Generic Finite Size Enhancement of Pairing in Mesoscopic Fermi Systems

The finite size dependent enhancement of pairing in mesoscopic Fermi systems is studied under the assumption that the BCS approach is valid and that the two body force is size independent. Different systems are investigated such as superconducting metallic grains and films as well atomic nuclei. It is shown that the finite size enhancement of pairing in these systems is in part due to the presence of a surface which accounts quite well for the data of nuclei and explains a good fraction of the enhancement in Al grains.Comment: Updated version 17/02/0

Density-induced BCS to Bose-Einstein crossover

We investigate the zero-temperature BCS to Bose-Einstein crossover at the mean-field level, by driving it with the attractive potential and the particle density.We emphasize specifically the role played by the particle density in this crossover.Three different interparticle potentials are considered for the continuum model in three spatial dimensions, while both s- and d-wave solutions are analyzed for the attractive (extended) Hubbard model on a two-dimensional square lattice. For this model the peculiar behavior of the crossover for the d-wave solution is discussed.In particular, in the strong-coupling limit when approaching half filling we evidence the occurrence of strong correlations among antiparallel-spin fermions belonging to different composite bosons, which give rise to a quasi-long-range antiferromagnetic order in this limit.Comment: 10 pages, 5 enclosed figure

Non-interacting Cooper pairs inside a pseudogap

I present a simple analytical model describing the normal state of a superconductor with a pseudogap in the density of states, such as in underdoped cuprates. In nearly two-dimensional systems, where the superconducting transition temperature is reduced from the mean-field BCS value, Cooper pairs may be present as slow fluctuations of the BCS pairing field. Using the self-consistent T-matrix (fluctuation exchange) approach I find that the fermion spectral weight exhibits two BCS-like peaks, broadened by fluctuations of the pairing field amplitude. The density of states becomes suppressed near the Fermi energy, which allows for long-lived low-energy Cooper pairs that propagate as a sound-like mode with a mass. A self-consistency requirement, linking the width of the pseudogap to the intensity of the pairing field, determines the pair condensation temperature. In nearly two-dimensional systems, it is proportional to the degeneracy temperature of the fermions, with a small prefactor that vanishes in two dimensions.Comment: LaTeX (prbbib.sty included), 24 pages, 4 PostScript figures To appear in Phys.Rev.

Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions

For an electron gas with delta-function attraction we investigate the crossover from weak- to strong-coupling supercoductivity in two and three dimensions. We derive analytic expressions for the stiffness of phase fluctuations and set up effective XY-models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature T_c as a monotonous function of the coupling strength and carrier density both in two and three dimensions, and give analytic formulas for the merging of the temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.Comment: Few typos corrected. Emails that were sent to the address [email protected] in June and July 1999 were lost in a computer crash, so if your comments were not answered please send them once mor

Superconducting transitions from the pseudogap state: d-wave symmetry, lattice, and low-dimensional effects

We investigate the behavior of the superconducting transition temperature within a previously developed BCS-Bose Einstein crossover picture. This picture, based on a decoupling scheme of Kadanoff and Martin, further extended by Patton, can be used to derive a simple form for the superconducting transition temperature in the presence of a pseudogap. We extend previous work which addressed the case of s-wave pairing in jellium, to explore the solutions for T_c as a function of variable coupling in more physically relevant situations. We thereby ascertain the effects of reduced dimensionality, periodic lattices and a d-wave pairing interaction. Implications for the cuprate superconductors are discussed.Comment: REVTeX, 11 pages, 6 EPS figures included, Replace with published versio

Optical Absorption of an Interacting Many-Polaron Gas

The optical absorption of a many (continuum) polaron gas is derived in the framework of a variational approach at zero temperature and weak or intermediate electron-phonon coupling strength. We derive a compact formula for the optical conductivity of the many-polaron system taking into account many-body effects in the electron or hole system. Within the method presented here, these effects are contained completely in the dynamical structure factor of the electron or hole system. This allows to build on well-established studies of the interacting electron gas. Based on this approach a novel feature in the absorption spectrum of the many-polaron gas, related to the emission of a plasmon together with a phonon, is identified. As an application and illustration of the technique, we compare the theoretical many-polaron optical absorption spectrum as derived in the present work with the `d-band' absorption feature in Nd$_{2}$CuO$_{2}$. Similarities are shown between the theoretically and the experimentally derived first frequency moment of the optical absorption of a family of differently doped Nd$_{2-x}$Ce$_{x}$CuO$_{4-y}$ materials.Comment: 24 pages, 5 figures; revised and expanded versio

