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Unidirectional coherent quasiparticles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors

Nature Physics volume 19, pages 637–643 (2023)Cite this article

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Abstract

Kagome metals AV3Sb51 (where the A can stand for K, Cs or Rb) display a rich phase diagram of correlated electron states, including superconductivity2,3,4 and density waves5,6,7. Within this landscape, recent experiments have revealed signs of a transition below approximately 35 K attributed to an electronic nematic phase that spontaneously breaks the rotational symmetry of the lattice8. Here we show that the rotational symmetry breaking initiates universally at a high temperature in these materials, towards the 2 × 2 charge density wave transition temperature. We do this via spectroscopic-imaging scanning tunnelling microscopy and study the atomic-scale signatures of the electronic symmetry breaking across several materials in the AV3Sb5 family: CsV3Sb5, KV3Sb5 and Sn-doped CsV3Sb5. Below a substantially lower temperature of about 30 K, we measure the quantum interference of quasiparticles, a key signature for the formation of a coherent electronic state. These quasiparticles display a pronounced unidirectional feature in reciprocal space that strengthens as the superconducting state is approached. Our experiments reveal that high-temperature rotation symmetry breaking and the charge ordering states are separated from the superconducting ground state by an intermediate-temperature regime with coherent unidirectional quasiparticles. This picture is phenomenologically different compared to that in high-temperature superconductors, shedding light on the complex nature of rotation symmetry breaking in AV3Sb5 kagome superconductors.

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Fig. 1: Low-temperature electronic state of CsV3Sb5.
Fig. 2: High-temperature rotation symmetry breaking before the condensation of the 4a0 charge stripe order.
Fig. 3: Universality of the high-temperature C2-symmetric signature across different members of the AV3Sb5 family.
Fig. 4: Emergence of quasi-1D electron scattering below intermediate temperature of about 30 K.

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Data availability

The data used for analysis can be found at https://doi.org/10.5281/zenodo.7388403. All other 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 L. Balents, R. Fernandes, L. Wu and R. Comin for their insightful conversations. I.Z. gratefully acknowledges the support from grant no. NSF-DMR 2216080. S.D.W. and B.R.O. acknowledge support from the UC Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i program under award no. DMR-1906325. Z.W. acknowledges the support of the US Department of Energy, Basic Energy Sciences grant no. DE-FG02-99ER45747 and the Cottrell SEED award no. 27856 from the Research Corporation for Science Advancement.

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Authors and Affiliations

  1. Department of Physics, Boston College, Chestnut Hill, MA, USA

    Hong Li, He Zhao, Ziqiang Wang & Ilija Zeljkovic

  2. Materials Department, University of California Santa Barbara, Santa Barbara, CA, USA

    Brenden R. Ortiz, Yuzki Oey & Stephen D. Wilson

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  1. Hong Li
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Contributions

The STM experiments and data analysis were performed by H.L. and H.Z. under the supervision of I.Z. B.R.O. and Y.O. synthesized and characterized the samples under the supervision of S.D.W. Z.W. provided theoretical input. H.L., H.Z., S.D.W., Z.W. and I.Z. wrote the paper, with input from all authors. I.Z. supervised the project.

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Correspondence to Ilija Zeljkovic.

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Nature Physics thanks Rahul Nandkishore and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 The comparison of electron scattering on the Sb-terminated and full Cs-terminated surface of CsV3Sb4.98Sn0.02.

(a) STM topograph of the full Cs termination. (b) STM topograph of the Sb-terminated surface. (c,d) dI/dV(r, V) maps taken over regions in (a, b), respectively, and (e,f) associated Fourier transforms (FTs) of (c, d). Both C2-symmetric scattering arising from portions of the V bands (q2) and the scattering from Sb pocket near Γ (q1) are apparent on the Sb surface in (f); however only q1 related to the Sb pocket is seen on the full Cs surface in (e). This suggests that Vanadium kagome bands are difficult to detect on the Cs termination. (g, h) FTs of dI/dV(r, V) maps taken on (g) Cs and (h) Sb surface with bias settings V of: 2 mV, 0 mV, −2 mV and −5 mV. No C2-symmetric scattering can be seen at these other energies near Fermi level on the Cs surface, thus further signaling the difficulty of detecting the V bands on Cs termination. STM setup conditions: (a, c, e, g): Vsample = 30 mV, Vexc = 1 mV, Iset = 300 pA; (b, d, f, h): Vsample = 20 mV, Vexc = 1 mV, Iset = 400 pA.

Extended Data Fig. 2 Constant energy contour auto-correlation.

(a) The schematic of the Fermi surface of CsV3Sb5. Thick blue lines denote portions of the V bands that primarily contribute to the unidirectional features in QPI data. (b) Auto-correlation of (a), with a larger spectral weight allotted to the thick blue lines in (a). (c) FT of dI/dV(r, V = −6 mV) map on the Sb surface of CsV3Sb5 showing qualitative similarity to the auto-correlation in (b). STM setup conditions: (c) Vsample = −6 mV, Vexc = 1 mV, Iset = 80 pA.

