Isotope effect on the superfluid density in conventional and high-temperature superconductors

We investigate the isotope effect on the London penetration depth of a superconductor which measures $n_S/m^*$, the ratio of superfluid density to effective mass. We use a simplified model of electrons weakly coupled to a single phonon frequency $\omega_E$, but assume that the energy gap $\Delta$ does not have any isotope effect. Nevertheless we find an isotope effect for $n_S/m^*$ which is significant if $\Delta$ is sufficiently large that it becomes comparable to $\omega_E$, a regime of interest to high $T_c$ cuprate superconductors and possibly other families of unconventional superconductors with relatively high $T_c$. Our model is too simple to describe the cuprates and it gives the wrong sign of the isotope effect when compared with experiment, but it is a proof of principle that the isotope effect exists for $n_S/m^*$ in materials where the pairing gap and $T_c$ is not of phonon origin and has no isotope effect.Comment: 9 pages, 6 figure

Transport phenomena in three-dimensional system close to the magnetic quantum critical point: The conserving approximation with the current vertex corrections

It is known that various transport coefficients strongly deviate from conventional Fermi-liquid behaviors in many electron systems which are close to antiferromagnetic (AF) quantum critical points (QCP). For example, Hall coefficients and Nernst coefficients in three-dimensional heavy fermion CeCoIn5 and CeCu6-xAux increase strikingly at low temperatures, whose overall behaviors are similar to those in high-Tc cuprates. These temperature dependences are too strong to explain in terms of the relaxation time approximation. To elucidate the origin of these anomalous transport phenomena in three-dimensional systems, we study the current vertex corrections (CVC) based on the fluctuation exchange (FLEX) approximation, and find out decisive role of the CVC. The main finding of the present paper is that the Hall coefficient and the Nernst coefficient strongly increase thanks to the CVC in the vicinity of the AF QCP, irrespective of dimensionality. We also study the relaxation time of quasi-particles, and find that "hot points" and "cold lines" are formed in general three-dimensional systems due to strong AF fluctuations.Comment: 11 pages, 18 figures. Accepted for publication in Phys. Rev.

Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

It is shown that one can obtain quantitatively accurate values for the superconducting critical temperature within a Hamiltonian framework. This is possible if one uses a renormalized Hamiltonian that contains an attractive electron-electron interaction and renormalized single particle energies. It can be obtained by similarity renormalization or using flow equations for Hamiltonians. We calculate the critical temperature as a function of the coupling using the standard BCS-theory. For small coupling we rederive the McMillan formula for Tc. We compare our results with Eliashberg theory and with experimental data from various materials. The theoretical results agree with the experimental data within 10%. Renormalization theory of Hamiltonians provides a promising way to investigate electron-phonon interactions in strongly correlated systems.Comment: 6 pages, LaTeX, using EuroPhys.sty, one eps figure included, accepted for publication in Europhys. Let

Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid

Recent experiments on the organic compound \kappa-(ET)_2Cu_2(CN)_3 have provided a promising example of a two dimensional spin liquid state. This phase is described by a two-dimensional spinon Fermi sea coupled to a U(1) gauge field. We study Kohn-Luttinger-like pairing instabilities of the spinon Fermi surface due to singular interaction processes with twice-the-Fermi-momentum transfer. We find that under certain circumstances the pairing instability occurs in odd-orbital-angular-momentum/spin-triplet channels. Implications to experiments are discussed.Comment: 4 pages, 1 figur

The electron-phonon coupling strength at metal surfaces directly determined from the Helium atom scattering Debye-Waller factor

A new quantum-theoretical derivation of the elastic and inelastic scattering probability of He atoms from a metal surface, where the energy and momentum exchange with the phonon gas can only occur through the mediation of the surface free-electron density, shows that the Debye-Waller exponent is directly proportional to the electron-phonon mass coupling constant $\lambda$. The comparison between the values of $\lambda$ extracted from existing data on the Debye-Waller factor for various metal surfaces and the $\lambda$ values known from literature indicates a substantial agreement, which opens the possibility of directly extracting the electron-phonon coupling strength in quasi-2D conducting systems from the temperature or incident energy dependence of the elastic Helium atom scattering intensities.Comment: 14 pages, 2 figures, 1 tabl

Temperature dependence of the superheating field for superconductors in the high-k London limit

We study the metastability of the superheated Meissner state in type II superconductors with k >> 1 beyond Ginzburg-Landau theory, which is applicable only in the vicinity of the critical temperature. Within Eilenberger's semiclassical approximation, we use the local electrodynamic response of the superconductor to derive a generalized thermodynamic potential valid at any temperature. The stability analysis of this functional yields the temperature dependence of the superheating field. Finally, we comment on the implications of our results for superconducting cavities in particle accelerators.Comment: 7.5 pages, 2 figure

