Universality in Heavy Fermions Revisited

A previous scaling analysis of pressure experiments in heavy fermion is reviewed and enlarged. We show that the critical exponents obtained from this analysis indicate that a one-parameter scaling describes these experiments. We obtain explicitly the enhancemente factors showing that these systems are indeed near criticality and that the scaling approach is appropriate. The physics responsible for the one-parameter scaling and breakdown of hyperscaling is clarified. We discuss a microsocopic theory that is in agreement with the experiments. The scaling theory is generalized for the case the shift and crossover exponents are different. The exponents governing the physical behavior along the non-Fermi liquid trajectory are obtained for this case.Comment: 7 pages, Latex, 3 Postscript figures, to be published in Physical Review

Isotope effect in superconductors with coexisting interactions of phonon and nonphonon mechanisms

We examine the isotope effect of superconductivity in systems with coexisting interactions of phonon and nonphonon mechanisms in addition to the direct Coulomb interaction. The interaction mediated by the spin fluctuations is discussed as an example of the nonphonon interaction. Extended formulas for the transition temperature Tc and the isotope-effect coefficient alpha are derived for cases (a) omega_np omega_D, where omega_np is an effective cutoff frequency of the nonphonon interaction that corresponds to the Debye frequency omega_D in the phonon interaction. In case (a), it is found that the nonphonon interaction does not change the condition for the inverse isotope effect, i.e., mu^* > lambda_ph/2, but it modifies the magnitude of alpha markedly. In particular, it is found that a giant isotope shift occurs when the phonon and nonphonon interactions cancel each other largely. For instance, strong critical spin fluctuations may give rise to the giant isotope effect. In case (b), it is found that the inverse isotope effect occurs only when the nonphonon interaction and the repulsive Coulomb interaction, in total effect, work as repulsive interactions against the superconductivity. We discuss the relevance of the present result to some organic superconductors, such as kappa-(ET)2Cu(NCS)2 and Sr2RuO4 superconductors, in which inverse isotope effects have been observed, and briefly to high-Tc cuprates, in which giant isotope effects have been observed.Comment: 4 pages, 2 figures, (with jpsj2.cls, ver.1.2), v2:linguistic correction

Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wavevector and temperature dependent static spin susceptibility, \chi_s(Q,T), of clean interacting Fermi systems is considered in dimensions 1\leq d \leq 3. We show that at zero temperature \chi_s is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q|^{d-1} for 1<d<3, and Q^2\ln|Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence T^{d-1} for 1<d<3. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular for itinerant ferromagnetism, are discussed. We also point out the relation between our findings and established perturbative results for 1-d systems, as well as for the temperature dependence of \chi_s(Q=0) in d=3.Comment: 12pp., REVTeX, 5 eps figures, final version as publishe

Nonmonotonic d_{x^2-y^2} Superconducting Order Parameter in Nd_{2-x}Ce_xCuO_4

Low energy polarized electronic Raman scattering of the electron doped superconductor Nd_1.85Ce_0.15CuO_4 (T_c=22 K) has revealed a nonmonotonic d_{x^2-y^2} superconducting order parameter. It has a maximum gap of 4.4 k_BT_c at Fermi surface intersections with antiferromagnetic Brillouin zone (the ``hot spots'') and a smaller gap of 3.3 k_BT_c at fermionic Brillouin zone boundaries. The gap enhancement in the vicinity of the ``hot spots'' emphasizes role of antiferromagnetic fluctuations and similarity in the origin of superconductivity for electron- and hole-doped cuprates.Comment: 4 pages, 4 figure

Coexistence of Singlet and Triplet Attractive Channels in the Pairing Interactions Mediated by Antiferromagnetic Fluctuations

We propose a phase diagram of quasi-low-dimensional type II superconductors in parallel magnetic fields, when antiferromagnetic fluctuations contribute to the pairing interactions. We point out that pairing interactions mediated by antiferromagnetic fluctuations necessarily include both singlet channels and triplet channels as attractive interactions. Usually, a singlet pairing is favored at zero field, but a triplet pairing occurs at high fields where the singlet pairing is suppressed by the Pauli paramagnetic pair-breaking effect. As a result, the critical field increases divergently at low temperatures. A possible relation to experimental phase diagrams of a quasi-one-dimensional organic superconductor is briefly discussed. We also discuss a possibility that a triplet superconductivity is observed even at zero field.Comment: 4 pages, 1 figure (Latex, revtex.sty, epsf.sty