Extended Data Fig. 3 Suppression of symmetry breaking in QPI wave vectors at an intermediate temperature of about 30 K in Sn-doped CsV3Sb5.

(a) dI/dV(r, V = −5 mV) map taken over a 45 nm square region of the Sb-terminated surface of CsV3Sb4.98Sn0.02, and (b) associated Fourier transform (FT). Atomic Bragg peaks are enclosed in black circles, while the blue arrows point along the unidirectional electron scattering features. (c) FTs of dI/dV(r, V) maps taken at 10 K, 20 K and 30 K over the same region of the sample in (a,b). (d) Energy-dependent FT linecut shown as a waterfall plot acquired along the red dashed line in (b). Wave vector q2 is detectable within about +/−15 meV around the Fermi level. (e) Temperature-dependent FT linecuts along the red dashed lines in (b,c) normalized by subtracting the average FT ‘baseline’ away from any prominent peaks. We use 0.29 Å−1 average transverse to and 0.04 Å−1 average along the linecut direction to create curves shown in (e). STM setup condition: (a–c) Vsample = −5 mV, Vexc = 1 mV, Iset = 50 pA; (d) Vsample = 20 mV, Vexc = 1 mV, Iset = 400 pA.

Extended Data Fig. 4 Suppression of symmetry breaking QPI wave vectors at an intermediate temperature in KV3Sb5.

(a) dI/dV(r, V = 10 mV) map taken over a 50 nm square region of the Sb-terminated surface of KV3Sb5, and (b) associated two-fold symmetrized Fourier transform (FT). Atomic Bragg peaks are enclosed in black circles, while the blue arrows point along the electron scattering wave vectors q2. Wave vector q2 is detectable within about +/−10 meV around the Fermi level. (c-e) FTs of dI/dV(r, V) maps taken at 15 K, 26 K and 31 K over the same region of the sample as (a, b). (f) Temperature-dependent FT linecuts along the red dashed lines in (b–e), normalized by subtracting the baseline of the linecut, showing the weakening of the QPI features,. Small red dots in (f) are the data and gray lines are the Gaussian fits. We use 0.11 Å−1 average transverse to and 0.025 Å−1 average along the linecut direction to create curves shown in (f). The red and blue down arrows denote the two sides of the q2 wave vector. (g) A schematic phase diagram of KV3Sb5 denoting the onset of each phenomenon in KV3Sb5. (h) Linecut along the red dashed line in (b), showing the dispersive nature of the scattering wave vector q2 in KV3Sb5. (i) 5 K and 31 K linecut along the green dashed lines in (b-e), normalized by subtracting the baseline of the linecut, showing the weakening of the QPI features. (j, k) Amplitude of the two sides of the q2 wave vector (blue and red circles) extracted from linecuts in (f, i), corresponding to the peak heights denoted by red and blue arrows as a function of temperature for KV3Sb5, showing their gradual suppression. Thick gray line in (j, k) is a visual guide portraying this suppression at about 35 K. Error bars in (j, k) represent standard errors of q2 intensity obtained by Gaussian fits to FT linecuts, such as those in panel (f). STM setup conditions: (a–e) Vsample = 10 mV, Vexc = 2 mV, Iset = 50 pA; (h) Vsample = 20 mV, Vexc = 1 mV, Iset = 400 pA.

Extended Data Fig. 5 C2-symmetric electron scattering signature on the Sb surface of KV3Sb5.

(a) A 48 nm square STM topograph of the Sb-terminated surface of KV3Sb5, and (b) dI/dV(r, V = 4 mV) map acquired over the same region. (c) Fourier transform of (b). The six atomic Bragg peaks are circled in black; red arrows denote the C2-symmetric electron scattering. STM setup conditions: (a) Vsample = −20 mV, Iset = 100 pA; (b) Vsample = 20 mV, Vexc = 1 mV, Iset = 400 pA.

Extended Data Fig. 6 Reproducibility of rotation symmetry breaking in another CsV3Sb5 sample.

(a,c) STM topographs of two other Sb surface regions that are more than 10 micrometers away from each other, and their FTs (lower panels). (b,d) FT amplitudes of the three Q2a0 peaks at 55 K for regions in (a, c) as a function of energy. Similarly to the data presented in Fig. 3(a,b) on a different CsV3Sb5 sample, these amplitude dispersions show that the two-fold anisotropy is detected at temperature as high as 55 K, where the 4a0 chare-stripe had been suppressed. (e–h) Additional supporting data set in CV3Sb5 showing a complete suppression of C2-symmetric QPI at around 30 K, similarly to what has been shown in main Fig. 4. (e) A dI/dV(r,V = −6 mV) map taken over a 40 nm square region of CsV3Sb5 at 4.5 K, and (f) its associated FT. (g) FT of a dI/dV map at 30 K showing the complete disappearance of q2 vectors. (h) FT linecuts at 4.5 K and 30 K along the red dashed lines in (f, g), normalized by subtracting the FT background amplitude. For visual purposes, the center vertical line in the FT in (f,g) was suppressed by subtracting the 2nd polynomial fit from each row in the raw dI/dV map. STM setup conditions: (a, c) Vsample = 100 mV, Iset = 100 pA; (e–g) Vsample = −6 mV, Vexc = 2 mV, Iset = 50 pA.

