The electrical resistance of two samples of ortho-II ordered YBa 2 Cu 3 O 6.5 was measured in a magnetic field up to 62 T applied normal to the CuO 2 planes (B || c).(Sample characteristics and details of the measurements are given in the Methods section below.) With a T c of 57.5 K, these samples have a hole doping per planar copper atom of p = 0.10, i.e., they are well into the underdoped region of the phase diagram (see Fig. 1a). ARPES data for underdoped Na 2-x Ca x Cu 2 O 2 Cl 2 (Na-CCOC) at precisely the same doping (reproduced in Fig. 1b from ref. 6) shows most of the spectral intensity to be concentrated in a small region near the nodal position (π/2, π/2), suggesting a Fermi surface broken up into disconnected arcs, while ARPES studies on overdoped Tl 2 Ba 2 CuO 6+δ at p = 0.25 reveal a large, continuous cylinder (reproduced in The Hall resistance R xy as a function of magnetic field is displayed in Fig. 2 for sample A, and in Fig. S1 for sample B, where oscillations are clearly seen above the resistive superconducting transition. Note that a vortex liquid phase is believed to extend well above the irreversibility field, beyond our highest field of 62 T, which may explain why R xy is negative at these low temperatures, as opposed to positive at temperatures above T c . Nevertheless, quantum oscillations are known to exhibit the very same diagnostic characteristics of frequency in the vortex state as in the field-induced normal state above H c2 (0) (e.g. ref. 7). They are caused by the passage of quantized Landau levels across the Fermi level as the applied magnetic field is varied, and as such 3 they are considered the most robust and direct signature of a coherent Fermi surface (FS). The inset of Fig. 2 shows the 2-K isotherm and a smooth background curve. We extract the oscillatory component, plotted in Fig. 3a as a function of inverse field, by subtracting the monotonic background (shown for all temperatures in Fig. S2). This shows that the oscillations are periodic in 1/B, as expected of oscillations that arise from Landau quantization. A Fourier transform yields the power spectrum, displayed in Fig. 3b, which consists of a single frequency, F = 530 ± 10 T. In Fig. 3c, we plot the amplitude of the oscillations as a function of temperature, from which we deduce a carrier mass m* = 1.9 ± 0.1 m 0 , where m 0 is the bare electron mass. Within error bars, both F and m* are the same in sample B, for which J || b (see Fig. S1). Oscillations of the same frequency are also observed in R xx (in both samples), albeit with a smaller amplitude. We note that while at 7.5 K the oscillations are still perceptible, they are absent at 11 K, as expected from thermally damped quantum oscillations (see Fig. S5).While quantum oscillations in YBa 2 Cu 3 O 6+y (YBCO) have been the subject of a number of earlier studies 8 , 9 , 10 , the data reported so far do not exhibit clear oscillations as a function of 1/B and, as such, have not been accepted as convincing evidence for a Fermi surface 11 . Furthermore, we note that a...

We have measured the Nernst coefficient ν(T) of the high-T c superconductor YBa 2 Cu 3 O y (YBCO) as a function of temperature up to ~ 300 K for a hole concentration 13 (doping) ranging from p = 0.08 to p = 0.18, in untwinned crystals where the temperature gradient ΔT was applied along either the a-axis or the b-axis of the orthorhombic plane. In Fig. 1, a typical data set is seen to consist of two contributions:1) a positive, strongly field-dependent contribution due to superconducting fluctuations 14,15,16 ; 2) a field-independent contribution due to normal-state quasiparticles 17 , which drops from small and positive to large and negative with decreasing temperature. We define as T ν the temperature below which ν / T starts its downward drop. In Fig. 2, we plot T ν as a function of doping. We also plot T ρ , the temperature below which the in-plane resistivity ρ(T) of YBCO deviates downward from its linear temperature dependence at high temperature, a standard definition of the pseudogap temperature T* (refs. 18, 19). We see that T ν = T ρ , within error bars, as also found in a recent study on YBCO films 20 . We also see that T ν obtained with ΔT || a is the same as T ν obtained with ΔT || b, within error bars. We therefore conclude that the drop in the quasiparticle Nernst signal to large negative values is a signature of the pseudogap phase, detectable up to the highest measured doping, p = 0.18.In Fig. 3, we see that the dip in ν / T between T c and T ν gets deeper with decreasing p as the separation between T c and T ν grows (Fig. 2). This characteristic dip is hugely anisotropic, being roughly 10 times deeper when ΔT || b. In Fig. S6, the Nernst anisotropy is plotted as a ratio, seen to reach ν b / ν a ≈ 7 at 90 K for p = 0.12. To our knowledge, this is the largest in-plane anisotropy reported in any macroscopic physical property of any high-T c superconductor 12 . In Fig. 4a, a plot of the anisotropy differenceshowing that it is a property of the pseudogap phase, since T ν = T*. In Fig. 4b, we plot the difference normalized by the sum S(T) ≡ -(ν a + ν b ) / T; this relative anisotropy,, can be viewed as a Nernst-derived nematic order parameter, in analogy with that defined from the resistivity 21 .In the orthorhombic crystal structure of YBCO, there are CuO chains along the b-axis, between the CuO 2 planes common to all cuprates. These one-dimensional chains can conduct charge, causing an anisotropy in the conductivity σ such that σ b / σ a > 1.In principle these chains could also cause an anisotropy in ν, but we next show that the chains make a negligible contribution to ν. We first consider the low doping regime at p = 0.08 (y = 6.45), for which the anisotropy ratio of both σ and ν is displayed in Fig. S6a. As established previously 5 , the conductivity of chains decreases with decreasing p until it becomes negligible by p ≈ 0.08, as shown by the fact that σ b / σ a ≈ 1 at high temperature. In that context of negligible chain conduction, a small rise in the anisotropy ratio σ b / σ a with decreasing ...

