Superconductivity often emerges in the proximity of, or in competition with, symmetry breaking ground states such as antiferromagnetism or charge density waves (CDW) 1--5 . A number of materials in the cuprate family, which includes the high--transition--temperature (high--T c ) superconductors, show spin and charge density wave order 5--7 . Thus a fundamental question is to what extent these ordered states exist for compositions close to optimal for superconductivity. Here we use high--energy x--ray diffraction to show that a CDW develops at zero field in the normal state of superconducting YBa 2 Cu 3 O 6.67 (T c = 67 K). Below T c , the application of a magnetic field suppresses superconductivity and enhances the CDW. Hence, the CDW and superconductivity are competing orders in this typical high--T c superconductor, and high--T c superconductivity can form from a pre--existing CDW state. Our results explain observations of small Fermi surface pockets 8 , negative Hall and Seebeck effect 9,10 and the "T c plateau" 11 in this material when underdoped.Charge density waves in solids are periodic modulations of conduction electron density. They are often present in low dimensional systems such as NbSe 2 4 . Certain cuprate materials such as La 2--x--y Nd y Sr x CuO 4 (Nd--LSCO) and La 2--x Ba x CuO 4 , (LBCO) also show charge modulations that suppress superconductivity near x=1/8 6,7 . In some cases, these are believed to be unidirectional in the CuO 2 plane, and have been dubbed 'stripes' 2,3 . There is now a mounting body of indirect evidence that charge and/or spin density waves may be present at high magnetic fields in samples with high T c : quantum oscillation experiments on underdoped YBa 2 Cu 3 O y (YBCO) have revealed the existence of at least one small Fermi surface pocket 8,9 which may be created by a charge modulation 10 . More recently, NMR studies have shown a magnetic--field--induced splitting of the Cu2F lines of YBCO 12 . An important issue is the extent to which the tendency towards charge order exists in high--T c superconductors 2,3 .Here we report a hard (100 keV) X--ray diffraction study, in magnetic fields up to 17 T, of a de-twinned single crystal of YBa 2 Cu 3 O 6.67 (with ortho--VIII oxygen ordering 11,13 , T c = 67 K and p = 0.12 where p is the hole concentration per planar Cu). We find that a CDW forms in the normal state below T CDW ≈ 135 K. The charge modulation has two fundamental wavevectors q CDW = q 1 = (δ 1 , 0, 0.5) and q 2 = (0, δ 2 , 0.5), where δ 1 ≈ 0.3045(2) and δ 2 ≈0.3146(7). These give satellites of the parent crystal Bragg peaks at positions such as Q=(2±δ 1 , 0, 0.5). Although the satellite intensities have a strong temperature and magnetic field dependence, the CDW is not field-induced and is unaffected by field in the normal state. Below T c it competes with superconductivity, and a decrease of the CDW amplitude in zero field becomes an increase when superconductivity is suppressed by field. Figure 1a,g shows scans through the (2--δ 1 , 0, 0.5) and (0, 2--δ 2 , 0.5) p...

Electronic charges introduced in copper-oxide (CuO 2 ) planes generate hightransition temperature (T c ) superconductivity but, under special circumstances, they can also order into filaments called stripes (1). Whether an underlying tendency of charges to order is present in all cuprates and whether this has any relationship with superconductivity are, however, two highly controversial issues (2,3). In order to uncover underlying electronic orders, magnetic fields strong enough to destabilise superconductivity can be used. Such experiments, including quantum oscillations (4-6) in YBa 2 Cu 3 O y (a notoriously clean cuprate where charge order is not observed) have suggested that superconductivity competes with spin, rather than charge, order (7-9). Here, using nuclear magnetic resonance, we demonstrate that high magnetic fields actually induce charge order, without spin order, in the CuO 2 planes of YBa 2 Cu 3 O y . The observed static, unidirectional, modulation of the charge density breaks translational symmetry, thus explaining quantum oscillation results, and we argue that it is most likely the same 4a- The ortho II structure of YBa 2 Cu 3 O 6.54 (p=0.108) leads to two distinct planar Cu NMR sites: Cu2F are those Cu located below oxygen-filled chains and Cu2E those below oxygen-empty chains (10). The main discovery of our work is that, on cooling in a field H 0 of 28.5 T along the c axis (i.e. in the conditions for which quantum oscillations are resolved; See supplementary materials), the Cu2F lines undergo a profound change while the Cu2E lines do not (Fig. 1). To first order, this change can be described as a splitting of Cu2F into two sites having both different hyperfine shifts K=/H 0 ( is the hyperfine field due to electronic spins) and quadrupole frequencies ν Q (Related to the electric field gradient). Additional effects might be present ( Fig. 1), but they are minor compared to the observed splitting. Field and temperature dependent orbital occupancy (e.g. d x 2 -y 2 vs. d z 2 -r 2 ) changes without on-site electronic density change are implausible and any out-of-plane charge-density or lattice change would affect Cu2E sites as well. Thus, the change of ν Q can only arise from a differentiation in the charge density among Cu2F sites (or at the oxygen sites bridging them). A change in the asymmetry parameter and/or in the direction of the principal axis of the electric field gradient could also be associated with this charge differentiation, but these are relatively small effects.Remarkably, the charge differentiation occurs below T charge =50±10 K for p=0.108 whatever the precise profile of the static charge modulation is, the reconstruction must be related to the translational symmetry breaking by the charge ordered state.The absence of any splitting or broadening of Cu2E lines implies a onedimensional character of the modulation within the planes and imposes strong constraints on the charge pattern. Actually, only two types of modulations are compatible with a Cu2F splitting (Fig. 2). T...

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.