Softening of a flat phonon mode in the kagome ScV${}_6$Sn${}_6$

Abstract

The long range electronic modulations recently discovered in the geometrically frustrated kagome lattice have opened new avenues to explore the effect of correlations in materials with topological electron flat bands. The observation of the lattice response to the emergent new phases of matter, a soft phonon mode, has remained elusive and the microscopic origin of charge density waves (CDWs) is still unknown. Here, we show, for the first time, a complete melting of the ScV${}_6$Sn${}_6$ (166) kagome lattice. The low energy phonon with propagation vector $\frac{1}{3}\frac{1}{3}\frac{1}{2}$ collapses at 98 K, without the emergence of long-range charge order, which sets in with a propagation vector $\frac{1}{3}\frac{1}{3}\frac{1}{3}$. The CDW is driven (but locks at a different vector) by the softening of an overdamped phonon flat plane at k${}_z$=$\pi$. We observe broad phonon anomalies in momentum space, pointing to (1) the existence of approximately flat phonon bands which gain some dispersion due to electron renormalization, and (2) the effects of the momentum dependent electron-phonon interaction in the CDW formation. Ab initio and analytical calculations corroborate the experimental findings to indicate that the weak leading order phonon instability is located at the wave vector $\frac{1}{3}\frac{1}{3}\frac{1}{2}$ of a rather flat collapsed mode. We analytically compute the phonon frequency renormalization from high temperatures to the soft mode, and relate it to a peak in the orbital-resolved susceptibility, obtaining an excellent match with both ab initio and experimental results, and explaining the origin of the approximately flat phonon dispersion. Our data report the first example of the collapse of a softening of a flat phonon plane and promote the 166 compounds of the kagome family as primary candidates to explore correlated flat phonon-topological flat electron physics.

10 pages, 4 figures

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• Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
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• Quantum oscillations revealing topological band in kagome metal ScV6Sn6
• Dynamics and Resilience of the Charge Density Wave in a bilayer kagome metal
• Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals
• Pseudogap behavior in charge density wave kagome material ScV${}_6$Sn${}_6$ revealed by magnetotransport measurements
• Universal sublinear resistivity in vanadium kagome materials hosting charge density waves
• Stability frontiers in the AM${}_6$X${}_6$ kagome metals: The LnNb${}_6$Sn${}_6$ (Ln:Ce-Lu,Y) family and density-wave transition in LuNb${}_6$Sn${}_6$
• Annealing-induced long-range charge density wave order in magnetic kagome FeGe: fluctuations and disordered structure
• Van-Hove annihilation and nematic instability on a Kagome lattice
• Charge order above room-temperature in a prototypical kagome superconductor La(Ru${}_{1-x}$Fe${}_x$)${}_3$Si${}_2$
• FeGe as a building block for the kagome 1:1, 1:6:6, and 1:3:5 families: hidden d-orbital decoupling of flat band sectors, effective models and interaction Hamiltonians
• Kagome metals
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• Phonon collapse and anharmonic melting of the 3D charge-density wave in kagome metals
• Low-Energy Electronic Structure in the Unconventional Charge-Ordered State of ScV${}_6$Sn${}_6$
• Frustrated charge density wave and quasi-long-range bond-orientational order in the magnetic kagome FeGe
• Order-by-disorder charge density wave condensation at $\text{q}=(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ in kagome metal ScV${}_6$Sn${}_6$
• Instability of the charge density wave in Kagome magnet FeGe
• Ground-state magnetic structures of topological kagome metals RV${}_6$Sn${}_6$ (R = Tb, Dy, Ho, Er)
• Quantum Oscillations Evidence for Topological Bands in Kagome Metal ScV6Sn6
• Frustrated Ising charge correlations in the kagome metal ScV${}_6$Sn${}_6$
• Quantum-metric-induced giant and reversible nonreciprocal transport phenomena in chiral loop-current phases of kagome metals
• Origin of competing charge density waves in kagome metal ScV${}_6$Sn${}_6$
• High-order van Hove singularities and nematic instability in the kagome superconductor CsTi${}_3$Bi${}_5$
• Orbital selective commensurate modulations of the local density of states in ScV6Sn6 probed by nuclear spins
• Competing Lattice Instability and Magnetism on the Surface of Kagome Metals
• Discovery of an Intermediate Nematic State in a Bilayer Kagome Metal ScV6Sn6
• Encoding innumerable charge density waves of FeGe into polymorphs of LiFe6Ge6
• Incommensurate and commensurate antiferromagnetic orders in the kagome compound UV${}_6$Sn${}_6$
• Successive orthorhombic distortions in kagome metals by molecular orbital formation
• Interlayer charge transfer induced by electronic instabilities in the natural van der Waals hetrostructure 4H${}_b$-TaS${}_2$
• Origin of the charge density wave state in BaFe${}_2$Al${}_9$
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• Anomalous Nernst Effect and Its Implications for Time-Reversal Symmetry Breaking in Kagome Metal ScV6Sn6
• Beyond kagome: $p$-bands in kagome metals
• Magnetism of kagome metals $\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)\text{Sn}$ studied by $\mu$SR
• Topological electron and phonon flat bands in novel kagome superconductor XPd5 (X=Ca, Sr, Ba)
• Evolution from three-dimensional charge density wave to one-dimensional stripe order in CsV${}_{3-x}$Ti${}_x$Sb${}_5$
• Synergistic doping and stabilization of magnetically tunable LnTi${}_3$(Sb,Sn)${}_4$ (Ln:Ce--Gd) kagome metals
• Electronic and structural properties of Rh- and Pd-based kagome layered shandites from first principles