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Kagome-nets, appearing in electronic, photonic and cold-atom systems, host frustrated fermionic and bosonic excitations. However, it is rare to find a system to study their fermion–boson many-body interplay. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet, CoSn. We image the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through the self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice bosonic analog of the kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials. Frustrated kagome magnets host both fermionic and bosonic excitations, but evidence of their interplay has been elusive. Here, the authors report a pronounced renormalization of electron bands near the Fermi surface due to the coupling with a flat phonon band in a kagome paramagnet, CoSn.

The nature of the pseudogap phase of hole-doped cuprate superconductors is still not understood fully. Several experiments have suggested that this phase ends at a critical hole doping level p *, but the nature of the ground state for lower doping is still debated. Here, we use local nuclear magnetic resonance and bulk ultrasound measurements to show that, once competing effects from superconductivity are removed by high magnetic fields, the spin-glass phase of La 2− x Sr x CuO 4 survives up to a doping level consistent with p *. In this material, the antiferromagnetic-glass phase extends from the doped Mott insulator at p = 0.02 up to p * ≈ 0.19, which provides a connection between the pseudogap and the physics of the Mott insulator. Furthermore, the coincidence of the pseudogap boundary with a magnetic quantum phase transition in the non-superconducting ground state has implications for the interpretation of other experiments, particularly for transport and specific-heat measurements in high magnetic fields. NMR and ultrasound measurements show that the spin-glass phase exists in a cuprate all the way up to the doping that marks the end of the pseudogap phase. This highlights the possible connection between the pseudogap and Mott physics.

Symmetry plays an important role in determining the physical properties in condensed matter physics, as the symmetry operations of any physical property must include the symmetry operations of the point group of the crystal. As a consequence, crystallographic polarity and chirality are expected to have an impact on the Cooper pairing in a superconductor. While superconductivity with crystallographic polarity and chirality have both been found in a few crystalline phases separately; however, their coexistence and material realizations have not been studied. Here, by utilizing transport, Raman scattering, and transmission electron microscopy, we unveil a unique realization of superconductivity in single-crystalline Mo 3 Al 2 C (superconducting T c =8 K) with a polar charge-density-wave phase and well-defined crystallographic chirality. We show that the intriguing charge density wave order leads to a noncentrosymmetric-nonpolar to polar transition below T *=155K via breaking both the translational and rotational symmetries. Superconductivity emerges in this polar and chiral crystal structure below T c =8 K. Our results establish that Mo 3 Al 2 C is a superconductor with crystallographic polarity and chirality simultaneously, and motivate future studies of unconventional superconductivity in this category. The coexistence of crystallographic polarity and chirality is rare in a superconductor. Here, the authors establish that Mo 3 Al 2 C is a superconductor with crystallographic polarity and chirality simultaneously.

SignificanceThe family of iron selenide (FeSe) superconductors is of great interest because it harbors an unusual nonmagnetic nematic state, exhibits a peculiar orbital-selective Cooper pairing, and has a strong potential for high-temperature superconductivity. Here, for FeSe1−xSx nonmagnetic metal, we report discovery of a pseudogap in the spectra of electronic long-wavelength charge quadrupole excitation below the nematic phase transition with temperature dependence of the gap’s magnitude reminiscent of a nematic order parameter. We argue that the intense continuum of excitations in the high-temperature phase with tetragonal symmetry arises due to non-Fermi liquid dynamics governed by Pomeranchuk fluctuations and that these fluctuations are suppressed in the symmetry-broken orthorhombic low-temperature phase, enabling the recovery of Fermi liquid properties. We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic FeSe1−xSx superconductor. We observe two types of long-wavelength XY symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at TS(x), a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the XY symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward TS(x). The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration xcr≈0.16, while the pseudogap size decreases with the suppression of TS(x). We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

The family of iron selenide (FeSe) superconductors is of great interest because it harbors an unusual nonmagnetic nematic state, exhibits a peculiar orbital-selective Cooper pairing, and has a strong potential for high-temperature superconductivity. Here, for F e S e 1 − x S x nonmagnetic metal, we report discovery of a pseudogap in the spectra of electronic long-wavelength charge quadrupole excitation below the nematic phase transition with temperature dependence of the gap’s magnitude reminiscent of a nematic order parameter. We argue that the intense continuum of excitations in the high-temperature phase with tetragonal symmetry arises due to non-Fermi liquid dynamics governed by Pomeranchuk fluctuations and that these fluctuations are suppressed in the symmetry-broken orthorhombic low-temperature phase, enabling the recovery of Fermi liquid properties. We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic F e S e 1 − x S x superconductor. We observe two types of long-wavelength X Y symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at T S ( x ) , a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the X Y symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward T S ( x ) . The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration x c r ≈ 0.16 , while the pseudogap size decreases with the suppression of T S ( x ) . We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic FeSe1–x Sₓ superconductor. We observe two types of long-wavelength XY symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at TS (x), a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the XY symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward TS (x). The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration xcr ≈ 0.16, while the pseudogap size decreases with the suppression of TS (x). We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic [Formula: see text] superconductor. We observe two types of long-wavelength [Formula: see text] symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at [Formula: see text], a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the [Formula: see text] symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward [Formula: see text] The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration [Formula: see text], while the pseudogap size decreases with the suppression of [Formula: see text] We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic [Formula: see text] superconductor. We observe two types of long-wavelength [Formula: see text] symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at [Formula: see text], a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the [Formula: see text] symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward [Formula: see text] The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration [Formula: see text], while the pseudogap size decreases with the suppression of [Formula: see text] We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

Symmetry plays an important role in determining the physical properties in condensed matter physics, as the symmetry operations of any physical property must include the symmetry operations of the point group of the crystal. As a consequence, crystallographic polarity and chirality are expected to have an impact on the Cooper pairing in a superconductor. While superconductivity with crystallographic polarity and chirality have both been found in a few crystalline phases separately; however, their coexistence and material realizations have not been studied. Here, by utilizing transport, Raman scattering, and transmission electron microscopy, we unveil a unique realization of superconductivity in single-crystalline Mo3Al2C (superconducting Tc=8K) with a polar charge-density-wave phase and well-defined crystallographic chirality. We show that the intriguing charge density wave order leads to a noncentrosymmetric-nonpolar to polar transition below T*=155K via breaking both the translational and rotational symmetries. Superconductivity emerges in this polar and chiral crystal structure below Tc=8K. Our results establish that Mo3Al2C is a superconductor with crystallographic polarity and chirality simultaneously, and motivate future studies of unconventional superconductivity in this category.

We employ polarization-resolved Raman spectroscopy combined with first-principles calculations to study the sodium-ion lattice dynamics in a sodium zig-zag ordered cobaltate compound Na\\(_0.5\\)CoO\\(_2\\). We detect two sodium phonon modes for the first time, and their mode frequencies are consistent with first-principles phonon calculations based on an orthorhombic unit cell. We find that they appear below around \\(T^*30050\\)K with large linewidth broadening, much lower than the sodium zig-zag ordering temperature \\(T_S460\\)K, and then narrow at lower temperatures. We interpret the sodium-phonon anomalies occurring at \\(T^*\\) as a dynamical-to-static crossover involving mainly the motion of sodium ions. Our results suggest that the gradual freezing of the sodium ions and the well-defined static sodium-zigzag order below \\(T^*\\) set the stage for the emergent electronic and magnetic orders in the CoO\\(_2\\) layer of Na\\(_0.5\\)CoO\\(_2\\).