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An account is given of the main steps that led the research group in Rome, to which the author belongs, to the formulation of the charge-density-wave scenario for high- T c superconducting cuprates. The early finding of the generic tendency of strongly correlated electron systems with short range interactions to undergo electron phase separation was subsequently contrasted with the homogenizing effect of the long-range Coulomb interaction. The two effects can find a compromise in the formation of incommensurate charge density waves. These charge density waves are inherently dynamical and are overdamped as a consequence of the possibility to decay in electron-hole pairs, yet tend to maintain a (quantum) critical character, which is mirrored in their marked momentum and frequency dependence and in their strong variation with temperature and doping. These dynamical incommensurate charge density waves act as mediators of pairing lading to high- T c superconductivity, and provide the scattering mechanism that produces the observed violation of the Fermi-liquid paradigm in the metallic phase.

The universality of the strange metal phase in many quantum materials is often attributed to the presence of a quantum critical point (QCP), a zero-temperature phase transition ruled by quantum fluctuations. In cuprates, where superconductivity hinders direct QCP observation, indirect evidence comes from the identification of fluctuations compatible with the strange metal phase. Here we show that the recently discovered charge density fluctuations (CDF) possess the right properties to be associated to a quantum phase transition. Using resonant x-ray scattering, we studied the CDF in two families of cuprate superconductors across a wide doping range (up to p  = 0.22). At p * ≈ 0.19, the putative QCP, the CDF intensity peaks, and the characteristic energy Δ is minimum, marking a wedge-shaped region in the phase diagram indicative of a quantum critical behavior, albeit with anomalies. These findings strengthen the role of charge order in explaining strange metal phenomenology and provide insights into high-temperature superconductivity. It has been suggested that the strange metal phase in cuprates stems from a quantum critical point slightly above optimal doping. By resonant x-ray scattering in two cuprate families in a wide doping range, Arpaia et al. show that charge density fluctuations could be associated with this quantum critical point.

Increasing experimental evidence suggests the occurrence of filamentary superconductivity in different (quasi) two-dimensional physical systems. In this piece of work, we discuss the proposal that under certain circumstances, this occurrence may be related to the competition with a phase characterized by charge ordering in the form of charge-density waves. We provide a brief summary of experimental evidence supporting our argument in two paradigmatic classes of materials, namely transition metal dichalcogenides and cuprates superconductors. We present a simple Ginzburg–Landau two-order-parameters model as a starting point to address the study of such competition. We finally discuss the outcomes of a more sophisticated model, already presented in the literature and encoding the presence of impurities, and how it can be further improved in order to really address the interplay between charge-density waves and superconductivity and the possible occurrence of filamentary superconductivity at the domain walls between different charge-ordered regions.

Inspired by the phenomenology of high-critical-temperature superconducting cuprates, we investigate the effect of an anisotropic scattering rate on the magnetoresistance of a metal, relying on Chambers’ solution to the Boltzmann equation. We find that if the scattering rate is enhanced near points of the Fermi surface with a locally higher density of states, an extended regime is found where the magnetoresistance varies linearly with the magnetic field. We then apply our results to fit the experimental magnetoresistance of La1.6−xNd0.4SrxCuO4 and speculate about the possible source of anisotropic scattering.

Recently, the quest for high-Tc superconductors has evolved from the trial-and-error methodology to the growth of nanostructured artificial high-Tc superlattices (AHTSs) with tailor-made superconducting functional properties by quantum design. Here, we report the growth by molecular beam epitaxy (MBE) of a superlattice of Mott insulator metal interfaces (MIMIs) made of nanoscale superconducting layers of quantum confined-space charge in the Mott insulator La2CuO4 (LCO), with thickness L intercalated by normal metal La1.55Sr0.45CuO4 (LSCO) with period d. The critical temperature shows the superconducting dome with Tc as a function of the geometrical parameter L/d showing the maximum at the magic ratio L/d = 2/3 where the Fano–Feshbach resonance enhances the superconducting critical temperature. The normal state transport data of the samples at the top of the superconducting dome exhibit Planckian T-linear resistivity. For L/d > 2/3 and L/d < 2/3, the heterostructures show a resistance following Kondo universal scaling predicted by the numerical renormalization group theory for MIMI nanoscale heterostructures. We show that the Kondo temperature, TK, and the Kondo scattering amplitude, R0K, vanish at L/d = 2/3, while TK and R0K increase at both sides of the superconducting dome, indicating that the T-linear resistance regime competes with the Kondo proximity effect in the normal phase of MIMIs.

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. Fermi-liquid theory has been used to successfully describe the behaviour of metals for decades but there are a number of instances where expected behaviour is violated, such as for high-temperature superconductors. Here, the authors identify parameters which could be responsible for the strange metal behaviour and establish how this affects resistivity and specific heat measurements.

Solid 4He may acquire superfluid characteristics due to the frustration of the solid phase at grain boundaries. Here, introducing a negative-U generalized Hubbard model and a coarse-grained semiclassical pseudospin model, we show that an analogous effect occurs in systems with competition among charge-density-waves (CDW) and superconductivity in the presence of disorder, as cuprate or dichalcogenide superconductors. The CDW breaks apart in domains with topologically protected filamentary superconductivity at the interfaces. Our transport measurements, carried out in underdoped La2−xSrxCuO4, with the magnetic field acting as a control parameter, are shown to be in excellent agreement with our theoretical prediction. Assuming superconductivity and CDW phases have similar energies, at intermediate temperatures, the magnetic field drives the system from a fluctuating superconductor to a CDW as expected in the clean limit. Lowering the temperature, the expected clean quantum critical point is avoided and a filamentary phase appears, analogous to 'glassy' supersolid phenomena in 4He. The transition line ends at a second quantum critical point at high-fields. Within our scenario, the filamentary superconducting phase is parasitic with CDW and bulk superconducting phases playing the role of primary competing order parameters.

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. The strange metallic state of cuprates occurring in a broad region of their phase diagram outside the superconducting and pseudogapped regions remains a mystery. Here the authors consider the charge density fluctuations recently discovered in resonant X-ray experiments as a possible source of scattering and show that these fluctuations can account for the strange metallic behavior.

We discuss how the interaction of electrons with an overdamped optical phonon can give rise to a strange-metal behavior over extended temperature and frequency ranges. Although the mode has a finite frequency, an increasing damping shifts spectral weight to progressively lower energies so that despite the ultimate Fermi liquid character of the system at the lowest temperatures and frequencies, the transport and optical properties of the electron system mimic a marginal Fermi liquid behavior. Within this shrinking Fermi liquid scenario, we extensively investigate the electron self-energy in all frequency and temperature ranges, emphasizing similarities and differences with respect to the marginal Fermi liquid scenario.

We study one-dimensional structures that may be formed at the LaAlO 3 /SrTiO 3 oxide interface by suitable top gating. These structures are modeled via a single-band model with Rashba spin-orbit coupling, superconductivity and a magnetic field along the one-dimensional chain. We first discuss the conditions for the occurrence of a topological superconducting phase and the related formation of Majorana fermions at the chain endpoints, highlighting a close similarity between this model and the Kitaev model, which also reflects in a similar condition the formation of a topological phase. Solving the model in real space, we also study the spatial extension of the wave function of the Majorana fermions and how this increases with approaching the limit condition for the topological state. Using a scattering matrix formalism, we investigate the stability of the Majorana fermions in the presence of disorder and discuss the evolution of the topological phase with increasing disorder.