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We discuss a recent resonant ultrasound spectroscopy (RUS) study of YBa$_2$Cu$_3$O$_{6+\delta}$, which infers a line of phase transitions bounding the pseudogap phase and argue that this scenario is not supported by thermodynamic evidence. We show that the anomalies in RUS, heat capacity and thermal expansion at the superconducting transition temperatures agree well. But there are large discrepancies between RUS and thermodynamic measurements at $T^*$ where the pseudogap phase transitions are purported to occur. Moreover, the frequency and temperature dependence of the RUS data for the crystal with $\delta = 0.98$, interpreted in terms of critical slowing down near an electronic phase transition, is five orders of magnitude smaller than what is expected. For this crystal the RUS data near $T^*$ are more consistent with non-equilibrium effects such as oxygen relaxation., Comment: Published version

Using a high-resolution differential technique we have determined the electronic specific heat coefficient gamma(T) of Ba1-xKxFe2As2 with x=0 to 1.0, at temperatures (T) from 2K to 380K and in magnetic fields H=0 to 13T. In the normal state gamma_n(x,T) increases strongly with x at low temperature, compatible with a mass renormalisation ~12 at x=1, and decreases weakly with x at high temperature. A superconducting transition is seen in all samples from x=0.2 to 1, with transition temperatures and condensation energies peaking sharply at x=0.4. Superconducting coherence lengths xi_{ab}~20{\AA} and xi_c~3{\AA} are estimated from an analysis of Gaussian fluctuations. For many dopings we see features in the H and T-dependences of gamma_s(T,H) in the superconducting state that suggest superconducting gaps in three distinct bands. A broad "knee" and a sharp mean-field-like peak are typical of two coupled gaps. However, several samples show a shoulder above the sharp peak with an abrupt onset at T_{c,s} and a T-dependence gamma_s(T)\propto\sqrt{1-T/T_{c,s}}. We provide strong evidence that the shoulder is not due to doping inhomogeneity and suggest it is a distinct gap with an unconventional T-dependence Delta_s(T)\propto(1-T/T_{c,s})^{0.75} near T_{c,s}. We estimate band fractions and T=0 gaps from 3-band alpha-model fits to our data and compare the x-dependences of the band fractions with spectroscopic studies of the Fermi surface., Comment: 20 pages, 23 figures, published in Physical Review B

Using a differential technique, we have measured the specific heats of polycrystalline Ba1-xKxFe2As2 samples with x=0, 0.1 and 0.3, between 2K and 380K and in magnetic fields 0 to 13 Tesla. From this data we have determined the electronic specific heat coefficient, gamma, over the entire range for the three samples. The most heavily doped sample (x=0.3) exhibits a large superconducting anomaly Delta gamma(Tc)~48mJ/molK^2 at Tc=35K, and we determine the energy gap, condensation energy, superfluid density and coherence length. In the normal state for the x=0.3 sample, gamma~47 mJ/molK^2 is constant from Tc to 380K. In the parent compound (x=0) there is a large almost first order anomaly at the spin density wave (SDW) transition at To=136K. This anomaly is smaller and broader for x=0.1. At low T, gamma is strongly reduced by the SDW gap for both x=0 and 0.1, but above To, gamma for all three samples are similar., Comment: 5 pages, 5 figures, submitted to Physical Review B

We analyse fluctuations about $T_c$ in the specific heat of (Y,Ca)Ba$_2$Cu$_3$O$_{7-\delta}$, YBa$_2$Cu$_4$O$_8$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The mean-field transition temperature, $T_c^{mf}$, in the absence of fluctuations lies well above $T_c$ especially at low doping where it reaches as high as 150K. We show that phase and amplitude fluctuations set in simultaneously and $T_c^{mf}$ scales with the gap, $\Delta_0$, such that $2\Delta_0/k_BT_c^{mf}$ is comparable to the BCS weak-coupling value, 4.3, for d-wave superconductivity. We also show that $T_c^{mf}$ is unrelated to the pseudogap temperature, $T^*$., Comment: 4 pages, 2 figures, submitted to PRL. A key follow up paper to this work is on the arXiv:0908.4430

