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]

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.

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.

2Close to optimal doping, the copper oxide superconductors show 'strange metal' behavior 1,2 , suggestive of strong fluctuations associated with a quantum critical point [3][4][5][6] . Such a critical point requires a line of classical phase transitions terminating at zero temperature near optimal doping inside the superconducting 'dome'. The underdoped region of the temperature-doping phase diagram from which superconductivity emerges is referred to as the 'pseudogap' 7-13 because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBa 2 Cu 3 O 6+δ is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behavior and therefore superconductivity in the cuprates.Resonant ultrasound spectroscopy (RUS) measures the frequencies f n and widths Γ n of the vibrational normal modes of a crystal acting as a free mechanical resonator. The frequencies of the normal modes are determined by density and geometry of the crystal as well as its elastic properties. The elastic component of the temperature evolution of these frequencies, ∆f n (T ), depends on a linear combination of all elastic moduli and reflects changes in the thermodynamic state of the system such as those associated with a phase transi- (Figure 4(a,b)). Causality requires that the maxima in energy absorption are accompanied by elastic stiffening over the same temperature range. This stiffening is observed in addition to the distinct break in slope at T * (Figure 2(b)).The potential for RUS to determine the broken symmetry in the pseudogap phase was limited in this study by the precision with which crystal shape could be controlled, an issue that may be resolvable as sample preparation techniques improve. The pseudogap phase 5 transition is located by our RUS measurements with ±3K uncertainty, improving on the ±30K uncertainty in onset of neutron spin-flip scattering. This clearly separates the onset of magnetic order 8-11 at T * from the onset T K of the Kerr rotation signal 27 and charge order 28 at lower temperature (Figure 3). In our measurements we observe an increase in energy absorption over a broad region near T K (Figure 2(c)), however we do not observe an accompanying thermodynamic signature there. Our observed evolution of the pseudogap phase boundary from underdoped to overdoped establishes the presence of a quantum critical point inside the superconducting dome, suggesting a quantum-critical origin for both the strange metallic behavior and the mechanism of superconducting pairing.

In the quest for superconductors with higher transition temperatures ( ), one emerging motif is that electronic interactions favourable for superconductivity can be enhanced by fluctuations of a broken-symmetry phase. Recent experiments have suggested the existence of the requisite broken symmetry phase in the highcuprates, but the impact of such a phase on the ground-state electronic interactions has remained unclear. We use magnetic fields exceeding 90 tesla to access the underlying metallic state of the cuprate YBa 2 Cu 3 O 6+δ over a wide range of doping, and observe magnetic quantum oscillations that reveal a strong enhancement of the quasiparticle effective mass toward optimal doping. This mass enhancement results from increasing electronic interactions approaching optimal doping, and suggests a quantum-critical point at a hole doping of ≈ . .In several classes of unconventional superconductors, such as the heavy fermions, organics, and iron pnictides, superconductivity has been linked to a quantum critical point (QCP). At a QCP, the system undergoes a phase transition and a change in symmetry at zero temperature; the associated quantum fluctuations enhance interactions, which can give rise to (or enhance) superconductivity [1, 2]. As the QCP is approached, these fluctuations produce stronger and stronger electronic correlations, resulting in an experimentally-observable enhancement of the electron effective mass [1, 3, 4, 5]. It is widely believed that spin fluctuations in the vicinity of an antiferromagnetic QCP are important for superconductivity in many heavy-fermion, organic, and pnictide superconductors [6, 2], leading to the ubiquitous phenomenon of a superconducting dome surrounding a QCP. The role of quantum-criticality in cuprate high-temperature superconductors is more controversial [7]: do the collapsing experimental energy scales [8], enhanced superconducting properties (see Fig. 1), and evidence for a change in ground-state symmetry near optimal doping [9, 10, 11, 12, 13, 14, 15, 16] support the existence of strong fluctuations that are relevant to superconductivity [17, 18, 19, 2]? Alternative explanations for the phenomenology of the cuprate phase diagram focus on the physics of a lightly doped Mott insulator [7, 20], rather than a metal with competing broken-symmetry phases. Several investigations, both theoretical and experimental, suggest that competing order is present in the cuprates, and is associated with the charge (rather than spin) degree of freedom (such as charge density wave order, orbital current order, or nematicity, see Fig. 1) [12, 15, 16,17, 18, 21, 22, 23, 24, 25, 26, 27, 28]. What has been missing is direct, low-temperature evidence that the disappearance of competing order near optimal doping, and the associated change in ground-state symmetry, is accompanied by enhanced electronic interactions in the ground state.A powerful technique for measuring low-temperature Fermi surface properties is the magnetic quantum-oscillation phenomenon, which directly accesses quasi...

The anomalous metallic state in the high-temperature superconducting cuprates is masked by superconductivity near a quantum critical point. Applying high magnetic fields to suppress superconductivity has enabled detailed studies of the normal state, yet the direct effect of strong magnetic fields on the metallic state is poorly understood. We report the high-field magnetoresistance of thin-film La Sr CuO cuprate in the vicinity of the critical doping, 0.161 ≤ ≤ 0.190. We find that the metallic state exposed by suppressing superconductivity is characterized by magnetoresistance that is linear in magnetic fields up to 80 tesla. The magnitude of the linear-in-field resistivity mirrors the magnitude and doping evolution of the well-known linear-in-temperature resistivity that has been associated with quantum criticality in high-temperature superconductors.