Condensed matter systems have now become a fertile ground to discover emerging topological quasiparticles with symmetry protected modes. While many studies have focused on fermionic excitations, the same conceptual framework can also be applied to bosons yielding new types of topological states. Motivated by Zhang et al.'s recent theoretical prediction of double Weyl phonons in transition metal monosilicides [Phys. Rev. Lett. 120, 016401 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.016401], we directly measure the phonon dispersion in parity-breaking FeSi using inelastic x-ray scattering. By comparing the experimental data with theoretical calculations, we make the first observation of double Weyl points in FeSi, which will be an ideal material to explore emerging bosonic excitations and its topologically nontrivial properties.

Observation of Double Weyl Phonons in Parity-Breaking FeSi

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 AV(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 x 2 x 2 superstructure in (Rb, Cs)V3Sb5. 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 AV(3)Sb(5) and support an unconventional CDW that was proposed in the kagome lattice at van Hove filling.

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

Experiments discover, for the first time, the collective excitations of the stripe ordered charge-density wave in high-temperature cuprate superconductors, shedding light on a 20-year-old mystery about how the high-temperature superconductivity arises.

https://link.aps.org/pdf/10.1103/PhysRevX.9.031042

Formation of Incommensurate Charge Density Waves in Cuprates

Although charge density waves (CDWs) are omnipresent in cuprate high-temperature superconductors, they occur at significantly different wavevectors, confounding efforts to understand their formation mechanism. Here, we use resonant inelastic x-ray scattering to investigate the doping- and temperature-dependent CDW evolution in La2-xBaxCuO4 (x=0.115-0.155). We discovered that the CDW develops in two stages with decreasing temperature. A precursor CDW with quasi-commensurate wavevector emerges first at high-temperature. This doping-independent precursor CDW correlation originates from the CDW phase mode coupled with a phonon and "seeds" the low-temperature CDW with strongly doping dependent wavevector. Our observation reveals the precursor CDW and its phase mode as the building blocks of the highly intertwined electronic ground state in the cuprates.

Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level Here, we investigate underdoped Bi2Sr14La06CuO6+δ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs Comparing to slightly overdoped Bi2Sr18La02CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates

https://www.pnas.org/content/pnas/117/28/16219.full.pdf

Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ.

New experiments find strong evidence for a universal mechanism underlying charge density waves in high-temperature cuprate superconductors, shedding light on a two-decade-old mystery about the electronic state from which high-temperature superconductivity arises.

https://link.aps.org/pdf/10.1103/PhysRevX.8.011008

Incommensurate Phonon Anomaly and the Nature of Charge Density Waves in Cuprates

While charge density wave (CDW) instabilities are ubiquitous to superconducting cuprates, the different ordering wavevectors in various cuprate families have hampered a unified description of the CDW formation mechanism. Here we investigate the temperature dependence of the low energy phonons in the canonical CDW ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$. We discover that the phonon softening wavevector associated with CDW correlations becomes temperature dependent in the high-temperature precursor phase and changes from a wavevector of 0.238 reciprocal space units (r.l.u.) below the ordering transition temperature up to 0.3~r.l.u. at 300~K. This high-temperature behavior shows that "214"-type cuprates can host CDW correlations at a similar wavevector to previously reported CDW correlations in non-"214"-type cuprates such as YBa$_{2}$Cu$_{3}$O$_{6+\delta}$. This indicates that cuprate CDWs may arise from the same underlying instability despite their apparently different low temperature ordering wavevectors.

Incommensurate phonon anomaly and the nature of charge density waves in cuprates

The mixing of orbital and spin character in the wave functions of the $5d$ iridates has led to predictions of strong couplings among their lattice, electronic, and magnetic degrees of freedom. As well as realizing a novel spin-orbit assisted Mott-insulating ground state, the perovskite iridate ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ has strong similarities with the cuprate ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$, which on doping hosts a charge-density wave that appears intimately connected to high-temperature superconductivity. These phenomena can be sensitively probed through momentum-resolved measurements of the lattice dynamics, made possible by $\mathrm{meV}$-resolution inelastic x-ray scattering. Here we report the first such measurements for both parent and electron-doped ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$. We find that the low-energy phonon dispersions and intensities in both compounds are well described by the same nonmagnetic density functional theory calculation. In the parent compound, no changes of the phonons on magnetic ordering are discernible within the experimental resolution, and in the doped compound no anomalies are apparent due to charge-density waves. These measurements extend our knowledge of the lattice properties of (${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{)}_{2}{\mathrm{IrO}}_{4}$ and constrain the couplings of the phonons to magnetic and charge order.

/pdf/momentum-resolved-lattice-dynamics-of-parent-and-electron-3e6yungfd0.pdf

Momentum-resolved lattice dynamics of parent and electron-doped Sr 2 IrO 4

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Incommensurate Phonon Anomaly and the Nature of Charge Density Waves in Cuprates

Incommensurate phonon anomaly and the nature of charge density waves in cuprates

Momentum-resolved lattice dynamics of parent and electron-doped Sr 2 IrO 4