Electronic inhomogeneity appears to be an inherent characteristic of the enigmatic cuprate superconductors. Here we report the observation of charge-density-wave correlations in the model cuprate superconductor HgBa2CuO(4+δ) (T(c)=72 K) via bulk Cu L3-edge-resonant X-ray scattering. At the measured hole-doping level, both the short-range charge modulations and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which these two phenomena are preceded at the higher pseudogap temperature by q=0 magnetic order and the build-up of significant dynamic antiferromagnetic correlations. The magnitude of the charge modulation wave vector is consistent with the size of the electron pocket implied by quantum oscillation and Hall effect measurements for HgBa2CuO(4+δ) and with corresponding results for YBa2Cu3O(6+δ), which indicates that charge-density-wave correlations are universally responsible for the low-temperature quantum oscillation phenomenon.

The kagome lattice based on 3d transition metals is a versatile platform for novel topological phases hosting symmetry-protected electronic excitations and exotic magnetic ground states. However, the paradigmatic states of the idealized two-dimensional (2D) kagome lattice -Dirac fermions and topological flat bands -have not been simultaneously observed, partly owing to the complex stacking structure of the kagome compounds studied to date. Here, we take the approach of examining FeSn, an antiferromagnetic single-layer kagome metal with spatially-decoupled kagome planes. Using polarization-and termination-dependent angleresolved photoemission spectroscopy (ARPES), we detect the momentum-space signatures of coexisting flat bands and Dirac fermions in the vicinity of the Fermi energy. Intriguingly, when complemented with bulk-sensitive de Haas-van Alphen (dHvA) measurements, our data reveal an even richer electronic structure that exhibits robust surface Dirac fermions on specific crystalline terminations. Through band structure calculations and matrix element simulations, we demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals under kagome symmetry, while the surface state realizes a rare example of fully spin-polarized 2D Dirac fermions when combined with spin-layer locking in FeSn. These results highlight FeSn as a prototypical host for the emergent excitations of the kagome lattice. The prospect to harness these excitations for novel topological phases and spintronic devices is a frontier of great promise at the confluence of topology, magnetism, and strongly-correlated electron physics.

Upon introducing charge carriers into the copper-oxygen sheets of the enigmatic lamellar cuprates, the ground state evolves from an insulator to a superconductor and eventually to a seemingly conventional metal (a Fermi liquid). Much has remained elusive about the nature of this evolution and about the peculiar metallic state at intermediate hole-carrier concentrations (p). The planar resistivity of this unconventional metal exhibits a linear temperature dependence (ρ ∝ T) that is disrupted upon cooling toward the superconducting state by the opening of a partial gap (the pseudogap) on the Fermi surface. Here, we first demonstrate for the quintessential compound HgBa 2 CuO 4+δ a dramatic switch from linear to purely quadratic (Fermi liquid-like, ρ ∝ T 2 ) resistive behavior in the pseudogap regime. Despite the considerable variation in crystal structures and disorder among different compounds, our result together with prior work gives insight into the p-T phase diagram and reveals the fundamental resistance per copper-oxygen sheet in both linear (ρ ☐ = A 1☐ T) and quadratic (ρ ☐ = A 2☐ T 2 ) regimes, with A 1☐ ∝ A 2☐ ∝ 1/p. Theoretical models can now be benchmarked against this remarkably simple universal behavior. Deviations from this underlying behavior can be expected to lead to new insight into the nonuniversal features exhibited by certain compounds.

Cuprate high-T c superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near "optimal doping" (with respect to the highest T c s) the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasiparticle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ(ω, T) of a quasi-particle depends on its energy ω as well as on the temperature T. For a Fermi liquid, 1/τ(ω, T) is expected to collapse on a universal function proportional to (h ω) 2 + (pπk B T) 2 . Magnetotransport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T 2 dependence of the dc (ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω-and T dependence of 1/τ(ω, T), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.optical spectroscopy | superconductivity | mass renormalization | self energy T he compound HgBa 2 CuO 4+δ (Hg1201) is the single-layer cuprate that exhibits the highest T c (97 K). We therefore measured the optical conductivity of strongly underdoped single crystals of Hg1201 ðT c = 67 KÞ. Here we are interested in the optical conductivity of the CuO 2 layers. We therefore express the optical conductivity as a 2D sheet conductance GðωÞ = d c σðωÞ, where d c is the interlayer spacing. The real part of the sheet conductance normalized by the conduction quantum G 0 = 2e 2 =h is shown in Fig. 1. As seen in the figure, a gap-like suppression below 140 meV is clearly observable for temperatures below T c and remains visible in the normal state up to ∼250 K. This is a clear optical signature of the pseudogap. We also observe the zero-energy mode due to the free charge carrier response, which progressively narrows upon lowering the temperature. In materials where the charge carrier relaxation is dominated by impurity scattering, the width of this "Drude" peak corresponds to the relaxation rate of the charge carriers. Relaxation processes arising from interactions have the effect of replacing the constant (frequency-independent) relaxation rate with a frequencydependent one. The general expression for the optical conductivity of interacting electrons is then Gðω; TÞ = iπK Zω + Mðω; TÞ G 0 :[1]The spectral weight K corresponds to minus the kinetic energy if the frequency integration of the experimental data is restricted to intraband transitions. The effect of electron-electron interactions and coupling to collective mo...