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Recent quantum oscillation measurements in high-temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here, we explain the observations with the theory that the alleged normal state exhibits a hidden order, the d-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle π/2, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but we also touch on the consequences if the order were to incommensurate. It is shown that whereas commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets.

The extreme variability of observables across the phase diagram of the cuprate high-temperature superconductors has remained a profound mystery, with no convincing explanation for the superconducting dome. Although much attention has been paid to the underdoped regime of the hole-doped cuprates because of its proximity to a complex Mott insulating phase, little attention has been paid to the overdoped regime. Experiments are beginning to reveal that the phenomenology of the overdoped regime is just as puzzling. For example, the electrons appear to form a Landau Fermi liquid, but this interpretation is problematic; any trace of Mott phenomena, as signified by incommensurate antiferromagnetic fluctuations, is absent, and the uniform spin susceptibility shows a ferromagnetic upturn. Here, we show and justify that many of these puzzles can be resolved if we assume that competing ferromagnetic fluctuations are simultaneously present with superconductivity, and the termination of the superconducting dome in the overdoped regime marks a quantum critical point beyond which there should be a genuine ferromagnetic phase at zero temperature. We propose experiments and make predictions to test our theory and suggest that an effort must be mounted to elucidate the nature of the overdoped regime, if the problem of high-temperature superconductivity is to be solved. Our approach places competing order as the root of the complexity of the cuprate phase diagram.

We consider quantum oscillation experiments in YBa ₂Cu ₃O ₆₊δ from the perspective of Fermi surface reconstruction using an exact transfer matrix method and the Pichard–Landauer formula for the conductivity. The specific density wave order responsible for reconstruction is a period-8 d -density wave in which the current density is unidirectionally modulated, which is also naturally accompanied by a period-4 charge order, consistent with recent nuclear magnetic resonance experiments. This scenario leads to a natural explanation as to why only oscillations from a single electron pocket of a frequency of about 500 T is observed, and a hole pocket of roughly twice the frequency as dictated by the twofold commensurate order and the Luttinger sum rule is not observed. In contrast period-8 d -density wave leads to a hole pocket of roughly half the frequency of the electron pocket. The observation of this slower frequency will require higher, but not unrealistic, magnetic fields than those commonly employed. There is already some suggestion of the slower frequency in a measurement in fields as high as 85 T.

A remarkable mystery of the copper oxide high-transition-temperature ( T c ) superconductors is the dependence of T c on the number of CuO 2 layers, n , in the unit cell of a crystal. In a given family of these superconductors, T c rises with the number of layers, reaching a peak at n = 3, and then declines 1 : the result is a bell-shaped curve. Despite the ubiquity of this phenomenon, it is still poorly understood and attention has instead been mainly focused on the properties of a single CuO 2 plane. Here we show that the quantum tunnelling of Cooper pairs between the layers 2 simply and naturally explains the experimental results, when combined with the recently quantified charge imbalance of the layers 3 and the latest notion of a competing order 4 , 5 , 6 , 7 , 8 , 9 nucleated by this charge imbalance that suppresses superconductivity. We calculate the bell-shaped curve and show that, if materials can be engineered so as to minimize the charge imbalance as n increases, T c can be raised further.

A combination of positively and negatively charged current carriers may provide a key to understanding cuprate superconductors.

A quantitative analysis of a recent model of high-temperature superconductors based on an interlayer tunneling mechanism is presented. This model can account well for the observed magnitudes of the high transition temperatures in these materials and implies a gap that does not change sign, can be substantially anisotropic, and has the same symmetry as the crystal. The experimental consequences explored so far are consistent with the observations.

At quantum critical points (QCPs) quantum fluctuations exist on all length scales, from microscopic to macroscopic, which, remarkably, can be observed at finite temperatures—the regime to which all experiments are necessarily confined. But how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? We answer these questions by examining exact solutions of models of systems with strong electronic correlations and find that QCPs can influence physical properties at surprisingly high temperatures. As a powerful illustration of quantum criticality, we predict that the zero-temperature superfluid density, ρ s (0), and the transition temperature, T c , of the high-temperature copper oxide superconductors are related by T c ∝ρ s (0) y , where the exponent y is different at the two edges of the superconducting dome, signifying the presence of the respective QCPs. This relationship can be tested in high-quality crystals.

A theory of the electronic properties of doped fullerenes is proposed in which electronic correlation effects within single fullerene molecules play a central role, and qualitative predictions are made which, if verified, would support this hypothesis. Depending on the effective intrafullerene electron-electron repulsion and the interfullerene hopping amplitudes (which should depend on the dopant species, among other things), the calculations indicate the possibilities of singlet superconductivity and ferromagnetism.

We consider quantum oscillation experiments in YBa 2 Cu 3 O 6+δ from the perspective of Fermi surface reconstruction using an exact transfer matrix method and the Pichard–Landauer formula for the conductivity. The specific density wave order responsible for reconstruction is a period-8 d -density wave in which the current density is unidirectionally modulated, which is also naturally accompanied by a period-4 charge order, consistent with recent nuclear magnetic resonance experiments. This scenario leads to a natural explanation as to why only oscillations from a single electron pocket of a frequency of about 500 T is observed, and a hole pocket of roughly twice the frequency as dictated by the twofold commensurate order and the Luttinger sum rule is not observed. In contrast period-8 d -density wave leads to a hole pocket of roughly half the frequency of the electron pocket. The observation of this slower frequency will require higher, but not unrealistic, magnetic fields than those commonly employed. There is already some suggestion of the slower frequency in a measurement in fields as high as 85 T.