Extended Data Fig. 7 QPI analysis of raw Fourier transforms.

(a, d) Raw Fourier transform (FT) of dI/dV maps in (a) Fig. 4a and (d) Extended Data Fig. 3a at 4.5 K. It is evident that rotation symmetry is broken even before two-fold symmetrizing the data. Black circles enclose the Bragg peaks, and blue circles enclose the 2a0 CDW peaks. (b, e) FT linecut taken along the red dashed lines in (a,d) at different temperatures, normalized by subtracting the average FT background determined for each FT away from any prominent FT peaks. Red and blue arrows in the top panel point to the left and the right side of the q2 scattering wave vector, which are almost the same height. (c,f) Amplitudes of the two sides of the q2 wave vector (blue and red circles) corresponding to the peak heights denoted by red and blue arrows in (b, e) as a function of temperature. The amplitude suppression plotted in (c, f) is nearly identical to that presented in symmetrized data in Fig. 4. We use 0.36 Å−1 average transverse to and 0.02 Å−1 average along the linecut direction to create curves shown in (b); we use 0.29 Å−1 average transverse to and 0.04 Å−1 average along the linecut direction to create curves shown in (e). Error bars in (c, f) represent standard errors obtained by Lorentzian fits to data shown in (b, e). STM setup conditions: (a–c) Vsample = −6 mV, Vexc = 1 mV, Iset = 80 pA; (d, e) Vsample = −5 mV, Vexc = 1 mV, Iset = 50 pA.

Extended Data Fig. 8 Complete suppression of symmetry breaking QPI wave vectors at an intermediate temperature in CsV3Sb4.98Sn0.02.

(a) dI/dV(r, V = −5 mV) map taken over a 40 nm square region of the Sb-terminated surface of CsV3Sb4.98Sn0.02, and (b) associated Fourier transform (FT). Atomic Bragg peaks are enclosed in black circles, while the blue arrows point along the unidirectional electron scattering features. (c) FTs of dI/dV(r, V) maps taken at 15 K, 25 K and 36 K over the same region of the sample in (a, b). (d) Temperature-dependent FT linecuts along the red dashed lines in (b, c) normalized by subtracting the average FT ‘baseline’ away from any prominent peaks. We use 0.29 Å−1 average transverse to and 0.04 Å−1 average along the linecut direction to create curves shown in (d). (e) Amplitudes of the two sides of the q2 wave vector (blue and red circles) corresponding to the peak heights denoted by red and blue arrows in (d). Error bars in (e) represent standard errors obtained by Lorentzian fits to data shown in (d). STM setup condition: (a–c) Vsample = −5 mV, Vexc = 1 mV, Iset = 50 pA.

Extended Data Fig. 9 The suppression of the 4a0 charge stripe order in CsV3Sb4.98Sn0.02.

(a-f) STM topographs taken on the Sb termination of CsV3Sb4.98Sn0.02 at 4.5 K, 15 K, 25 K, 35 K, 45 K and 55 K, respectively. (g) Linecuts taken along Q4a0 direction in Fourier transforms of topographs in (a–f). The Q4a0 ≈ 0.25 QBragg wave vector is gradually suppressed with increased temperature, and it disappears around 55 K. This can also be seen by eye in the 55 K topograph in (f). STM setup conditions: Vsample = 50 mV, Iset = 400 pA.

Extended Data Fig. 10 Raw Fourier transforms (FTs) of representative dI/dV maps in AV3Sb5.

Raw (not symmetrized) FTs corresponding to two-fold symmetrized data presented in (a) Fig. 4b, (b) Extended Data Fig. 3b and (c) Extended Data Fig. 4b. It can be clearly seen that the scattering in all AV3Sb5 samples studied here is intrinsically C2-symmetric. The four pairs of blue arrows in (c) denote the C2 symmetric q2 wave vectors. STM setup conditions: (a) Vsample = −6 mV, Vexc = 1 mV, Iset = 80 pA; (b) Vsample = −5 mV, Vexc = 1 mV, Iset = 50 pA; (c) Vsample = 10 mV, Vexc = 2 mV, Iset = 50 pA.

Supplementary information

Supplementary Information

Supplementary Note 1 and Figs. 1–3.

Source data

Source Data Fig. 1

CDW amplitude dispersion data.

Source Data Fig. 2

CDW amplitude dispersion data.

Source Data Fig. 3

CDW amplitude dispersion data for different materials.

Source Data Fig. 4

Fourier transform linecuts and temperature dependence of QPI.

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Li, H., Zhao, H., Ortiz, B.R. et al. Unidirectional coherent quasiparticles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors. Nat. Phys. 19, 637–643 (2023). https://doi.org/10.1038/s41567-022-01932-1

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