The pseudogap region of the phase diagram is an important unsolved puzzle in the field of high-transition-temperature (high-T(c)) superconductivity, characterized by anomalous physical properties. There are open questions about the number of distinct phases and the possible presence of a quantum-critical point underneath the superconducting dome. The picture has remained unclear because there has not been conclusive evidence for a new type of order. Neutron scattering measurements for YBa(2)Cu(3)O(6+delta) (YBCO) resulted in contradictory claims of no and weak magnetic order, and the interpretation of muon spin relaxation measurements on YBCO and of circularly polarized photoemission experiments on Bi(2)Sr(2)CaCu(2)O(8+delta)(refs 12, 13) has been controversial. Here we use polarized neutron diffraction to demonstrate for the model superconductor HgBa(2)CuO(4+delta) (Hg1201) that the characteristic temperature T* marks the onset of an unusual magnetic order. Together with recent results for YBCO, this observation constitutes a demonstration of the universal existence of such a state. The findings appear to rule out theories that regard T* as a crossover temperature rather than a phase transition temperature. Instead, they are consistent with a variant of previously proposed charge-current-loop order that involves apical oxygen orbitals, and with the notion that many of the unusual properties arise from the presence of a quantum-critical point.

Superconductivity involves the formation of electron pairs (Cooper pairs) and their condensation into a macroscopic quantum state. In conventional superconductors, such as Nb 3 Ge and elemental Hg, weakly interacting electrons pair through the electron-phonon interaction. In contrast, unconventional superconductivity occurs in correlated-electron materials in which electronic interactions are significant and the pairing mechanism may not be phononic. In the cuprates, the superconductivity arises on doping charge carriers into the copperoxygen layers of antiferromagnetic Mott insulators . Here we demonstrate the existence of a universal linear relation, E r ∝ 2∆, between the magnetic resonance energy (E r ) and the superconducting pairing gap (∆), which spans two orders of magnitude in energy. This relationship is valid for the three different classes of unconventional superconductors, which range from being close to the Mott-insulating limit to being on the border of itinerant magnetism. As the common excitonic picture of the resonance has not led to such universality, our observation suggests a much deeper connection between antiferromagnetic fluctuations and unconventional superconductivity.The resonance is a widely discussed feature in the magnetic excitation spectrum of the cuprates. It is a collective mode at a well-defined energy that appears in the superconducting (SC) state at the two-dimensional antiferromagnetic wavevector (π/a, π/a; refs 4, 5). Early inelastic neutron scattering experiments for YBa 2 Cu 3 O 6+δ (YBCO) revealed a single resonance mode. However, the crystal structure of YBCO contains two nearby Cu-O layers per unit cell, and later experiments revealed at higher energy an even-parity resonance that differs from the previously observed odd-parity mode in its symmetry with respect to the exchange of the two layers 9-11 . The resonance is also observed in neutron scattering measurements of other hole-doped cuprates: For the cuprates, the mode energy E r of the resonance is commonly compared with the superconducting transition temperature T c . Figure 1 shows that the linear correlation E r = 5-6k B T c is approximately satisfied for the odd-parity mode of the double-layer compounds YBCO and Bi2212, for the resonance in Tl2201 and even for the characteristic energy of the (momentum-integrated) local susceptibility in La 2−x Sr x CuO 4 (LSCO; refs 19,20), in which no resonance occurs at (π/a, π/a). However, recent experiments reveal a violation of the proportionality between E r and T c for single-layer Hg1201 (ref. 15) and for electron-doped NCCO (ref. 17). Furthermore, below optimal doping (hole concentration p < 0.16), the odd and even resonance energies of the double-layer compounds differ significantly. The average of the two is considerably larger than 6 k B T c for the most underdoped YBCO samples in which both modes have been studied 11,21 (Fig. 1). The characteristic energy scale of superconductivity is the SC gap ∆ in the low-energy single-particle response. As seen from Fig. 2, our...

The interactions that lead to the emergence of superconductivity in iron-based materials remain a subject of debate. It has been suggested that electron-electron correlations enhance electron-phonon coupling in iron selenide (FeSe) and related pnictides, but direct experimental verification has been lacking. Here we show that the electron-phonon coupling strength in FeSe can be quantified by combining two time-domain experiments into a "coherent lock-in" measurement in the terahertz regime. X-ray diffraction tracks the light-induced femtosecond coherent lattice motion at a single phonon frequency, and photoemission monitors the subsequent coherent changes in the electronic band structure. Comparison with theory reveals a strong enhancement of the coupling strength in FeSe owing to correlation effects. Given that the electron-phonon coupling affects superconductivity exponentially, this enhancement highlights the importance of the cooperative interplay between electron-electron and electron-phonon interactions.

An approach to microwave measurements is used in order to determine both, the in-plane and out-of-plane conductivity of the high-T c superconductor HgBa 2 CuO 4+␦ near optimal doping. Unlike the ab-plane conductivity, the c-axis conductivity is highly sensitive to superconducting fluctuations. From a single c-axis data set, we can clearly discern the opening of the pseudogap at T ‫ء‬ = 185͑15͒ K, the appearance of the superconducting fluctuations at a much lower temperature TЈ = 105͑2͒ K, and the full transition to the superconducting state at the critical temperature T c = 94.3 K. Thus, with the present high sensitivity, we establish that the extent of the superconducting fluctuations is only about 10 K above T c .

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Inelastic neutron-scattering measurements of single-CuO 2 -layer HgBa 2 CuO 4+␦ reveal an antiferromagnetic resonance with energy r =56 meV ͑Ϸ6.8k B T c ͒ below the superconducting transition temperature T c Ϸ 96 K. The resonance is energy-resolution limited and exhibits an intrinsic momentum width of about 0.2 Å −1 , consistent with prior work on several other cuprates. The rather large value of r is identical to the characteristic energy of the electron-boson spectral density obtained from recent optical conductivity work, consistent with the notion that the charge carriers are strongly coupled to magnetic fluctuations.

It is well known that the superconducting transition temperature (T(c)) of cuprate superconductors can be enhanced by varying certain structural and electronic parameters, such as the flatness of the CuO₂ planes or their doping level. We determine the uniaxial and hydrostatic pressure derivatives of T(c) in the structurally simple tetragonal compound HgBa₂CuO(4+δ) near optimal doping. Our results provide experimental evidence for two further methods to enhance T(c): (i) reducing the area of the CuO₂ planes, and (ii) increasing the separation of the CuO₂ planar groups. T(c) is found to couple much more strongly to the ratio c/a of the lattice constants than to the unit cell volume. A comparison with prior results for structurally more complicated cuprates reveals a general trend of uniaxial pressure derivatives with T(c).

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