Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover

We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite bosons at leading order in the density ("dilute limit"), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless, that the two-dimensional mean-field solution is not consistent with our general result in the "dilute limit", to the extent that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low energy in two dimensions.Comment: Revised version to be published on Eur. Phys. Jour. B, 7 pages, 1 figur

Linear response theory around a localized impurity in the pseudogap regime of an anisotropic superconductor: precursor pairing vs the d-density-wave scenario

We derive the polarizability of an electron system in (i) the superconducting phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azymuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave-vector Q=(pi,pi), albeit imperfect, due to a nonzero value of the hopping ratio t'/t in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also exhibited by the (q,omega) dependence of the retarded polarizability.Comment: accepted in Phys. Rev.

Size-shrinking of deuterons in very dilute superfluid nuclear matter

It is shown within the strong-coupling BCS approach that, starting from the zero-density limit of superfluid nuclear matter, with increasing density deuterons first shrink before they start expanding.Comment: 2 pages, Latex, 1 figure included, submitted to Phys. Rev.

Internal structure of preformed Cooper pairs

In order to obtain information about the internal structure of the preformed pairs in the pseudogap state of high $T_c$ superconductors, we calculate the propagator of a singlet pair with center of mass coordinate $\mathbf{r}$, and relative distance $\pmb{\rho}$, by solving the Bethe-Salpeter equation, representing the sum over repeated two-particle scattering events due to a distance dependent attraction. We define then a ``pair structure function'' $g_{P}(\mathbf{P},\pmb{\rho})$ that depends on the internal distance $\pmb{\rho}$ between the partners and on the momentum $\mathbf{P}$ of the pair. We calculate this function both for a local potential and $s-$wave symmetry of the order parameter and for a separable potential and $d-$wave symmetry of the order parameter. The influence of the center of mass momentum, strenght of the interaction, temperature, density of particles and of the pseudogap in the one-electron spectrum is studied for both cases.Comment: 12 pages, REVTeX4, 8 EPS figure

Internal structure of fluctuating Cooper pairs

Abstract.: In order to obtain information about the internal structure of fluctuating Cooper pairs in the pseudogap state and below the transition temperature of high Tc superconductors, we solve the Bethe-Salpeter equation for the two-electron propagator in order to calculate a "pair structure function” $g_{P}({\mathbf{P}},\pmb{\rho})$ that depends on the internal distance $\pmb{\rho}$ between the partners and on the center of mass momentum P of the pair. We use an attractive Hubbard model with a local potential for s-wave and a separable potential for d-wave symmetry. The amplitude of gP for small ρ depends on temperature, chemical potential and interaction symmetry, but the ρ dependence itself is rather insensitive to the interaction strength. Asymptotically gP decreases as an inverse power of ρ for weak coupling, but exponentially when a pseudogap develops for stronger interaction. Some possibilities of observing the pair structure experimentally are mentione

Linear Response Theory Around a Localized Impurity in the Pseudogap Regime of an Anisotropic Superconductor

We compare and contrast the polarizability of a d-wave superconductor in the pseudogap regime, within the precursor pairing scenario (dPG), and of a d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Our study is motivated by STM imaging experiments around an isolated impurity, which may in principle distinguish between precursor pairing and dDW order in the pseudogap regime of the high-$$T_{c}$$ superconductors. In both cases, the $${\bf q}$$-dependence of the polarizability is characterized by an azimuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave vector $${{\bf Q}}=(\pi,\pi)$$, albeit imperfect, due to a nonzero value of the hopping ratio $$t^\prime /t$$ in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also reflected by the $$({\bf q},\omega)$$ dependence of the retarded polarizabilit

Architectures and Key Technical Challenges for 5G Systems Incorporating Satellites

Satellite Communication systems are a promising solution to extend and complement terrestrial networks in unserved or under-served areas. This aspect is reflected by recent commercial and standardisation endeavours. In particular, 3GPP recently initiated a Study Item for New Radio-based, i.e., 5G, Non-Terrestrial Networks aimed at deploying satellite systems either as a stand-alone solution or as an integration to terrestrial networks in mobile broadband and machine-type communication scenarios. However, typical satellite channel impairments, as large path losses, delays, and Doppler shifts, pose severe challenges to the realisation of a satellite-based NR network. In this paper, based on the architecture options currently being discussed in the standardisation fora, we discuss and assess the impact of the satellite channel characteristics on the physical and Medium Access Control layers, both in terms of transmitted waveforms and procedures for enhanced Mobile BroadBand (eMBB) and NarrowBand-Internet of Things (NB-IoT) applications. The proposed analysis shows that the main technical challenges are related to the PHY/MAC procedures, in particular Random Access (RA), Timing Advance (TA), and Hybrid Automatic Repeat reQuest (HARQ) and, depending on the considered service and architecture, different solutions are proposed.Comment: Submitted to Transactions on Vehicular Technologies, April 201

Critical Temperature and Energy Gap for the BCS Equation

We derive upper and lower bounds on the critical temperature $T_c$ and the energy gap $\Xi$ (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local two-body interaction potential $\lambda V(x)$. At weak coupling $\lambda \ll 1$ and under appropriate assumptions on $V(x)$, our bounds show that $T_c \sim A \exp(-B/\lambda)$ and $\Xi \sim C \exp(-B/\lambda)$ for some explicit coefficients $A$, $B$ and $C$ depending on the interaction $V(x)$ and the chemical potential $\mu$. The ratio $A/C$ turns out to be a universal constant, independent of both $V(x)$ and $\mu$. Our analysis is valid for any $\mu$; for small $\mu$, or low density, our formulas reduce to well-known expressions involving the scattering length of $V(x)$.Comment: RevTeX4, 23 pages. Revised version, to appear in Phys. Rev.

Superconductivity with hard-core repulsion: BCS-Bose crossover and s-/d-wave competition

We consider fermions on a 2D lattice interacting repulsively on the same site and attractively on the nearest neighbor sites. The model is relevant, for instance, to study the competition between antiferromagnetism and superconductivity in a Kondo lattice. We first solve the two-body problem to show that in the dilute and strong coupling limit the s-wave Bose condensed state is always the ground state. We then consider the many-body problem and treat it at mean-field level by solving exactly the usual gap equation. This guarantees that the superconducting wave-function correctly vanishes when the two fermions (with antiparallel spin) sit on the same site. This fact has important consequences on the superconducting state that are somewhat unusual. In particular this implies a radial node-line for the gap function. When a next neighbor hopping t' is present we find that the s-wave state may develop nodes on the Fermi surface.Comment: 10 pages, 9 fig

Ward identity and optical-conductivity sum rule in the d-density wave state

We consider the role of the Ward identity in dealing with the transport properties of an interacting system forming a d-wave modulated charge-density wave or staggered flux phase. In particular, we address this issue from the point of view of the restricted optical-conductivity sum rule. Our aim is to provide a controlled approximation for the current-current correlation function which allows us also to determine analytically the corresponding sum rule. By analyzing the role of the vertex functions in both the microscopic interacting model and in the effective mean-field Hamiltonian, we propose a non-standard low-energy sum-rule for this system. We also discuss the possible applicability of these results for the description of cuprate superconductors in the pseudogap regime.Comment: Revised version, accepted for publication in Phys. Rev.