High-temperature superconductivity in copper oxides occurs when the materials are chemically tuned to have a carrier concentration intermediate between their metallic state at high doping and their insulating state at zero doping. The underlying evolution of the electron system in the absence of superconductivity is still unclear, and a question of central importance is whether it involves any intermediate phase with broken symmetry. The Fermi surface of the electronic states in the underdoped 'YBCO' materials YBa2Cu3O(y) and YBa2Cu4O8 was recently shown to include small pockets, in contrast with the large cylinder that characterizes the overdoped regime, pointing to a topological change in the Fermi surface. Here we report the observation of a negative Hall resistance in the magnetic-field-induced normal state of YBa2Cu3O(y) and YBa2Cu4O8, which reveals that these pockets are electron-like rather than hole-like. We propose that these electron pockets most probably arise from a reconstruction of the Fermi surface caused by the onset of a density-wave phase, as is thought to occur in the electron-doped copper oxides near the onset of antiferromagnetic order. Comparison with materials of the La2CuO4 family that exhibit spin/charge density-wave order suggests that a Fermi surface reconstruction also occurs in those materials, pointing to a generic property of high-transition-temperature (T(c)) superconductors.

The pseudogap is a partial gap in the electronic density of states that opens in the normal (non-superconducting) state of cuprate superconductors and whose origin is a long-standing puzzle. Its connection to the Mott insulator phase at low doping (hole concentration, p) remains ambiguous and its relation to the charge order that reconstructs the Fermi surface at intermediate doping is still unclear. Here we use measurements of the Hall coefficient in magnetic fields up to 88 tesla to show that Fermi-surface reconstruction by charge order in the cuprate YBa2Cu3Oy ends sharply at a critical doping p = 0.16 that is distinctly lower than the pseudogap critical point p* = 0.19 (ref. 11). This shows that the pseudogap and charge order are separate phenomena. We find that the change in carrier density n from n = 1 + p in the conventional metal at high doping (ref. 12) to n = p at low doping (ref. 13) starts at the pseudogap critical point. This shows that the pseudogap and the antiferromagnetic Mott insulator are linked.

The Hall coefficient RH of the cuprate superconductor YBa2Cu3Oy was measured in magnetic fields up to 60 T for a hole concentration p from 0.078 to 0.152, in the underdoped regime. In fields large enough to suppress superconductivity, RH(T ) is seen to go from positive at high temperature to negative at low temperature, for p > 0.08. This change of sign is attributed to the emergence of an electron pocket in the Fermi surface at low temperature. At p < 0.08, the normal-state RH(T ) remains positive at all temperatures, increasing monotonically as T → 0. We attribute the change of behaviour across p = 0.08 to a Lifshitz transition, namely a change in Fermi-surface topology occurring at a critical concentration pL = 0.08, where the electron pocket vanishes. The loss of the high-mobility electron pocket across pL coincides with a ten-fold drop in the conductivity at low temperature, revealed in measurements of the electrical resistivity ρ at high fields, showing that the so-called metal-insulator crossover of cuprates is in fact driven by a Lifshitz transition. It also coincides with a jump in the in-plane anisotropy of ρ, showing that without its electron pocket the Fermi surface must have strong two-fold in-plane anisotropy. These findings are consistent with a Fermi-surface reconstruction caused by a unidirectional spin-density wave or stripe order. PACS numbers:arXiv:1009.2078v2 [cond-mat.supr-con]

The perfectly linear temperature dependence of the electrical resistivity observed as T → 0 in a variety of metals close to a quantum critical point 1,2,3,4 is a major puzzle of condensed matter physics 5 . Here we show that T-linear resistivity as T → 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bi-layer cuprate Bi2Sr2CaCu2O8+δ and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi2Sr2CuO6+δ (ref. 6), La1.6-xNd0.4SrxCuO4 (ref. 7) and La2-xSrxCuO4 (ref. 8), despite their very different Fermi surfaces and structural, superconducting and magnetic properties.We then show that the T-linear coefficient (per CuO2 plane), A1 ☐ , is given by the universal relation A1 ☐ TF = h / 2e 2 , where e is the electron charge, h is the Planck constant and TF is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1 / τ of charge carriers reaches the Planckian limit 9,10 , whereby ħ / τ = kB T, works not only for hole-doped cuprates 6,7,8,11,12 but also for electrondoped cuprates 13,14 , despite the different nature of their quantum critical point and strength of their electron correlations.

A fundamental question for high-temperature superconductors is the nature of the pseudogap phase, which lies between the Mott insulator at zero doping and the Fermi liquid at high doping p (refs 1,2). Here we report on the behaviour of charge carriers near the zero-temperature onset of this phase, namely at the critical doping p *

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