Tunneling spectra of submicron Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} intrinsic Josephson junctions: evolution from superconducting gap to pseudogap

Tunneling spectra of near optimally doped, submicron Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ intrinsic Josephson junctions are presented, and examined in the region where the superconducting gap evolves into pseudogap. The spectra are analyzed using a self-energy model, proposed by Norman {\it et al.}, in which both quasiparticle scattering rate $\Gamma$ and pair decay rate $\Gamma_{\Delta}$ are considered. The density of states derived from the model has the familiar Dynes' form with a simple replacement of $\Gamma$ by $\gamma_+$ = ($\Gamma$ + $\Gamma_{\Delta}$)/2. The $\gamma_+$ parameter obtained from fitting the experimental spectra shows a roughly linear temperature dependence, which puts a strong constraint on the relation between $\Gamma$ and $\Gamma_{\Delta}$. We discuss and compare the Fermi arc behavior in the pseudogap phase from the tunneling and angle-resolved photoemission spectroscopy experiments. Our results indicate an excellent agreement between the two experiments, which is in favor of the precursor pairing view of the pseudogap.Comment: 7 pages, 6 figure

Low energy collective modes, Ginzburg-Landau theory, and pseudogap behavior in superconductors with long-range pairing interactions

We study the superconducting instability in systems with long but finite ranged, attractive, pairing interactions. We show that such long-ranged superconductors exhibit a new class of fluctuations in which the internal structure of the Cooper pair wave function is soft, and thus lead to "pseudogap" behavior in which the actual transition temperature is greatly depressed from its mean field value. These fluctuations are {\it not} phase fluctuations of the standard superconducting order parameter, and lead to a highly unusual Ginzburg-Landau description. We suggest that the crossover between the BCS limit of a short-ranged attraction and our problem is of interest in the context of superconductivity in the underdoped cuprates.Comment: 20 pages with one embedded ps figure. Minor revisions to the text and references. Final version to appear in PRB on Nov. 1st, 200

Impurity induced resonant state in a pseudogap state of a high temperature superconductor

We predict a resonance impurity state generated by the substitution of one Cu atom with a nonmagnetic atom, such as Zn, in the pseudogap state of a high-T_c superconductor. The precise microscopic origin of the pseudogap is not important for this state to be formed, in particular this resonance will be present even in the absence of superconducting fluctuations in the normal state. In the presence of superconducting fluctuations, we predict the existence of a counterpart impurity peak on a symmetric bias. The nature of impurity resonance is similar to the previously studied resonance in the d-wave superconducting state.Comment: 4 pages, 2 figure

Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x

The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature dependence of the in-plane optical conductivity of optimally-doped YBa_2Cu_3O_{6.95} and underdoped YBa_2Cu_3O_{6.60}. Within the accuracy of the experiment, the sum rule is obeyed in both materials. However, the energy scale \omega_c required to recover the full strength of the superfluid \rho_s in the two materials is dramatically different; \omega_c \simeq 800 cm^{-1} in the optimally doped system (close to twice the maximum of the superconducting gap, 2\Delta_0), but \omega_c \gtrsim 5000 cm^{-1} in the underdoped system. In both materials, the normal-state scattering rate close to the critical temperature is small, \Gamma < 2\Delta_0, so that the materials are not in the dirty limit and the relevant energy scale for \rho_s in a BCS material should be twice the energy gap. The FGT sum rule in the optimally-doped material suggests that the majority of the spectral weight of the condensate comes from energies below 2\Delta_0, which is consistent with a BCS material in which the condensate originates from a Fermi liquid normal state. In the underdoped material the larger energy scale may be a result of the non-Fermi liquid nature of the normal state. The dramatically different energy scales suggest that the nature of the normal state creates specific conditions for observing the different aspects of what is presumably a central mechanism for superconductivity in these materials.Comment: RevTeX 4 file, 9 pages with 7 embedded eps figure

