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 ...

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]

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.

No abstract

The Nernst effect in metals is highly sensitive to two kinds of phase transition: superconductivity and density-wave order. The large, positive Nernst signal observed in hole-doped high-T(c) superconductors above their transition temperature (T(c)) has so far been attributed to fluctuating superconductivity. Here we report that in some of these materials the large Nernst signal is in fact the result of stripe order, a form of spin/charge modulation that causes a reconstruction of the Fermi surface. In La(2-x)Sr(x)CuO(4) (LSCO) doped with Nd or Eu, the onset of stripe order causes the Nernst signal to change from being small and negative to being large and positive, as revealed either by lowering the hole concentration across the quantum critical point in Nd-doped LSCO (refs 6-8) or by lowering the temperature across the ordering temperature in Eu-doped LSCO (refs 9, 10). In the second case, two separate peaks are resolved, respectively associated with the onset of stripe order at high temperature and superconductivity near T(c).

Charge-density-wave order has been observed in cuprate superconductors whose crystal structure breaks the square symmetry of the CuO 2 planes, such as orthorhombic YBa 2 Cu 3 O y (YBCO), but not so far in cuprates that preserve that symmetry, such as tetragonal HgBa 2 CuO 4þ (Hg1201). We have measured the Hall (R H ), Seebeck (S), and Nernst () coefficients of underdoped Hg1201 in magnetic fields large enough to suppress superconductivity. The high-field R H ðTÞ and SðTÞ are found to drop with decreasing temperature and become negative, as also observed in YBCO at comparable doping. In YBCO, the negative R H and S are signatures of a small electron pocket caused by Fermi-surface reconstruction, attributed to charge-density-wave modulations observed in the same range of doping and temperature. We deduce that a similar Fermi-surface reconstruction takes place in Hg1201, evidence that density-wave order exists in this material. A striking similarity is also found in the normal-state Nernst coefficient ðTÞ, further supporting this interpretation. Given the model nature of Hg1201, Fermi-surface reconstruction appears to be common to all hole-doped cuprates, suggesting that density-wave order is a fundamental property of these materials. There is a growing body of evidence that competing ordered states shape the phase diagram of the cuprates, and the identification of those states is currently a central challenge of high-temperature superconductivity. In the La 2 CuO 4 -based cuprates, whose maximal T c does not exceed 40 K, the existence of unidirectional densitywave order involving spin and charge modulations, known as stripe order [1,2] [9,10], a material with a maximal T c of 93 K, shows that its Fermi surface also undergoes a reconstruction [11,12]. Comparative measurements of the Seebeck coefficient in YBCO and Eu-LSCO reveal a detailed similarity [7,8], suggesting that Fermi-surface reconstruction (FSR) in YBCO is caused by some form of stripe order.Charge-density-wave modulations were recently detected in YBCO, via high-field nuclear magnetic resonance (NMR) [13] and x-ray-scattering [14][15][16][17][18] measurements, in the range of temperature and doping where FSR occurs [8,19]. Although the detailed structure of these modulations remains to be clarified, there is little doubt that they are responsible for the FSR in YBCO.The fundamental question, then, is whether such charge modulations are a generic property of the cuprates. Because both the low-temperature tetragonal structure of Eu-LSCO and the orthorhombic structure of YBCO distort the square CuO 2 planes and impose a preferred direction, charge modulations are perhaps triggered or stabilized by these particular forms of unidirectional distortion. To answer that question, we need to examine a cuprate material with square CuO 2 planes. For that purpose, the model material is HgBa 2 CuO 4þ (Hg1201), a tetragonal cuprate with the highest maximal T c of all single-layer cuprates (97 K) [20,21], in which no charge or spin modulations have yet been reported. ...

We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperaturedoping phase diagram of hole-doped cuprate superconductors. New data for the Nernst coefficient ν(T ) of YBa2Cu3Oy (YBCO), La1.8−xEu0.2SrxCuO4 (Eu-LSCO) and La1.6−xNd0.4SrxCuO4 (Nd-LSCO) are presented and compared with previously published data on YBCO, Eu-LSCO, Nd-LSCO, and La2−xSrxCuO4 (LSCO). The temperature Tν at which ν / T deviates from its hightemperature linear behaviour is found to coincide with the temperature at which the resistivity ρ(T ) deviates from its linear-T dependence, which we take as the definition of the pseudogap temperature T -in agreement with the temperature at which the antinodal spectral gap detected in angleresolved photoemission spectroscopy (ARPES) opens. We track T as a function of doping and find that it decreases linearly vs p in all four materials, having the same value in the three LSCObased cuprates, irrespective of their different crystal structures. At low p, T is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of T (p) to p = 0 yields T (p → 0) TN(0), the Néel temperature for the onset of antiferromagnetic order at p = 0, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing p, T (p) extrapolates linearly to zero at p pc2, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above the critical temperature Tc, as a function of doping, and find that a narrow fluctuation regime tracks Tc, and not T . This confirms that the pseudogap phase is not a form of precursor superconductivity, and fluctuations in the phase of the superconducting order parameter are not what causes Tc to fall on the underdoped side of the Tc dome.