The effects of planar hole content, p (= x), on the static magnetic susceptibility, chi(T), of polycrystalline La2-xSrxCu1-yZnyO4 compounds were investigated over a wide range of Sr (x) and Zn (y) contents. The magnetic behavior caused by Zn was found to depend strongly on the hole content. The apparent magnetic moment induced by Zn was larger in underdoped La2-xSrxCu1-yZnyO4, decreased quite sharply around p ~ 0.19, and did not change much for further overdoping. This is interpreted in terms of the effect of the pseudogap on the Zn-induced magnetic behavior, as there is growing evidence that the pseudogap vanishes quite abruptly at p ~ 0.19 +/- 0.01. From a detailed analysis of chi(T) data the Zn-induced magnetic contribution was found to be rather complex and showed non-Curie-like features over a wide range of temperature. The observed behavior was scrutinized in terms of two scenarios (a) that of independent localized-moments and (b) low energy quasiparticle resonances associated with each Zn atom. Our study points towards the latter scenario and more generally suggests that there is a re-distribution of quasiparticle spectral weight due to Zn substitution, the features of which are greatly influenced by the presence and magnitude of the pseudogap., Comment: Submitted to Phys. Rev. B

The effects of planar hole content, p, on the static magnetic susceptibility, chi(T), of Y1-xCaxBa2Cu3O7-delta polycrystalline samples were investigated over a wide range of Ca (x) and oxygen contents. Non-magnetic Ca2+, in the 3p6 state, induces a Curie-like contribution to chi(T) that increases systematically and non-linearly with x but is almost independent of p. We argue that this arises from statistical clusters containing two or more nearest neighbor Ca atoms. We have again found that the pseudogap in the quasi-particle spectral weight appears abruptly below a planar hole content p = 0.190 +/- 0.005., Comment: Submitted to Phys. Rev. B

Using an energy-momentum dispersion for Bi2Sr2CaCu2O8 obtained from angle-resolved photoelectron spectroscopy we show that the shrinking Fermi arc model of the pseudogap is inconsistent with Raman scattering below Tc and specific heat near T*. By simulating the quasiparticle energy dispersion curves we show that Fermi arcs are an artifact of a T-dependent scattering rate., Comment: 5 pages, 6 figures, accepted for publication as a Rapid Communication in Physical Review B

Scanning tunneling spectroscopy studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ suggest the presence of electronic inhomogeneity with a large spatial variation in gap size. Andersen {\it et al} have modelled this variation by assuming a spatially-varying pairing interaction. We show that their calculated specific heat is incompatible with the experimental data which exhibit narrow transitions. This calls into question the now-common assumption of gap and pairing inhomogeneity., Comment: 4 pages, 6 figures, submitted to Phys. Rev. B

The effects of planar hole content, p (= x), on the uniform (q = 0) magnetic susceptibility, c(T), of La2-xSrxCu1-yZnyO4 were investigated over a wide range of Sr (x) and Zn (y) contents. A strongly p-dependent Zn-induced magnetic behavior was observed. The apparent Zn-induced magnetic moment is larger in underdoped La2-xSrxCu1-yZnyO4 and it decreases quite sharply around p ~ 0.19. It does not change much for further overdoping. This indicates a possible role of the pseudogap on the Zn induced magnetic behavior, as there is growing evidence that pseudogap vanishes quite abruptly at p ~ 0.19., Comment: Submitted to Physica C (Proceedings of the M2S-HTSC-VIII Conference)

Julien et al. have commented on two of our publications claiming that we have made erroneous interpretations of the nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) data. Specifically, they believe that their model of an extended staggered moment about a Zn impurity is the only interpretation of the data [Julien et al., Phys. Rev Lett. 84, 3422 (2000)]. Not only does their claim ignore models presented by other authors, we show that the model of Julien et al. [Phys. Rev Lett. 84, 3422 (2000)] does not consistently reproduce all of the NMR data., Comment: 16 pages in PDF format

A universal scaling relation, $\rho_s \propto \sigma(T_c)\times T_c$ has been reported by Homes $et$ $al$. (Nature (London) {\bf 430}, 539 (2004)) where $\rho_s$ is the superfluid density and $\sigma(T)$ is the DC conductivity. The relation was shown to apply to both c-axis and in-plane dynamics for high-$T_c$ superconductors as well as to the more conventional superconductors Nb and Pb, suggesting common physics in these systems. We show quantitatively that the scaling behavior has several possible origins including, marginal Fermi-liquid behavior, Josephson coupling, dirty-limit superconductivity and unitary impurity scattering for a d-wave order parameter. However, the relation breaks down seriously in overdoped cuprates, and possibly even at lower doping., Comment: Paper in press as Rapid Comm in Phys. Rev. B. 4 pages, 1 figure, in response to the Nature paper by Homes et al

