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“Strange metals” with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-1=2 fermions interacting via onsite Hubbard interaction and random infinite-ranged spin–spin interaction.We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of SU(M) symmetric models to models with physical SU(2) spin-1/2 electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

High-temperature superconductivity is known to involve the pairing of charge carriers, but the precise nature of these carriers and the mechanism of their pairing remain unclear. The copper oxides are known to exhibit a strong Jahn–Teller effect — in which spontaneous lattice distortions remove the degeneracy of the electronic ground state — and it has been suggested that the charge carriers are Jahn–Teller polarons (bare charge carriers accompanied by local lattice distortions). In fact, the demonstration 1 that a strong Jahn–Teller effect can lead to the formation of such polarons led to the original discovery of high-temperature superconductivity 2 . Still, direct evidence that Jahn–Teller polarons exist in the superconducting state of the copper oxides has been lacking, although some indirect evidence comes from their recent discovery 3 in the structurally similar but non-superconducting manganite La 1– x Ca x MnO 3 . Here we report the results of magnetization and thermal expansion measurements on samples of the copper oxide superconductor La 2– x Sr x CuO 4 which characterize the oxygen-isotope effects on the carrier density and on the in-plane penetration depth. We find a negligible isotope effect on the former, but a large effect on the latter. Specific quantitative features of the results show that polaronic charge carriers exist and condense into Cooper pairs in the copper oxide superconductors.

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 present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.

Cooper’s formalism for the fermionic pairing has been revisited considering up to third-neighbour hopping terms, firstly with a Fermi liquid-like background on a square lattice keeping in mind the overdoped cuprates. Then the whole scheme is repeated with a marginal Fermi liquid-like background, taking into account the self-energy correction of the mobile electrons to include a more realistic density of states in the calculation. A detailed comparison of our theoretical results with those from experiments strongly supports the marginal Fermi liquid-like character of the normal phase with exciton-mediated superconducting pairing in the concerned materials, in the lightly overdoped phase.

When insulating curates are doped with hole carriers, the antiferromagnetic ordering disappears and superconductivity emerges. This superconductivity is caused by the condensed state of the electrons in spin singlet pairs.