Sum Rules and Ward Identities in the Kondo Lattice

We derive a generalized Luttinger-Ward expression for the Free energy of a many body system involving a constrained Hilbert space. In the large $N$ limit, we are able to explicity write the entropy as a functional of the Green's functions. Using this method we obtain a Luttinger sum rule for the Kondo lattice. One of the fascinating aspects of the sum rule, is that it contains two components, one describing the heavy electron Fermi surface, the other, a sea of oppositely charged, spinless fermions. In the heavy electron state, this sea of spinless fermions is completely filled and the electron Fermi surface expands by one electron per unit cell to compensate the positively charged background, forming a ``large'' Fermi surface. Arbitrarily weak magnetism causes the spinless Fermi sea to annihilate with part of the Fermi sea of the conduction electrons, leading to a small Fermi surface. Our results thus enable us to show that the Fermi surface volume contracts from a large, to a small volume at a quantum critical point. However, the sum rules also permit the possible formation of a new phase, sandwiched between the antiferromagnet and the heavy electron phase, where the charged spinless fermions develop a true Fermi surface.Comment: 24 pages, 4 figures. Version two contains a proof of the "Entropy formula" which connects the entropy directly to the Green's functions. Version three contains corrections to typos and a more extensive discussion of the physics at finite

The Complex Gap in Color Superconductivity

We solve the gap equation for color-superconducting quark matter in the 2SC phase, including both the energy and the momentum dependence of the gap, \phi=\phi(k_0,\vk). For that purpose a complex Ansatz for \phi is made. The calculations are performed within an effective theory for cold and dense quark matter. The solution of the complex gap equation is valid to subleading order in the strong coupling constant g and in the limit of zero temperature. We find that, for momenta sufficiently close to the Fermi surface and for small energies, the dominant contribution to the imaginary part of $\phi$ arises from Landau-damped magnetic gluons. Further away from the Fermi surface and for larger energies the other gluon sectors have to be included into Im\phi. We confirm that Im$\phi$ contributes a correction of order g to the prefactor of \phi for on-shell quasiquarks sufficiently close to the Fermi surface, whereas further away from the Fermi surface Im\phi and Re\phi are of the same order. Finally, we discuss the relevance of Im\phi for the damping of quasiquark excitations.Comment: 23 pages, 3 figures, 8 tables. Typos corrected, minor corrections to the text. Accepted for publication in PR

Non-equilibrium Enhancement of Cooper Pairing in Cold Fermion Systems

Non-equilibrium stimulation of superfluidity in trapped Fermi gases is discussed by analogy to the work of Eliashberg [G. M. Eliashberg, in "Nonequilibrium Superconductivity," edited by D. N. Langenberg and A. I. Larkin (North-Holland, New York, 1986)] on the microwave enhancement of superconductivity. Optical excitation of the fermions balanced by heat loss due to thermal contact with a boson bath and/or evaporative cooling enables stationary non-equilibrium states to exist. Such a state manifests as a shift of the quasiparticle spectrum to higher energies and this effect effectively raises the pairing transition temperature. As an illustration, we calculate the effective enhancement of Cooper pairing and superfluidity in both the normal and superfluid phases for a mixture of Rb and Li in the limit of small departure from equilibrium. It is argued that in experiment the desirable effect is not limited to such small perturbations and the effective enhancement of the pairing temperature may be quite large.Comment: 7 pages, 6 figure

Suppression of superconductivity by Neel-type magnetic fluctuations in the iron pnictides

Motivated by recent experimental detection of Neel-type ($(\pi,\pi)$) magnetic fluctuations in some iron pnictides, we study the impact of competing $(\pi,\pi)$ and $(\pi,0)$ spin fluctuations on the superconductivity of these materials. We show that, counter-intuitively, even short-range, weak Neel fluctuations strongly suppress the $s^{+-}$ state, with the main effect arising from a repulsive contribution to the $s^{+-}$ pairing interaction, complemented by low frequency inelastic scattering. Further increasing the strength of the Neel fluctuations leads to a low-$T_{c}$ d-wave state, with a possible intermediate $s+id$ phase. The results suggest that the absence of superconductivity in a series of hole-doped pnictides is due to the combination of short-range Neel fluctuations and pair-breaking impurity scattering, and also that $T_{c}$ of optimally doped pnictides could be further increased if residual $(\pi,\pi)$ fluctuations were reduced.Comment: revised version accepted for publication in PR