DDW Order and its Role in the Phase Diagram of Extended Hubbard Models

We show in a mean-field calculation that phase diagrams remarkably similar to those recently proposed for the cuprates arise in simple microscopic models of interacting electrons near half-filling. The models are extended Hubbard models with nearest neighbor interaction and correlated hopping. The underdoped region of the phase diagram features $d_{{x^2}-{y^2}}$ density-wave (DDW) order. In a certain regime of temperature and doping, DDW order coexists with antiferromagnetic (AF) order. For larger doping, it coexists with $d_{{x^2}-{y^2}}$ superconductivity (DSC). While phase diagrams of this form are robust, they are not inevitable. For other reasonable values of the coupling constants, drastically different phase diagrams are obtained. We comment on implications for the cuprates.Comment: 7 pages, 3 figure

Electromotive forces and the Meissner effect puzzle

In a voltaic cell, positive (negative) ions flow from the low (high) potential electrode to the high (low) potential electrode, driven by an `electromotive force' which points in opposite direction and overcomes the electric force. Similarly in a superconductor charge flows in direction opposite to that dictated by the Faraday electric field as the magnetic field is expelled in the Meissner effect. The puzzle is the same in both cases: what drives electric charges against electromagnetic forces? I propose that the answer is also the same in both cases: kinetic energy lowering, or `quantum pressure'

Unconventional particle-hole mixing in the systems with strong superconducting fluctuations

Development of the STM and ARPES spectroscopies enabled to reach the resolution level sufficient for detecting the particle-hole entanglement in superconducting materials. On a quantitative level one can characterize such entanglement in terms of the, so called, Bogoliubov angle which determines to what extent the particles and holes constitute the spatially or momentum resolved excitation spectra. In classical superconductors, where the phase transition is related to formation of the Cooper pairs almost simultaneously accompanied by onset of their long-range phase coherence, the Bogoliubov angle is slanted all the way up to the critical temperature Tc. In the high temperature superconductors and in superfluid ultracold fermion atoms near the Feshbach resonance the situation is different because of the preformed pairs which exist above Tc albeit loosing coherence due to the strong quantum fluctuations. We discuss a generic temperature dependence of the Bogoliubov angle in such pseudogap state indicating a novel, non-BCS behavior. For quantitative analysis we use a two-component model describing the pairs coexisting with single fermions and study their mutual feedback effects by the selfconsistent procedure originating from the renormalization group approach.Comment: 4 pages, 4 figure

Insulin-Like Growth Factor Levels During Pregnancy in the Cow are Affected by Protein Supplementation in the Maternal Diet

To determine if dietary protein supplementation in early pregnancy alters total circulating insulinlike growth factor (IGF) levels, genetically similar heifers were fed diets containing different levels of protein in the first and second trimesters of gestation. The groups were: low/low (L/L), fed a diet containing 7% crude protein (CP) per kg/DM (low protein) in the first and second trimesters; high/high (H/H), fed a diet containing 14% CP per kg/DM (high protein) in the first and second trimesters; low/high (L/H), fed low protein in the first trimester and high in the second trimester and vice versa for the high/low (H/L) group. At day 62 of gestation, there was a significant difference (

Phase fluctuations, dissipation and superfluid stiffness in d-wave superconductors

We study the effect of dissipation on quantum phase fluctuations in d-wave superconductors. Dissipation, arising from a nonzero low frequency optical conductivity which has been measured in experiments below $T_c$, has two effects: (1) a reduction of zero point phase fluctuations, and (2) a reduction of the temperature at which one crosses over to classical thermal fluctuations. For parameter values relevant to the cuprates, we show that the crossover temperature is still too large for classical phase fluctuations to play a significant role at low temperature. Quasiparticles are thus crucial in determining the linear temperature dependence of the in-plane superfluid stiffness. Thermal phase fluctuations become important at higher temperatures and play a role near $T_c$.Comment: Presentation improved, new references added (10 latex pages, 3 eps figures). submitted to PR

Effective Actions and Phase Fluctuations in d-wave Superconductors

We study effective actions for order parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the $c$-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero temperature superfluid stiffness, but thermal effects are small for $T << T_c$.Comment: Some numerical estimates corrected and figures changed. to appear in PRB, Sept.1 (2000