Systematics of two-component superconductivity in YBa2Cu3O6.95YBa_{2}Cu_{3}O_{6.95} from microwave measurements of high quality single crystals

Systematic microwave surface impedance measurements of YBCO single crystals grown in $BaZrO_3$ crucibles reveal new properties that are not directly seen in similar measurements of other YBCO samples. Two key observations obtained from complex conductivity are: a new normal conductivity peak at around 80K and additional pairing below 65K. High pressure oxygenation of one of the crystals still yields the same results ruling out any effect of macroscopic segregation of O-deficient regions. A single complex order parameter cannot describe these data, and the results suggest at least two superconducting components. Comparisons with model calculations done for various decoupled two-component scenarios (i.e. s+d, d+d) are presented. Systematics of three single crystals show that the 80K quasiparticle peak is correlated with the normal state inelastic scattering rate. Close to Tc, the data follow a mean-field behavior. Overall, our results strongly suggest the presence of multiple pairing temperature and energy scales in $YBa_{2}Cu_{3}O_{6.95}$.Comment: 14 pages, 2-column, Revtex, 5 embedded postscript figures, uses graphicx. Postscript version also available at http://sagar.physics.neu.edu/preprints.htm

Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors

The singlet s-, d- and triplet p-wave pairing symmetries in quasi-one-dimensional organic superconductors can be experimentally discriminated by probing the Andreev bound states at the sample edges. These states have the energy in the middle of the superconducting gap and manifest themselves as a zero-bias peak in tunneling conductance into the corresponding edge. Their existence is related to the sign change of the pairing potential around the Fermi surface. We present an exact self-consistent solution of the edge problem showing the presence of the midgap states for p_x-wave superconductivity. The spins of the edge state respond paramagnetically to a magnetic field parallel to the vector d that characterizes triplet pairing.Comment: 6 pages, 4 figures. V.2: New section on spin response is added and references are updated. V.3: Final version accepted to PRB. Typos are corrected and important note is added in proof

Phenomenological description of the microwave surface impedance and complex conductivity of high-TcT_c single crystals

Measurements of the microwave surface impedance $Z_s(T)=R_s(T)+iX_s(T)$ and of the complex conductivity $\sigma_s(T)$ of high-quality, high-$T_c$ single crystals of YBCO, BSCCO, TBCCO, and TBCO are analyzed. Experimental data of $Z_s(T)$ and $\sigma_s(T)$ are compared with calculations based on a modified two-fluid model which includes temperature-dependent quasiparticle scattering and a unique temperature variation of the density of superconducting carriers. We elucidate agreement as well as disagreement of our analysis with the salient features of the experimental data. Existing microscopic models are reviewed which are based on unconventional symmetry types of the order parameter and on novel mechanisms of quasiparticle relaxation.Comment: 15 pages, 17 figures, 1 tabl

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron

Electronic Raman scattering in HgBa_{2}Ca_{2}Cu_{3}O_{8+\delta} single crystals. Analysis of the superconducting state

Electronic Raman scattering measurements have been performed on $HgBa_{2}Ca_{2}Cu_{3}O_{8+\delta}$ single crystals in the superconducting state. Pure electronic Raman spectra with no phonon structures hindering the analysis of the electronic continuum have been obtained. As a consequence, the spectra in the pure $B_{1g}$ and $B_{2g}$ symmetries are directly and reliably analyzed and the pure $A_{1g}$ contribution can be easily identified. Below the critical temperature $T_{c},$ two electronic structures at $2\Delta \sim 6.4 k_{B}T_{c}$ and $2\Delta \sim 9.4$ $k_{B}T_{c}$ are clearly seen. Both are observed simultaneously in pure $A_{1g}$ symmetry, the highest energy one being located at the energy of the $B_{1g}$ maximum. These two maxima disappear at $T_{c}$ and do not soften significantly as the temperature is raised up to $T_{c}.$ The low energy frequency dependence of the $B_{1g}$ electronic response is strongly linear, for various excitation lines in the 476.5 to 647.1 nm range. Such experimental data cannot be reconciled with a pure $d_{x^{2}-y^{2}}$ symmetry. Instead, they strongly advocate in favor of an anisotropic superconducting gap with two distinct gap maxima and of nodes existing outside the [110] and [1,$\bar{1}$,0] directions in {\bf k}-space. We discuss in detail the simplest order parameter compatible with our experimental findings.Comment: 12 pages, revtex, 12 figure