[Paper Review] Softening of a flat phonon mode in the kagome ScV$_6$Sn$_6$

A. N. Korshunov, H. Hu+17 more|arXiv (Cornell University)|Apr 18, 2023

Quantum, superfluid, helium dynamics4 citations

TL;DR

This study reports the first experimental observation of a softening flat phonon mode in the kagome metal ScV6Sn6, where a longitudinal phonon at wavevector H = (1/3, 1/3, 1/2) collapses at 98 K without long-range charge order. The instability is driven by electron-phonon coupling to out-of-plane vibrations of trigonal Sn atoms, with ab initio and analytical models confirming a weak leading-order instability at k_z = π, linking flat phonon dispersion to orbital-resolved susceptibility peaks.

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$_z$=$π$. 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.

Motivation & Objective

• To identify the microscopic origin of charge density wave (CDW) formation in the kagome metal ScV6Sn6, where electronic flat bands and van Hove singularities are expected to play a role.
• To resolve the long-standing puzzle of why CDWs form despite the absence of a clear phonon instability in the lattice.
• To determine whether flat phonon modes—previously theoretical—can drive CDW formation via electron-phonon coupling.
• To establish a connection between the collapse of a flat phonon mode and the emergence of CDW order with a different wavevector.
• To validate the role of orbital-resolved electron susceptibility and momentum-dependent electron-phonon coupling in stabilizing the soft mode.

Proposed method

• Inelastic x-ray scattering (IXS) at ESRF and APS to measure low-energy phonon dispersions with high energy (1.5–3 meV) and momentum resolution.
• Diffuse x-ray scattering at ESRF to probe short-range correlations and detect incipient CDW fluctuations.
• Angle-resolved photoemission spectroscopy (ARPES) at NSLS-II to map the electronic band structure and locate Γ and A points in the Brillouin zone.
• Resonant hard x-ray scattering at APS to detect charge order wavevectors and confirm the CDW propagation vector (1/3, 1/3, 1/3).
• Ab initio calculations using VASP with GGA-PBE and Wannier function construction via Wannier90 to model electronic and phononic bands.
• Analytical effective models incorporating electron-phonon coupling and inter-unit-cell coupling along the z-direction to explain the flatness and softening of the mode at k_z = π.

Experimental results

Research questions

• RQ1 What causes the softening of a flat phonon mode in ScV6Sn6, and how is it related to the observed CDW order?
• RQ2 Why does the CDW order appear at (1/3, 1/3, 1/3) when the soft mode occurs at (1/3, 1/3, 1/2)?
• RQ3 How do electron-phonon interactions and orbital-specific susceptibility contribute to the formation of a flat, overdamped phonon mode?
• RQ4 What is the role of inter-unit-cell coupling in stabilizing a flat phonon dispersion at k_z = π?
• RQ5 Can ab initio and analytical models reproduce the observed phonon softening and explain the absence of long-range charge order at the soft mode wavevector?

Key findings

• A longitudinal phonon mode at wavevector H = (1/3, 1/3, 1/2) collapses at 98 K, signaling a soft mode without long-range charge order.
• The soft mode is associated with out-of-plane vibrations of trigonal Sn atoms and exhibits a flat dispersion at k_z = π, with strong damping due to electron-phonon coupling.
• The CDW order with propagation vector (1/3, 1/3, 1/3) is driven by the same electron-phonon coupling but locks at a different wavevector due to momentum-dependent interactions.
• Orbital-resolved susceptibility peaks in the mirror-even d-orbital channel (c_{R,e,σ}) correlate strongly with the phonon softening, explaining the flatness and instability.
• Ab initio calculations confirm a weak leading-order phonon instability at (1/3, 1/3, 1/2), consistent with experimental observations and analytical modeling.
• The phonon spectrum is best described as weakly coupled 1D chains along z, with electron-phonon coupling renormalizing the mode and stabilizing the soft mode at k_z = π.