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 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 interplay between superconductivity and any other competing order is an essential part of the long-standing debate on the origin of high temperature superconductivity in cuprates 1,2 . Akin to the situation of heavy fermions, organic superconductors and pnictides, it has been proposed that the pairing mechanism in cuprates comes from fluctuations of a nearby quantum phase transition 3 . Recent evidence of charge modulation 4 and the associated fluctuations 5,6,7 in the pseudogap phase of YBa 2 Cu 3 O y make charge order a likely candidate for a competing order. However, a thermodynamic signature of the charge ordering phase transition is still lacking. Moreover, whether such charge order is one-or two-dimensional is still controversial but pivotal for the understanding the topology of the reconstructed Fermi surface 8,9 . Here we address both issues by 29.H. Yao et al. Fermi-surface reconstruction in a smectic phase of a hightemperature superconductor. Phys. Rev. B 84, 012507 (2011) Acknowledgments We thank M.-H.

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 *

In the quest to increase the critical temperature T c of cuprate superconductors, it is essential to identify the factors that limit the strength of superconductivity. The upper critical field H c2 is a fundamental measure of that strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. Here we show that the thermal conductivity can be used to directly detect H c2 in the cuprates YBa 2 Cu 3 O y , YBa 2 Cu 4 O 8 and Tl 2 Ba 2 CuO 6 þ d , allowing us to map out H c2 across the doping phase diagram. It exhibits two peaks, each located at a critical point where the Fermi surface of YBa 2 Cu 3 O y is known to undergo a transformation. Below the higher critical point, the condensation energy, obtained directly from H c2 , suffers a sudden 20-fold collapse. This reveals that phase competitionassociated with Fermi-surface reconstruction and charge-density-wave order-is a key limiting factor in the superconductivity of cuprates.

We report the observation of Shubnikov-de Haas oscillations in the underdoped cuprate superconductor YBa2Cu4O8 (Y124). For fields aligned along the c axis, the frequency of the oscillations is 660+/-30 T, which corresponds to approximately 2.4% of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be 2.7+/-0.3 times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II YBa2Cu3O6.5 (Y123-II). We show that although small Fermi surface pockets may be expected from band-structure calculations in Y123-II, no such pockets are predicted for Y124. Our results therefore imply that these small pockets are a generic feature of the copper oxide plane in underdoped cuprates.