Recent experiments with strong THz fields in both conventional and unconventional superconductors have clearly evidenced a marked third-harmonic generation below the superconducting temperature $T_c$. Its interpretation challenged substantial theoretical work aimed at establishing the relative efficiency of quasiparticle excitations and collective modes in triggering such a resonant response. Here we compute the nonlinear current by implementing a time-dependent Bogoljubov–de Gennes approach, with the twofold aim to account nonperturbatively for the effect of local disorder, and to include the contribution of all collective modes, i.e., superconducting amplitude (Higgs) and phase fluctuations, and charge fluctuations. We show that, in agreement with previous work, already at small disorder the quasiparticle response is dominated by paramagnetic effects. We further demonstrate that paramagnetic processes mediate also the response of all collective modes, with a substantial contribution of charge/phase fluctuations. These processes, which have been overlooked so far, turn out to dominate the third-order current at strong disorder. In addition, we show that disorder strongly influences the polarization dependence of the nonlinear response, with a marked difference between the clean and the disordered case. Our results are particularly relevant for recent experiments in cuprates, whose band structure is in a first approximation reproduced by our lattice model.

Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broadband THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy $2\mathrm{\Delta }$. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency $\mathrm{\Omega }$ and exhibited a resonant enhancement at temperature when $\mathrm{\Omega }=2\mathrm{\Delta }$. General theoretical considerations show that such a resonance can arise only from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that, even for a small amount of disorder, the $\mathrm{\Omega }=2\mathrm{\Delta }$ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies.

Besides the mechanism responsible for high critical temperature superconductivity, the grand unresolved issue of the cuprates is the occurrence of a strange metallic state above the so-called pseudogap temperature T^*. Even though such state has been successfully described within a phenomenological scheme, the so-called Marginal Fermi-Liquid theory, a microscopic explanation is still missing. However, recent resonant X-ray scattering experiments identified a new class of charge density fluctuations characterized by low characteristic energies and short correlation lengths, which are related to the well-known charge density waves. These fluctuations are present over a wide region of the temperature-vs-doping phase diagram and extend well above T^*. Here we investigate the consequences of charge density fluctuations on the electron and transport properties and find that they can explain the strange metal phenomenology. Therefore, charge density fluctuations are likely the long-sought microscopic mechanism underlying the peculiarities of the metallic state of cuprates.

Restoring strangeness: Cuprate superconductors host a number of complex phases, and elucidating their relationship to each other may shed light on the nature of cuprate superconductivity. Two of these intriguing phases are the strange metal phase and the charge-density wave (CDW) order, which appear next to each other in the cuprate phase diagram. The hallmark of the strange metal phase, the linear dependence of electrical resistivity on temperature, disappears in the CDW phase. Wahlberg et al . strained thin films of the cuprate YBa ₂ Cu ₃ O _7–δ to suppress CDW order (see the Perspective by Le Tacon). Using resonant inelastic x-ray scattering and transport measurements, the researchers found that suppressing CDW restored the linear-in-temperature resistivity in the CDW portion of the phase diagram. —JS

We investigate the formation of partially filled domain walls in the two-dimensional Hubbard model in the presence of a long-range interaction. Using an unrestricted Gutzwiller variational approach we show that (i) the strong local interaction favors charge segregation in stripe domain walls, (ii) the long-range interaction favors the formation of half-filled vertical stripes with a period doubling due to the charge and a period quadrupling due to the spins along the wall. Our results show that, besides the underlying lattice structure, also the electronic interactions can contribute to determine the different domain wall textures observed in Nd-doped copper oxides and nickel oxides.

Anomalous metallic properties are often observed in the proximity of quantum critical points, with violation of the Fermi Liquid paradigm. We propose a scenario where, near the quantum critical point, dynamical fluctuations of the order parameter with finite correlation length mediate a nearly isotropic scattering among the quasiparticles over the entire Fermi surface. This scattering produces a strange metallic behavior, which is extended to the lowest temperatures by an increase of the damping of the fluctuations. We phenomenologically identify one single parameter ruling this increasing damping when the temperature decreases, accounting for both the linear-in-temperature resistivity and the seemingly divergent specific heat observed, e.g., in high-temperature superconducting cuprates and some heavy-fermion metals.