X-ray scattering reveals phonon softening in kagome metal

A topological material is defined by its electronic structure, which exhibits characteristics resembling knots or twists that cannot be untangled without breaking or changing the fundamental nature of the material. One notable feature is flat bands – that is, flat in momentum space, yet arising from the strong localisation of electrons in real space. This type of topology holds particular fascination as it is considered as a route to enhancing electron-correlation effects and engineering emergent phases of matter with rich, many-body physics, such as unconventional superconductivity, metal–insulator transitions, density-wave instabilities and quantum spin liquids.

Recently, charge-density waves (CDWs) have been observed in the geometrically frustrated kagome lattice [1]. This geometry, which resembles the overlapping triangles and hexagons of Japanese kagome basket-weaving, features topological electron flat bands both at, below and above the Fermi level. CDWs, magnetism, and superconducting phases are believed to be – depending on the electron number – the result of flat bands, multiple Dirac crossings, or so-called van Hove singularities close to the Fermi level. In the kagome AV₃Sb₅ (where A=Cs, Rb, K) and FeGe metals, which have phase diagrams populated with van Hove singularities and Dirac crossings, “multi-Q” CDWs highlight a complex interplay between CDWs, magnetism, and superconductivity. However, despite these findings, the hallmark of the CDW phase transition, a phonon’s ‘softening’ or collapsing to zero frequency, has never been observed, leaving the microscopic origin of the CDWs still unresolved [2]. This phonon softening is obscured by a dynamical disorder of the kagome plane, which usually precludes the emergence of superconductivity and other coexisting or competing instabilities in the Fermi surface.

Click image to enlarge

Fig. 1: a) Side view of the ScV₆Sn₆ kagome structure. Green and gold balls denote V atoms that define the kagome net and Sc, respectively. Blue and cyan denote the trigonal Sn (Sn^T) and hexagonal Sn (Sn^H) atoms. b) Top view of the kagome net, highlighting the V and Sn^T atoms. Red dashed lines denote the unit cell. c) Brillouin zone of the space group P6/mmm (191) and the main symmetry directions. d) Vibration mode of the imaginary phonon mode at (1/3 1/3 1/2).

In this work, a series of diffuse and inelastic X-ray scattering (IXS) experiments carried out at beamline ID28 reveal, for the first time, a complete phonon softening in the ScV₆Sn₆ (166) kagome lattice (Figure 1) [3]. The spectroscopic measurements show that the low-energy longitudinal phonon with propagation vector (1/3 1/3 1/2) collapses at 98 K, without the direct emergence of a CDW. Instead, a CDW arises sets in with a propagation vector (1/3 1/3 1/3). Despite propagating with a different vector, this CDW is driven by the phonon softening in an overdamped flat plane at k_z=π, characterised by an out-of-plane vibration of the trigonal Sn atoms. These phonon anomalies point to the existence of approximately flat phonon bands, slightly dispersed due to electron renormalisation, and emphasise the effects of momentum-dependent electron-phonon interaction in the CDW formation (Figure 2).

Click image to enlarge

Fig. 2: a) h k 6.5 plane at 300 K (top) and 100 K (bottom), showing the diffuse precursor of the 3D CDW at l = 1/2 that grows in intensity upon cooling. b) h h l map, where no precursor is visible at l = 1/3 at high temperature, but at l = 1/2. The diffuse signal is replaced by the CDW Bragg satellites at low temperature, (right panels). c) Normalised temperature dependence of the IXS spectra at the (1/3 1/3 13/2) r.l.u. position. d) IXS scans as a function of temperature at the (1/3 1/3 19/3) r.l.u. position. e) Momentum dependence of the (1/3 1/3 13/2) phonon frequency at selected temperatures, highlighting the large momentum softening.

Theory corroborates this experimental finding, indicating that the weak leading-order phonon instability is located at the wave vector (1/3 1/3 1/2) of a rather flat collapsed mode. In particular, analytical calculations of the renormalisation of the phonon frequency to zero from high temperatures relate it to a peak in the orbital-resolved susceptibility of the trigonal Sn atoms. These calculations align well with ab initio results and experimental findings, elucidating the origin of the approximately flat phonon dispersion. Further calculations demonstrate that a weak peak at the experimentally observed CDW wave vector emerges in the orbital-resolved charge susceptibility, attributable to both of the p_z orbitals of the trigonal Sn. Notably, both the soft phonon modes at (1/3 1/3 1/2) and the peak in the charge susceptibility at (1/3 1/3 1/2) appear to originate from the trigonal Sn, forming a series of effectively one-dimensional chains along the z-direction and yielding quasi-flat soft phonon modes in the k_z=π plane.

This is the first reported experimental example of the collapse of a kagome flat phonon plane, and promotes the 166 compounds of the kagome family as primary candidates to explore the physics of correlated flat phonons and topologically flat electrons.

Principal publication and authors
Softening of a flat phonon mode in the kagome ScV₆Sn₆, A. Korshunov (a), H. Hu (b) , D. Subires (b), Y. Jiang (c,d), D. Călugăru (e), X. Feng (b,f), A. Rajapitamahuni (g), C. Yi (f), S. Roychowdhury (f), M.G. Vergniory (b,f), J. Strempfer (h), C. Shekhar (f), E. Vescovo (g), D. Chernyshov (i), A.H. Said (h), A. Bosak (a), C. Felser (f), B. Andrei Bernevig (b,e), S. Blanco-Canosa (b,j), Nat. Commun. 14, 6646 (2023); https://doi.org/10.1038/s41467-023-42186-6
(a) ESRF
(b) Donostia International Physics Center (DIPC), San Sebastián (Spain)
(c) Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing (China)
(d) University of Chinese Academy of Sciences, Beijing (China)
(e) Department of Physics, Princeton University, Princeton, New Jersey (USA)
(f) Max Planck Institute for Chemical Physics of Solids, Dresden (Germany)
(g) National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York (USA)
(h) Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois (USA)
(i) Swiss-Norwegian Beamlines, ESRF
(j) IKERBASQUE, Basque Foundation for Science, Bilbao (Spain)

References
[1] B.R. Ortiz et al., Phys. Rev. Mater. 5, 034801 (2021).
[2] H. Miao et al., Nat. Commun. 14, 6183 (2023).
[3] H.W.S. Arachchige et al., Phys. Rev. Lett. 129, 216402 (2022).