We report in-plane resistivity (ρ) and transverse magnetoresistance (MR) measurements in underdoped HgBa2CuO 4+δ (Hg1201). Contrary to the longstanding view that Kohler's rule is strongly violated in underdoped cuprates, we find that it is in fact satisfied in the pseudogap phase of Hg1201. The transverse MR shows a quadratic field dependence, δρ/ρo = aH 2 , with a(T ) ∝ T −4 . In combination with the observed ρ ∝ T 2 dependence, this is consistent with a single Fermi-liquid quasiparticle scattering rate. We show that this behavior is universal, yet typically masked in cuprates with lower structural symmetry or strong disorder effects.The unusual metallic 'normal state' of the cuprates, from which superconductivity evolves upon cooling, has remained an enigma. A number of atypical observations seemingly at odds with the conventional Fermi-liquid theory of metals have been made particularly in the strangemetal regime above the pseudogap (PG) temperature T * (inset of Fig. 1(b)) [1]. In this regime, the in-plane resistivity exhibits an anomalous extended linear temperature dependence, ρ ∝ T [2], and the Hall effect is often described as R H ∝ 1/T [3,4]. In order to account for this anomolous behavior without abandoning a Fermi-liquid formalism, some descriptions have been formulated based on a scattering rate whose magnitude varies around the in-plane Fermi surface, for example due to anisotropic Umklapp scattering or coupling to a bosonic mode [1] (e.g., spin [5] or charge [6] fluctuations). Prominent nonFermi-liquid prescriptions with far-ranging implications for the cuprate phase-diagram, such as the two-lifetime picture [7] and the marginal-Fermi-liquid [8] have also been put forth. The former implies charge-spin separation while the latter is a signature of a proximate quantum critical point.The transport behavior in the PG state (T < T * ) seems to be even less clear. Interpretation of this regime has been complicated not only because of the opening of the PG along portions of the Fermi surface, but also due to possible superconducting [9], antiferromagnetic [5,10], and charge-spin stripe fluctuations [11], which might influence transport properties. Electrical transport for temperatures below T * therefore has been generally described as a deviation from the better-behaved hightemperature behavior [1].Recent developments, however, suggests that T * marks a phase transition [12] into a state with broken timereversal symmetry [13,14]. Additionally, the measurable extent of superconducting fluctuations is likely limited to only a rather small temperature range (≈ 30 K) above T c [15,16]. These strong indications that the PG regime is indeed a distinct phase calls for a clear description of its intrinsic properties. In fact, a simple ρ = A 2 T 2 dependence was recently reported for underdoped HgBa 2 CuO 4+δ (Hg1201) [17]. It was also found that this Fermi-liquid-like behavior universally appears below a characteristic temperature T

Resonant x-ray scattering clarifies the link between charge order and magnetism/superconductivity in n-doped cuprates.

The phase diagram of the cuprate superconductors continues to pose formidable scientific challenges. While these materials are typically viewed as doped Mott insulators, it is well known that they are Fermi liquids at high hole-dopant concentrations. It was recently demonstrated that at moderate doping, in the pseudogap (PG) region of the phase diagram, the charge carriers are also best described as a Fermi liquid. Nevertheless, the relationship between the two Fermi-liquid (FL) regions and the nature of the strange-metal (SM) state at intermediate doping have remained unsolved. Here we show for the case of the model cuprate superconductor HgBa 2 CuO 4+δ that the normal-state transport scattering rate determined from the cotangent of the Hall angle remains quadratic in temperature across the PG temperature, upon entering the SM state, and that it is doping-independent below optimal doping. Analysis of prior transport results for other cuprates reveals that this behavior is universal throughout the entire phase diagram and points to a pervasive FL transport scattering rate. These observations can be reconciled with a variety of other experimental results for the cuprates upon considering the possibility that the PG phenomenon is associated with the gradual, non-uniform localization of one hole per planar CuO 2 unit.

Motivated by recent attention to a potential antiferromagnetic quantum critical point at xc ∼ 0.19, we have used inelastic neutron scattering to investigate the low-energy spin excitations in crystals of La2−xSrxCuO4 bracketing xc. We observe a peak in the normal-state spin-fluctuation weight at ∼ 20 meV for both x = 0.21 and 0.17, inconsistent with quantum critical behavior. The presence of the peak raises the question of whether low-energy spin fluctuations limit the onset of superconducting order. Empirically evaluating the spin gap ∆spin in the superconducting state, we find that ∆spin is equal to the coherent superconducting gap ∆c determined by electronic spectroscopies. To test whether this is a general result for other cuprate families, we have checked through the literature and find that ∆c ≤ ∆spin for cuprates with uniform d-wave superconductivity. We discuss the implications of this result.

Systematic analysis of the planar resistivity, Hall effect and cotangent of the Hall angle for the electron-doped cuprates reveals underlying Fermi-liquid behavior even deep in the antiferromagnetic part of the phase diagram. The transport scattering rate exhibits a quadratic temperature dependence, and is nearly independent of doping, compound and carrier type (electrons vs. holes), and hence universal. Our analysis moreover indicates that the material-specific resistivity upturn at low temperatures and low doping has the same origin in both electron-and hole-doped cuprates.The cuprates feature a complex phase diagram that is asymmetric upon electron-versus hole-doping [1] and plagued by compound-specific features associated with different types of disorder and crystal structures [2], often rendering it difficult to discern universal from nonuniversal properties. What is known for certain is that the parent compounds are antiferromagnetic (AF) insulators, that AF correlations are more robust against doping with electrons than with holes [3,4], and that pseudogap (PG) phenomena, seemingly unusual charge transport behavior, and d-wave superconductivity appear upon doping the quintessential CuO 2 planes [1]. The nature of the metallic state that emerges upon doping the insulating parent compounds has remained a central open question. Moreover, below a compound specific doping level, the low-temperature resistivity for both types of cuprates develops a logarithmic upturn that appears to be related to disorder, yet whose microscopic origin has remained unknown [1,[5][6][7]. In contrast, at high dopant concentrations, the cuprates are good metals with welldefined Fermi surfaces and clear evidence for Fermi-liquid (FL) behavior [8][9][10][11][12][13][14].In a new development, the hole-doped cuprates were found to exhibit FL properties in an extended temperature range below the characteristic temperature T * * (T * * < T * ; T * is the PG temperature): (i) the resistivity per CuO 2 sheet exhibits a universal, quadratic temperature dependence, and is inversely proportional to the doped carrier density p, ρ ∝ T 2 /p [15]; (ii) Kohler's rule for the magnetoresistvity, the characteristic of a conventional metal with a single relaxation rate, is obeyed, with a Fermi-liquid scattering rate, 1/τ ∝ T 2 [16]; (iii) the optical scattering rate exhibits the quadratic frequency dependence and the temperature-frequency scaling expected for a Fermi liquid [17]. In this part of the phase diagram, the Hall coefficient is known to be approximately independent of temperature and to take on a value that corresponds to p, R H ∝ 1/p [18]. In order to explore the possible connection among the different regions of the phase diagram, an important quantity to consider is the cotangent of the Hall angle, cot(θ H ) = ρ/(HR H ). For simple metals, this quantity is proportional to the transport scattering rate, cot(θ H ) ∝ m * /τ (H the magnetic field, and m * the effective mass). It has long been known that cot(θ H ) ∝ T 2 in the "strange-metal" ...