Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{Rb}$, Cs)

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Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors ${A V}_{3} {Sb}_{5}$ ( $A = Rb$ , Cs)

Haoxiang Li, T. T. Zhang, T. Yilmaz, Y. Y. Pai, C. E. Marvinney, A. Said, Q. W. Yin, C. S. Gong, Z. J. Tu, E. Vescovo, C. S. Nelson, R. G. Moore, S. Murakami, H. C. Lei, H. N. Lee, B. J. Lawrie, and H. Miao

Phys. Rev. X 11, 031050 – Published 3 September 2021

Abstract

The combination of nontrivial band topology and symmetry-breaking phases gives rise to novel quantum states and phenomena such as topological superconductivity, quantum anomalous Hall effect, and axion electrodynamics. Evidence of intertwined charge density wave (CDW) and superconducting order parameters has recently been observed in a novel kagome material ${A V}_{3} {Sb}_{5}$ ( $A = K$ , Rb, Cs) that features a $Z_{2}$ topological invariant in the electronic structure. However, the origin of the CDW and its intricate interplay with the topological state has yet to be determined. Here, using hard-x-ray scattering, we demonstrate a three-dimensional CDW with $2 \times 2 \times 2$ superstructure in $(Rb, Cs) V_{3} {Sb}_{5}$ . Unexpectedly, we find that the CDW fails to induce acoustic phonon anomalies at the CDW wave vector but yields a novel Raman mode that quickly damps into a broad continuum below the CDW transition temperature. Our observations exclude strong electron-phonon-coupling-driven CDW in ${A V}_{3} {Sb}_{5}$ and support an unconventional CDW that was proposed in the kagome lattice at van Hove filling.

Received 24 March 2021
Revised 15 May 2021
Accepted 1 July 2021

DOI:https://doi.org/10.1103/PhysRevX.11.031050

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Charge density waves

Kagome lattice Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Haoxiang Li ¹, T. T. Zhang ^2,3, T. Yilmaz⁴, Y. Y. Pai ¹, C. E. Marvinney¹, A. Said⁵, Q. W. Yin⁶, C. S. Gong⁶, Z. J. Tu⁶, E. Vescovo⁴, C. S. Nelson⁴, R. G. Moore ¹, S. Murakami ^2,3, H. C. Lei^6,*, H. N. Lee ¹, B. J. Lawrie ¹, and H. Miao ^1,†

¹Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Department of Physics, Tokyo Institute of Technology, Okayama, Meguro-ku, Tokyo 152-8551, Japan
³Tokodai Institute for Element Strategy, Tokyo Institute of Technology, Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8503, Japan
⁴National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
⁵Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁶Department of Physics and Beijing Key Laboratory of Opto-Electronic Functional Materials and Micro-devices, Renmin University of China, Beijing, China

^*hlei@ruc.edu.cn
^†miaoh@ornl.gov

Popular Summary

In quantum materials, the electronic wave functions can propagate through different paths that are defined by the underlying lattice. When the lattice structure is geometrically frustrated, such as the kagome lattice, the electronic wave functions interfere, giving rise to novel quantum states of matter. Recently, a spatial periodic charge modulation, known as a charge-density wave, was discovered in a kagome metal, triggering extensive debate on the origin of the density wave and its interplay with the kagome lattice. Here, we examine the charge-density wave in that kagome metal by uncovering its electronic excitations and its interactions with collective lattice motions. Our results suggest an unconventional and electronic-driven charge-density wave in this system.

We use state-of-the-art x-ray techniques to establish a 3D charge-density wave that fails to induce acoustic phonon anomalies but yields a novel Raman continuum, supporting gapped charge-density wave excitations. Combining this observation with angle-resolved photoemission spectroscopy and first-principles calculations, we reveal two particle-hole scattering channels in the electronic band structure that are intimately related to the 3D charge-density wave.

Our results provide a vital characterization of the intertwined electronic and lattice state, from which an unconventional density wave and superconductivity can emerge.