The pseudogap state in superconductors: Extended Hartree approach to time-dependent Ginzburg-Landau Theory

It is well known that conventional pairing fluctuation theory at the Hartree level leads to a normal state pseudogap in the fermionic spectrum. Our goal is to extend this Hartree approximated scheme to arrive at a generalized mean field theory of pseudogapped superconductors for all temperatures $T$. While an equivalent approach to the pseudogap has been derived elsewhere using a more formal Green's function decoupling scheme, in this paper we re-interpret this mean field theory and BCS theory as well, and demonstrate how they naturally relate to ideal Bose gas condensation. Here we recast the Hartree approximated Ginzburg-Landau self consistent equations in a T-matrix form. This recasting makes it possible to consider arbitrarily strong attractive coupling, where bosonic degrees of freedom appear at $T^*$ considerably above $T_c$. The implications for transport both above and below $T_c$ are discussed. Below $T_c$ we find two types of contributions. Those associated with fermionic excitations have the usual BCS functional form. That they depend on the magnitude of the excitation gap, nevertheless, leads to rather atypical transport properties in the strong coupling limit, where this gap (as distinct from the order parameter) is virtually $T$-independent. In addition, there are bosonic terms arising from non-condensed pairs whose transport properties are shown here to be reasonably well described by an effective time-dependent Ginzburg-Landau theory.Comment: 14 pages, 5 figures, REVTeX4, submitted to PRB; clarification of the diagrammatic technique added, one figure update

Signatures of polaronic excitations in quasi-one-dimensional LaTiO3.41_{3.41}

The optical properties of quasi-one-dimensional metallic LaTiO$_{3.41}$ are studied for the polarization along the $a$ and $b$ axes. With decreasing temperature modes appear along both directions suggestive for a phase transition. The broadness of these modes along the conducting axis might be due to the coupling of the phonons to low-energy electronic excitations across an energy gap. We observe a pronounced midinfrared band with a temperature dependence consistent with (interacting) polaron models. The polaronic picture is corroborated by the presence of strong electron-phonon coupling and the temperature dependence of the dc conductivity.Comment: 5 pages, 5 figure

Determination of the Fermion Pair Size in a Resonantly Interacting Superfluid

Fermionic superfluidity requires the formation of pairs. The actual size of these fermion pairs varies by orders of magnitude from the femtometer scale in neutron stars and nuclei to the micrometer range in conventional superconductors. Many properties of the superfluid depend on the pair size relative to the interparticle spacing. This is expressed in BCS-BEC crossover theories, describing the crossover from a Bardeen-Cooper-Schrieffer (BCS) type superfluid of loosely bound and large Cooper pairs to Bose-Einstein condensation (BEC) of tightly bound molecules. Such a crossover superfluid has been realized in ultracold atomic gases where high temperature superfluidity has been observed. The microscopic properties of the fermion pairs can be probed with radio-frequency (rf) spectroscopy. Previous work was difficult to interpret due to strong and not well understood final state interactions. Here we realize a new superfluid spin mixture where such interactions have negligible influence and present fermion-pair dissociation spectra that reveal the underlying pairing correlations. This allows us to determine the spectroscopic pair size in the resonantly interacting gas to be 2.6(2)/kF (kF is the Fermi wave number). The pairs are therefore smaller than the interparticle spacing and the smallest pairs observed in fermionic superfluids. This finding highlights the importance of small fermion pairs for superfluidity at high critical temperatures. We have also identified transitions from fermion pairs into bound molecular states and into many-body bound states in the case of strong final state interactions.Comment: 8 pages, 7 figures; Figures updated; New Figures added; Updated discussion of fit function