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1. Softening of a flat phonon mode in the kagome ScV6Sn6

   https://doi.org/10.1038/s41467-023-42186-6  

   Korshunov, A ; Hu, H ; Subires, D ; Jiang, Y ; Călugăru, D ; Feng, X ; Rajapitamahuni, A ; Yi, C ; Roychowdhury, S ; Vergniory, M G ; et al ( December 2023 , Nature Communications)

   Geometrically frustrated kagome lattices are raising as novel platforms to engineer correlated topological electron flat bands that are prominent to electronic instabilities. Here, we demonstrate a phonon softening at thek_z = πplane in ScV₆Sn₆. The low energy longitudinal phonon collapses at ~98 K andq = $$\frac{1}{3}\frac{1}{3}\frac{1}{2}$$$\frac{1}{3}\frac{1}{3}\frac{1}{2}$due to the electron-phonon interaction, without the emergence of long-range charge order which sets in at a different propagation vectorq_CDW = $$\frac{1}{3}\frac{1}{3}\frac{1}{3}$$$\frac{1}{3}\frac{1}{3}\frac{1}{3}$. Theoretical calculations corroborate the experimental finding to indicate that the leading instability is located at$$\frac{1}{3}\frac{1}{3}\frac{1}{2}$$$\frac{1}{3}\frac{1}{3}\frac{1}{2}$of a rather flat mode. We relate the phonon renormalization to the orbital-resolved susceptibility of the trigonal Sn atoms and explain the approximately flat phonon dispersion. Our data report the first example of the collapse of a kagome bosonic mode and promote the 166 compounds of kagomes as primary candidates to explore correlated flat phonon-topological flat electron physics.

    

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2. Phonon mixing in the charge density wave state of ScV6Sn6

   https://doi.org/10.1038/s41535-023-00590-7  

   Gu, Yanhong ; Ritz, Ethan T. ; Meier, William R. ; Blockmon, Avery ; Smith, Kevin ; Madhogaria, Richa Pokharel ; Mozaffari, Shirin ; Mandrus, David ; Birol, Turan ; Musfeldt, Janice L. ( December 2023 , npj Quantum Materials)

   Kagomé metals are widely recognized, versatile platforms for exploring topological properties, unconventional electronic correlations, magnetic frustration, and superconductivity. In theRV₆Sn₆family of materials (R= Sc, Y, Lu), ScV₆Sn₆hosts an unusual charge density wave ground state as well as structural similarities with theAV₃Sb₅system (A= K, Cs, Rb). In this work, we combine Raman scattering spectroscopy with first-principles lattice dynamics calculations to reveal phonon mixing processes in the charge density wave state of ScV₆Sn₆. In the low temperature phase, we find at least four new peaks in the vicinity of the V-containing totally symmetric mode near 240 cm⁻¹suggesting that the density wave acts to mix modes ofP6/mmmand$$R\bar{3}m$$$R\overline{3}m$symmetry - a result that we quantify by projecting phonons of the high symmetry state onto those of the lower symmetry structure. We also test the stability of the short-range ordered density wave state under compression and propose that both physical and chemical pressure quench the effect. We discuss these findings in terms of symmetry and the structure-property trends that can be unraveled in this system.

    

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3. On Some Non-Rigid Unit Distance Patterns

   https://doi.org/10.1007/s00454-023-00503-2  

   Frankl, Nóra ; Woodruff, Dora ( July 2023 , Discrete & Computational Geometry)

   A recent generalization of the Erdős Unit Distance Problem, proposed by Palsson, Senger, and Sheffer, asks for the maximum number of unit distance paths with a given number of vertices in the plane and in 3-space. Studying a variant of this question, we prove sharp bounds on the number of unit distance paths and cycles on the sphere of radius$$1/{\sqrt{2}}$$$1/\sqrt{2}$. We also consider a similar problem about 3-regular unit distance graphs in $$\mathbb {R}^3$$$R^3$.

    

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4. Melting of charge order in the low-temperature state of an electronic ferroelectric-like system

   https://doi.org/10.1038/s41535-020-0217-5  

   Hassan, Nora M. ; Thirunavukkuarasu, Komalavalli ; Lu, Zhengguang ; Smirnov, Dmitry ; Zhilyaeva, Elena I. ; Torunova, Svetlana ; Lyubovskaya, Rimma N. ; Drichko, Natalia ( March 2020 , npj Quantum Materials)

   Strong electronic interactions can drive a system into a state with a symmetry breaking. Lattice frustration or competing interactions tend to prevent symmetry breaking, leading to quantum disordered phases. In spin systems frustration can produce a spin liquid state. Frustration of a charge degree of freedom also can result in various exotic states, however, experimental data on these effects is scarce. In this work we demonstrate how in a Mott insulator on a weakly anisotropic triangular lattice a charge ordered state melts on cooling down to low temperatures. Raman scattering spectroscopy finds that$$\kappa$$$\kappa$-(BEDT-TTF)$${}_{2}$$${}_2$Hg(SCN)$${}_{2}$$${}_2$Cl enters an insulating “dipole solid” state at$$T=30\,{\mathrm{K}}$$$T=30K$, but below$$T=15\,{\mathrm{K}}$$$T=15K$the order melts, while preserving the insulating energy gap. Based on these observations, we suggest a phase diagram relevant to other quantum paraelectric materials.

    

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5. High pressure raman spectroscopy and X-ray diffraction of K2Ca(CO3)2 bütschliite: multiple pressure-induced phase transitions in a double carbonate

   https://doi.org/10.1007/s00269-023-01262-5  

   Zeff, G. ; Kalkan, B. ; Armstrong, K. ; Kunz, M. ; Williams, Q. ( January 2024 , Physics and Chemistry of Minerals)

   The crystal structure and bonding environment of K₂Ca(CO₃)₂bütschliite were probed under isothermal compression via Raman spectroscopy to 95 GPa and single crystal and powder X-ray diffraction to 12 and 68 GPa, respectively. A second order Birch-Murnaghan equation of state fit to the X-ray data yields a bulk modulus,$${K}_{0}=46.9$$$K_0=46.9$GPa with an imposed value of$${K}_{0}^{\prime}= 4$$$K_0^{\prime }=4$for the ambient pressure phase. Compression of bütschliite is highly anisotropic, with contraction along thec-axis accounting for most of the volume change. Bütschliite undergoes a phase transition to a monoclinicC2/mstructure at around 6 GPa, mirroring polymorphism within isostructural borates. A fit to the compression data of the monoclinic phase yields$${V}_{0}=322.2$$$V_0=322.2$ Å³$$,$$$,$$${K}_{0}=24.8$$$K_0=24.8$GPa and$${K}_{0}^{\prime}=4.0$$$K_0^{\prime }=4.0$using a third order fit; the ability to access different compression mechanisms gives rise to a more compressible material than the low-pressure phase. In particular, compression of theC2/mphase involves interlayer displacement and twisting of the [CO₃] units, and an increase in coordination number of the K⁺ion. Three more phase transitions, at ~ 28, 34, and 37 GPa occur based on the Raman spectra and powder diffraction data: these give rise to new [CO₃] bonding environments within the structure.

    

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