Recent scanning tunnelling microscopy (STM) studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) revealed the presence of severe inhomogeneity with length scale $L_0 \approx \xi_0$, the coherence length. Other studies have been interpreted in terms of mesoscale or nanoscale phase segregation. Here we analyze heat capacity and NMR data on Bi-2212 and (Y,Ca)Ba$_2$Cu$_3$O$_{7-\delta}$ and find no evidence for phase segregation or gross inhomogeneity. For Bi-2212 the coherence scale $L_0$ increases with doping from 5 to 17$\xi_0$ and the hole density inhomogeneity decreases from 0.028 to 0.005 holes/Cu. We conclude that STM measurements considerably overstate the inhomogeneity in bulk Bi-2212., Comment: 4 pages, 5 figures, submitted to Phys. Rev. Letters

The doping dependence of the superfluid density, r_s, of high-Tc superconductors is usually considered in the context of the Uemura relation, namely Tc proportional to rs, which is generally assumed to apply in the underdoped regime. We show that a modified plot of Tc/Do versus rs, where Do is the maximum d-wave gap at T=0, exhibits universal features that point to an alternative interpretation of the underlying physics. In the underdoped region this plot exhibits the canonical negative curvature expected when a ground-state correlation competes with superconductivity (SC) by opening up a gap in the normal-state DOS. In particular rs is suppressed much faster than Tc/Do or indeed Tc. The pseudogap is found to strongly modify the SC ground state., Comment: 9 pages, 5 figures, submitted Phys. Rev. Lett

The low-energy excitation spectrum of HTS cuprates is examined in the light of thermodynamic, transport, quasiparticle and spin properties. Changes in the thermodynamic spectrum associated with the normal-state pseudogap disappear abruptly at a critical doping state, $p_{crit}$ = 0.19 holes per Cu. Moreover, ARPES data at 100K show that heavily damped quasiparticles (QP) near ($\pi$,0) suddenly recover long lifetimes at $p_{crit}$, reflecting an abrupt loss of scattering from AF spin fluctuations. This picture is confirmed by $\mu$SR zero-field relaxation measurements which indicate the presence of a novel quantum glass transition at $p_{crit}$. Consistent with this picture resistivity studies on thin films of Y$_{0.7}$Ca$_{0.3}$Ba$_2$Cu$_3$O$_{7-\delta}$ reveal linear behavior confined to a V-shaped domain focussed on $p_{crit}$ at $T$=0. The generic phase behavior of the cuprates may be governed by quantum critical fluctuations above $p_{crit}$ and the pseudogap appears to be caused by short-range AF correlations., Comment: MOS2002 oral paper, 8 pages, 3 colour figures. Paper in press J. Low Temp. Phys Replacement adds reference 19

From an analysis of the specific heat of one of the cuprate superconductors it is shown, that even if a large part of the experimental specific heat associated with the superconducting phase transition is due to fluctuations, this part must be counted when one tries to extract the condensation energy from the data. Previous work by Chakravarty, Kee and Abrahams, where the fluctuation part was subtracted, has resulted in an incorrect estimation of the condensation energy., Comment: 4 pages, 5 encapsulated Postscript figures, uses ReVTeX.sty

We have measured the electronic specific heat of $Y_{0.8}Ca_{0.2}Ba_2Cu_3O_{7-\delta}$ using a high-resolution differential technique from liquid helium temperature to room temperature in an applied magnetic field up to 13T. The field dependence of the electronic specific heat at low temperatures in the superconducting state behaves differently in the overdoped and underdoped regimes, varing as $\sqrt{H}$ in the overdoped regime but as $H$ in the underdoped regime. An entropy loss is observed in the normal state in optimal and underdoped samples, which can be attributed to the opening of a normal state psuedogap. From the temperature and field dependences of the free energy, the temperature dependence of the upper critical field $H_{c2}$ is determined. For the overdoped sample ($x=0.79$), we find $H_{c2}$ to have a negative curvature., Comment: 7 pages, 10 figures

