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

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

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

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

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

Dynamics of spin transport in voltage-biased Josephson junctions

We investigate spin transport in voltage-biased spin-active Josephson junctions. The interplay of spin filtering, spin mixing, and multiple Andreev reflection leads to nonlinear voltage dependence of the dc and ac spin current. We compute the voltage characteristics of the spin current (I_S) for superconductor-ferromagnet-superconductor (SFS) Josephson junctions. The sub-harmonic gap structure of I_S(V) is shown to be sensitive to the degree of spin mixing generated by the ferromagnetic interface, and exhibits a pronounced even-odd effect associated with spin transport during multiple Andreev reflection processes. For strong spin mixing both the magnitude and the direction of the dc spin current can be sensitively controlled by the bias voltage.Comment: 4 pages, 3 figure

Antiferromagnetism and singlet formation in underdoped high-Tc cuprates: Implications for superconducting pairing

The extended $t-J$ model is theoretically studied, in the context of hole underdoped cuprates. Based on results obtained by recent numerical studies, we identify the mean field state having both the antiferromagnetic and staggered flux resonating valence bond orders. The random-phase approximation is employed to analyze all the possible collective modes in this mean field state. In the static (Bardeen Cooper Schrieffer) limit justified in the weak coupling regime, we obtain the effective superconducting interaction between the doped holes at the small pockets located around $\bm{k}= (\pm \pi/2, \pm \pi/2)$. In contrast to the spin-bag theory, which takes into acccount only the antiferromagnetic order, this effective force is pair breaking for the pairing without the nodes in each of the small hole pocket, and is canceled out to be very small for the $d_{x^2-y^2}$ pairing with nodes which is realized in the real cuprates. Therefore we conclude that no superconducting instability can occur when only the magnetic mechanism is considered. The relations of our work with other approaches are also discussed.Comment: 20 pages, 7 figures, REVTeX; final version accepted for publicatio

The internal Josephson effect in a Fermi gas near a Feshbach resonance

We consider a two-component system of Fermi atoms and molecular bosons in the vicinity of a Feshbash resonance. We derive an effective action for the system, which has a term describing coherent tunneling of the molecular bosons into Cooper pairs and vice versa. In the equilibrium state, global phase coherence may be destroyed by thermal or quantum phase fluctuations. In the non-equilibrium regime, the system may show an internal AC Josephson effect leading to real time oscillations in the number of molecular bosons.Comment: 5 pages, 2 figure

Quasiparticle scattering time in superconducting films: from dirty to clean limit

We study the quasiparticle energy relaxation processes in superconducting Nb films of different thicknesses corresponding to different electron mean free paths in a state far from equilibrium, that is the highly dissipative flux-flow state driven up to the instability point. From the measured current-voltage curves we derive the vortex critical velocity $v^{*}$ for several temperatures. From the $v^{*}(T)$ values, the quasiparticle energy relaxation time $\tau_{\epsilon}$ is evaluated within the Larkin-Ovchinnikov model and numerical calculations of the quasiparticle energy relaxation rates are carried out to support the experimental findings. Besides the expected constant behavior of $\tau_{\epsilon}(T)$ for the dirty samples, we observe a strong temperature dependence of the quasiparticle energy relaxation time in the clean samples. This feature is associated with the increasing contribution from the electron-phonon scattering process as the dirty limit is approached from the clean regime