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Vol. 11, Iss. 3 — July - September 2021

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Condensed Matter Physics

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Figure 1
The crystal structure of ${A V}_{3} {Sb}_{5}$ and CDW-induced phonon anomalies. (a) shows the crystal structure of ${A V}_{3} {Sb}_{5}$ (space group $P 6 / mmm$ , no. 191), which consists of V-Sb slabs that are separated by alkali elements. The V-Sb slab contains a V-kagome lattice and two Sb sites laying in the kagome plane and above the V triangle. (b) shows the 3D BZ and high-symmetry points of ${A V}_{3} {Sb}_{5}$ . (c) and (d) show the valence and core electron density in the normal and CDW phase, respectively. Because of EPC, the core electrons will follow the CDW period and yield acoustic phonon anomalies. (e) Nesting-induced Kohn anomalies. (f) Strong-coupling-induced phonon softening in an extended momentum space near $Q_{CDW}$ . Red, yellow, green, blue, and purple colors represent temperatures from $T ≫ T_{CDW}$ to $T < T_{CDW}$ . The phonon hardening for $T < T_{CDW}$ is due to the CDW amplitude mode.
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Figure 2
3D CDW determined by meV-resolution XRD. (a),(b) The temperature-dependent CDW peaks of ${RbV}_{3} {Sb}_{5}$ at $Q = (3.5, 0, 0)$ and (3.5, 0, 0.5). The CDW peak at half-integer $L$ demonstrates a 3D CDW with $2 \times 2 \times 2$ superstructure. The CDW peaks are extremely sharp along $L$ , with HWHM of approximately 0.0025 r.l.u. at $T = 98 K$ . (c) and (d) show the extracted temperature-dependent CDW peak intensity at $Q = (3.5, 0, 0)$ and (3.5,0,0.5), respectively. The peak intensity takes a sharp upturn at the CDW onset temperature of 103 K for ${RbV}_{3} {Sb}_{5}$ , which is consistent with the specific heat measurement (see Appendix pp1). The absence of hysteresis is consistent with a second-order phase transition. CDW peaks in ${CsV}_{3} {Sb}_{5}$ are shown in (e) and (f). The peak intensity at $Q = (3, 0.5, 0)$ is over 10 times larger than the one at $Q = (3.5, 0, 0)$ [panel (e)], consistent with larger structure factors at $Q = (H, K + 0.5, 0)$ , $H = odd integer$ [8]. The absence of peaks at $Q = (3, 0, 0.5)$ , (3.5, 0.5, 0), (3.5, 0, 0.25) confirms the same $2 \times 2 \times 2$ superstructure in ${CsV}_{3} {Sb}_{5}$ . The error bars in panels (a),(b),(e),(f) represent 1 standard deviation assuming Poisson counting statistics. The error bars in panels (c) and (d) denote the $2 σ$ returned from the pseudo-Voigt fittings that extract the peak intensity.
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Figure 3
Evidence of unconventional electronically driven CDW. (a) compares the IXS determined LA of ${RbV}_{3} {Sb}_{5}$ along $Γ (3, 0, 0)$ to $M (3.5, 0, 0)$ at temperatures of $T = 300 K$ and 50 K ( $T_{CDW} = 103 K$ ). (b) Extracted-temperature-dependent phonon dispersions from (a). (c) TA in ${RbV}_{3} {Sb}_{5}$ measured along $Γ (3, 3, 0)$ to $M (3.5, 2.5, 0)$ at room temperature (300 K). (d) and (e) compare temperature-dependent IXS spectra at $Q = (3.47, 0, 0)$ and (3.5,2.5,0). The dashed lines in (d) and (e) highlight LA and TA, respectively. All IXS data are Bose-factor corrected, and the elastic contribution at $ω = 0$ is subtracted by fitting the IXS raw data (see Supplemental Material [31]). (f),(g) Temperature-dependent Raman spectra on ${CsV}_{3} {Sb}_{5}$ from 150 to 3 K. Beside the sharp optical phonon peak at 11, 15, and 17 meV, there is a continuum that is broadly centered near 19 meV (the 11-meV peak may actually be at lower energy but appears to be at 11 meV due to the cutoff of the longpass filter at 11 meV). The black dots in (f) mark the peak positions