The recent obervation of a Kondo-like temperature dependence in the Li NMR Knight shift in Ca- and Li- cosubstituted YBa2Cu3O7-d was attributed by Bobroff et al. to be evidence of Li-induced local moments in overdoped Y123. It is shown from Y-NMR measurements on Y0.8Ca0.2Ba2Cu3O7-d and heat capacity studies on Bi2Sr2CaCu2O8 that such a Kondo-like temperature dependence is an intrinsic overdoping effect quite generally present in cuprate superconductors which are free of strong scatterers such as Zn and Li. It is probable that Zn and Li only induce local moments in the underdoped pseudogap region and not in the overdoped region., Comment: 1 page, 1 figure, Comment on Bobroff et al., Phys. Rev. Lett. 83, 4381 (1999)

Underdoped high-Tc superconductors are frequently characterised by a temperature, T*, below which the normal-state pseudogap opens. Two different "phase diagrams" based on the doping (p) dependence of T* are currently considered: one where T* falls to zero at a critical doping state and the other where T* merges with Tc in the overdoped region. By examining the temperature dependence of the NMR Knight shift and relaxation rate, entropy, resistivity, infrared conductivity, Raman scattering, ARPES and tunnelling data it is concluded that the second scenario is not at all supported. Neither can one distinguish a small and a large pseudogap as is often done. T* is an energy scale which falls abruptly to zero at p=0.19., Comment: 13 pages, 11 figures, a response to confusion at M^2S Conference, Houston, regarding the phase behaviour of the HTS cuprates. Submitted to Physica C, 2 May 2000. More references added as well as section on c-axis resistivity

The impact of the normal-state pseudogap, present in all optimal and underdoped HTS cuprates, on critical currents and critical temperature is surveyed. With the opening of the pseudogap around a doping state of p=0.19 the condensation energy and superfluid density are rapidly suppressed due to reduction in the normal-state spectral weight. Even by optimal doping (p=0.16) these measures of the 'strength' of superconductivity are diminished by up to 40%. This results in a sharp reduction in critical currents and irreversibility field, respectively. The optimal doping state where these properties are maximised is therefore not at maximum Tc but in the lightly overdoped region where the pseudogap energy falls to zero at p=0.19. The presence of impurities and grain boundaries further heightens these effects., Comment: 9 pages, 8 figures, invited paper ChemHTS workshop, Tokyo Institute of Technology, 15-16 October, to be published Physica C

Evidence is presented from the scaling of the Knight shift, entropy and transport properties together with the sharp peaking of condensation energy, critical currents, superfluid density and a variety of other physical properties for the occurrence of a common critical doping point in lightly overdoped high-Tc superconductors (HTS). This critical doping lies at the point where the doping-dependent normal-state pseudogap energy, Eg, falls to zero and bears a strong, though incomplete, resemblance to a quantum critical point (QCP). A QCP scenario could lead directly to an explanation of the non-Fermi liquid behaviour of the normal-state metallic phase and the overall generic behaviour of the HTSC., Comment: 12 pages, 10 figures, presented at ICSSS-99, 7 September 1999

Resistivity, thermoelectric power and heat capacity are investigated in the ferromagnetic superconductor RuSr2GdCu2O8 with and without Zn substitution. The thermodynamic signatures of the ordering of the Ru moments and the paramagnetic Gd moments as well as the onset of superconductivity are all clearly seen and quantified. The materials are shown to exhibit bulk superconductivity which coexists with spatially-uniform ferromagnetism. They appear to be typical underdoped superconducting cuprates in which the pseudogap dominates normal-state transport, thermodynamic and substitutional properties. However, a field-induced increase in Tc could suggest some degree of triplet pairing., Comment: 9 pages, 6 figures, submitted to Phys. Rev. Lett 1 June 1999

The absolute values and temperature, T, dependence of the in-plane magnetic penetration depth, $\lambda_{ab}$, of La_{2-x}Sr_xCuO_4 and HgBa_2CuO_{4+\delta} have been measured as a function of carrier concentration. We find that the superfluid density, $\rho_s$, changes substantially and systematically with doping. The values of $\rho_{s}(0)$ are closely linked to the available low energy spectral weight as determined by the electronic entropy just above T_c and the initial slope of $\rho_{s}(T)/\rho_{s}(0)$ increases rapidly with carrier concentration. The results are discussed in the context of a possible relationship between $\rho_s$ and the normal-state (or pseudo) energy gap., Comment: 4 pages and 5 figures, submitted to Phys. Rev. Lett