GBMF8690 to UCSB. S.M.L.T. has been supported by the National Science Foundation Graduate Research Fellowship Program under grant no. DGE-1650114. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Z.W. acknowledges the support of US Department of Energy, Basic Energy Sciences grant no. DE-FG02-99ER45747.

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Contributions

STM experiments and data analysis were performed by H.Z. and H.L. B.R.O. synthesized and characterized the samples under the supervision of S.D.W. S.M.L.T. performed band structure calculations. T.P., M.Y., L.B. and Z.W. provided theoretical input on the underlying physics and the interpretation of data. H.Z., S.D.W., Z.W. and I.Z. wrote the paper, with input from all authors. I.Z. supervised the project.

Corresponding author

Correspondence to Ilija Zeljkovic.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Cs clustering on as-cleaved Sb-terminated surface.

(a) 3D portrayal of a large-scale morphology of the Sb layer from an STM topograph. Inset is a 3D zoom-in of a small square region covering three Cs atoms. (b) As-cleaved STM topograph with several Cs atoms scattered on the surface. The apparent height of Cs atoms in (b) is approximately 2 Angstroms, and the color scale is saturated to emphasize the 4a0-CO modulation. STM setup condition: (a) Vsample = 200 mV, Iset = 10 pA; (b) Vsample = 200 mV, Iset = 50 pA. T = 4.5 K in all panels.

Extended Data Fig. 2 Large-scale STM topograph of the Sb-terminated surface.

High resolution STM topograph over a large region encompassing the topograph from Fig. 3c. Inset shows a zoom-in on two defects that serve as main scattering sites for the wave-like QPI modulations, with different atoms superimposed on top (Cs – green, Sb – gray and V – red spheres). As it can be seen in the inset, the defects are located at the Cs site. STM setup condition: Vsample = −20 mV, Iset = 20 pA, T = 4.5 K; (inset) Vsample = 20 mV, Iset = 60 pA, T = 4.5 K.

Extended Data Fig. 3 Quasiparticle interference imaging of the electron pocket around Γ.

(a-f) Differential conductance (dI/dV(r, V)) maps over the same region of the sample used for the analysis of the dispersion in Fig. 2, and (g-l) corresponding Fourier transforms (FTs). Green, brown and blue circles denote the atomic Bragg peaks, 2a0 charge ordering peaks q2a0-CO and unidirectional stripe charge order peaks q4a0-CO in momentum-transfer space, respectively. The red and orange arrows indicate the QPI wave vectors that we attribute to the intra-electron pocket scattering around Γ. (m) Radially-averaged FT linecut as a function of STM bias V showing the presence of q1 across Fermi energy. STM setup condition: (a) Vsample = −400 mV, Iset = 800pA, Vexc = 5 mV; (b) Vsample = −300 mV, Iset = 600 pA, Vexc = 4 mV; (c) Vsample = −200 mV, Iset = 400 pA, Vexc = 4 mV; (d) Vsample = −100 mV, Iset = 200 pA, Vexc = 4 mV; (e) Vsample = −50 mV, Iset = 100 pA, Vexc = 4 mV; (f) Vsample = 200 mV, Iset = 400 pA, Vexc = 4 mV; (m) Vsample = 10 mV, Iset = 100 pA, Vexc = 1 mV; T = 4.5 K.

Extended Data Fig. 4 Identification of additional peaks in the Fourier transform linecut along the charge stripe direction.

Fourier transform linecut of L(r, V) maps along the q4a0-CO (charge stripe) direction at 4.5 K (same as Fig. 3g). The green dashed lines are visual guides showing the most prominent additional non-dispersive peaks. Green arrows denote all the satellite peaks we observe, approximately equally spaced from the dominant peaks. The black, blue and brown arrows indicate the dominant peaks: the low-frequency peak (qlow) likely associated with the satellite peaks, unidirectional charge order peak (q4a0-CO) and tri-directional charge order peak (q2a0-CO), respectively. STM setup condition: Vsample = 100 mV, Iset = 600pA, Vexc = 4 mV, T = 4.5 K.

Extended Data Fig. 5 Data reproducibility across different CsV3Sb5 single crystals.

(a-c) STM topographs acquired over different CsV3Sb5 samples. (d,e) Differential conductance (dI/dV(r, V)) maps obtained on sample #1 and #3, respectively. Panels (f-j) are the corresponding Fourier transforms of the images above. STM setup condition: (a) Vsample = −20 mV, Iset = 20 pA; (b) Vsample = 300 mV, Iset = 90 pA; (c) Vsample = −40 mV, Iset = 110 pA; (d) Vsample = −4 mV, Iset = 50 pA, Vexc = 1 mV; (e) Vsample = 4 mV, Iset = 40 pA, Vexc = 1 mV.

Extended Data Fig. 6 Bias dependence of STM topographs.

