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.

To understand the origin of superconductivity, it is crucial to ascertain the nature and origin of the primary carriers available to participate in pairing. Recent quantum oscillation experiments on high-transition-temperature (high-T(c)) copper oxide superconductors have revealed the existence of a Fermi surface akin to that in normal metals, comprising fermionic carriers that undergo orbital quantization. The unexpectedly small size of the observed carrier pocket, however, leaves open a variety of possibilities for the existence or form of any underlying magnetic order, and its relation to d-wave superconductivity. Here we report experiments on quantum oscillations in the magnetization (the de Haas-van Alphen effect) in superconducting YBa(2)Cu(3)O(6.51) that reveal more than one carrier pocket. In particular, we find evidence for the existence of a much larger pocket of heavier mass carriers playing a thermodynamically dominant role in this hole-doped superconductor. Importantly, characteristics of the multiple pockets within this more complete Fermi surface impose constraints on the wavevector of any underlying order and the location of the carriers in momentum space. These constraints enable us to construct a possible density-wave model with spiral or related modulated magnetic order, consistent with experimental observations.

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.

Evidence is mounting that charge order competes with superconductivity in high T c cuprates. Whether this has any relationship to the pairing mechanism is unknown as neither the universality of the competition nor its microscopic nature has been established. Here, we show using nuclear magnetic resonance that charge order in YBa 2 Cu 3 O y has maximum strength inside the superconducting dome, similar to compounds of the La 2 À x (Sr,Ba) x CuO 4 family. In YBa 2 Cu 3 O y , this occurs at doping levels of p ¼ 0.11-0.12. We further show that the overlap of halos of incipient charge order around vortex cores, similar to those visualised in Bi 2 Sr 2 CaCu 2 O 8 þ d , can explain the threshold magnetic field at which long-range charge order emerges. These results reveal universal features of a competition in which charge order and superconductivity appear as joint instabilities of the same normal state, whose relative balance can be field-tuned in the vortex state.

The origin of pairing in a superconductor resides in the underlying normal state. In the cuprate high-temperature superconductor YBa2Cu3Oy (YBCO), application of a magnetic field to suppress superconductivity reveals a ground state that appears to break the translational symmetry of the lattice, pointing to some density-wave order. Here we use a comparative study of thermoelectric transport in the cuprates YBCO and La1.8−xEu0.2SrxCuO4 (Eu-LSCO) to show that the two materials exhibit the same process of Fermi-surface reconstruction as a function of temperature and doping. The fact that in Eu-LSCO this reconstruction coexists with spin and charge modulations that break translational symmetry shows that stripe order is the generic non-superconducting ground state of hole-doped cuprates.