of the continuum near 19 meV. When cooling toward $T_{CDW}$ , the center of this continuum gradually shifts from 19.5 to 19 meV and starts to build a strong, sharp, and asymmetric peak at $T_{CDW} = 94 K$ . Moving to lower temperature, this peak is quickly damped and hardened to 20 meV at 30 K. Below 30 K, two new phonon modes at 25.4 and 27.5 meV are observed, which may correspond to the stripe phase observed by a recent STM study [16]. The error bars in panels (d),(e) represent 1 standard deviation assuming Poisson counting statistics. The error bars in panel (b) denote the $2 σ$ returned from the fitting that extracts the spectral peak position.
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Figure 4
3D-CDW-induced band inversion. (a) and (b) show Fermi-surface maps measured at photon energies of $h ν = 100$ and 90 eV corresponding to $k_{z} = π$ and $0.15 π$ around the $\bar{M}$ point, respectively. Data are taken at $T = 15 K$ . The blue lines in (a) and (b) mark the high-symmetry cuts shown in (c) and (d), respectively. The inner potential is extracted to be around 8.2 eV (see Supplemental Material [31]). (c) and (d) selectively enhance the electron band near the unfolded $L$ point and the hole band near the unfolded $M$ point. The yellow dots in (c) and (d) are extracted from the MDC peaks shown in (e). The blue dashed line in (d) is a guide to the eye. The blurry spectral weight near the Fermi level in (d) likely comes from the bulk projected surface state [8]. (e) and (f) show stacking plots of MDCs to further reveal the electron and hole bands in panels (c) and (d). (g) shows the electronic band structure of ${RbV}_{3} {Sb}_{5}$ calculated by vasp [45, 46, 47] after a full relaxation on atomic positions with an atom pairwise-correction method (DFT-D3) [48] since the van der Waals forces play an important role along the $c$ -layer stacking direction. The Fermi energy is shifted by 100 meV in order to match the experimental results. There is a hole pocket in the vicinity of the $M$ point ( $Γ − M$ direction) carrying a parity of “ $+$ ” and an electron pocket in the vicinity of the $L$ point carrying a parity of “ $-$ ” contributed by different bands. Our DFT result confirms the parity distribution of the band structure that is reported to possess a nontrivial $Z_{2}$ topological invariant and induce topological surface states around the $M$ point [8].
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Figure 5
(a) and (b) show transport and specific heat measurement of ${RbV}_{3} {Sb}_{5}$ (red) and ${CsV}_{3} {Sb}_{5}$ (blue).
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Figure 6
(a) schematically shows commensurate (yellow) and incommensurate (cyan) CDW periods with respect to the lattice (red). (b) Yellow and cyan curves are the calculated phase modes for CCDW and ICCDW, respectively. (c) shows the CDW mechanism without electron-acoustic phonon interaction. The temperature-dependent particle-hole excitations are shown as red, yellow, and blue curves. The dashed line show the LA mode, whose energy at $q_{CDW}$ is less than $ω_{ϕ}$ . Shaded pink area indicates the momentum position of the Raman measurement.
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Physical Review X

Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors AV3Sb5 (A=Rb, Cs)

Haoxiang Li, T. T. Zhang, T. Yilmaz, Y. Y. Pai, C. E. Marvinney, A. Said, Q. W. Yin, C. S. Gong, Z. J. Tu, E. Vescovo, C. S. Nelson, R. G. Moore, S. Murakami, H. C. Lei, H. N. Lee, B. J. Lawrie, and H. Miao

Phys. Rev. X 11, 031050 – Published 3 September 2021

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Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors ${A V}_{3} {Sb}_{5}$ ( $A = Rb$ , Cs)