(a-d) STM topographs acquired over an identical region at 60 K under different biases. (e-h) STM topographs acquired over another region at 4.5 K under different biases. Insets in (a-h) are the associated Fourier transforms. Green, brown and blue circles denote the atomic Bragg peaks, tri-directional charge order peaks and unidirectional stripe charge order peaks in momentum-transfer space, respectively. STM setup condition: (a) Vsample = 90 mV, Iset = 30 pA; (b) Vsample = 50 mV, Iset = 30 pA; (c) Vsample = −30 mV, Iset = 40 pA; (d) Vsample = −90 mV, Iset = 40 pA; (e) Vsample = 200 mV, Iset = 400 pA; (f) Vsample = 50 mV, Iset = 100 pA; (g) Vsample = 10 mV, Iset = 20 pA; (h) Vsample = −50 mV, Iset = 100 pA.

Extended Data Fig. 7 Density functional theory (DFT) calculation of the electronic band structure.

(a) DFT calculated band structure of CsV3Sb5 along high symmetry directions across the Brillouin zone, visualized by SUMO (Supplementary Section 1). The blue and red colors represent the contributions from Sb and V orbitals, respectively. (b) Schematic of different high-symmetry points.

Extended Data Fig. 8 Energy dependence of the quasiparticle interference (QPI) near Fermi level.

(a-g) Two-fold symmetrized Fourier transforms (FTs) of differential conductance (dI/dV(r, V)) maps acquired over the same field-of-view on an Sb-terminated surface of sample 1. The dispersive QPI stripes are denoted by magenta (along qa) and blue (along qb,c) rectangles. At bias lower than 12 mV, the stripe features along qa are clearly visible (solid magenta rectangles), while the equivalent features along qb and qc are absent (dashed blue rectangles). The trend is reversed at a bias higher than 12 mV. Green circles denote the atomic Bragg peaks. For visual purposes, noise streaks in (c-e) along ~45 degree direction with respect to the horizontal are removed by subtracting a polynomial from each row of the raw dI/dV map before the map is rotated, FT is performed and the FT is two-fold symmetrized. (h,i) Linecuts in FTs of dI/dV(r, V) maps as a function of bias along the magenta and blue dashed lines in (d). Orange curves in (h,i) are visual guides showing the dispersion of QPI wave vectors. STM setup condition: (a) Vsample = 18 mV, Iset = 90 pA, Vexc = 1 mV; (b) Vsample = 16 mV, Iset = 200 pA, Vexc = 1 mV; (c)Vsample = 14 mV, Iset = 100 pA, Vexc = 1 mV; (d)Vsample = 12 mV, Iset = 90 pA, Vexc = 1 mV; (e)Vsample = 10 mV, Iset = 70 pA, Vexc = 1 mV; (f)Vsample = 5 mV, Iset = 60 pA, Vexc = 1 mV; (g)Vsample = −5 mV, Iset = 60 pA, Vexc = 1 mV; T = 4.5 K.

Extended Data Fig. 9 Additional temperature-dependent STM data.

(a,b) STM topographs of an identical area of the sample at (a) 4.5 K, and (b) 50 K, and (c,d) corresponding spatially-averaged dI/dV spectra. As it can be seen from (b), the 4a0 charge ordering is nearly completely absent at this elevated temperature. The low-temperature dI/dV spectrum in (c) shows two shoulders at ±20 mV (black arrows) and gap-like features closer to Fermi energy around ± 5 to 10 mV (orange arrows). dI/dV spectrum at higher temperature in (d) (just before entering the 4a0-CO state) only shows the broad shoulders at higher energy. (e) Large-scale STM topograph and (f) Fourier transform of simultaneous dI/dV(r, V=−6 mV) map showing the presence of 4a0-CO peak and the absence of QPI (q2 and q’2 enclosed by dashed rectangles) seen at low temperature in Fig. 4 and Fig. S1. STM setup condition: (a-d) Vsample = 50 mV, Iset = 50 pA, Vexc = 1 mV; (e,f) Vsample = −8 mV, Iset = 80 pA, Vexc = 1 mV.

Extended Data Fig. 10 Magnetization and magnetotransport measurements of CsV3Sb5 single crystals.

(a) Temperature (T) dependence of magnetization M = 4πχ (χ is magnetic susceptibility). Zero-field cooled (field cooled at 5 Oe field) magnetization is denoted by a black solid (dashed) line. (b) Angle-dependent magnetotransport measurements, plotting resistivity \(\rho \) along the c-axis as a function of angle \(\theta \), which is the direction of magnetic field H = 14 T applied in the ab-plane, as denoted in the inset. (c) Resistivity anisotropy as a function of temperature, calculated from the three data sets in (b) as \(\delta =\frac{2(\rho (0^\circ )+\rho (180^\circ ))}{\rho (60^\circ )+\rho (120^\circ )+\rho (240^\circ )+\rho (300^\circ )}\).

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Zhao, H., Li, H., Ortiz, B.R. et al. Cascade of correlated electron states in the kagome superconductor CsV3Sb5. Nature 599, 216–221 (2021). https://doi.org/10.1038/s41586-021-03946-w

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