Related papers: Superconductivity in Ultrasmall Grains: Introducti…
The exact solution of the BCS pairing Hamiltonian was found by Richardson in 1963. While little attention was paid to this exactly solvable model in the remainder of the 20th century, there was a burst of work at the beginning of this…
We study integrable models for electrons in metals when the single particle spectrum is discrete. The electron-electron interactions are BCS-like pairing, Coulomb repulsion, and spin exchange coupling. These couplings are, in general,…
To describe the crossover from the bulk BCS superconductivity to a fluctuation-dominated regime in ultrasmall metallic grains, new order parameters and correlation functions, such as ``parity gap'' and ``pair-mixing correlation function'',…
The Richardson Hamiltonian describes superconducting correlations in a metallic nanograin. We do a perturbative analysis of this and related Hamiltonians, around the strong pairing limit, without having to invoke Bethe Ansatz solvability.…
In this paper, we revisit the problem of dirty superconductors using a replica-symmetric BCS (RS-BCS) theory. We apply the RS-BCS theory to dirty superconductor grains of size $L^d$, where $L$ is the localization length and $d$ is the…
Pairing effects manifests themselves in many aspects in nuclear systems ranging from finite nuclei to nuclear matter and compact stars. Although with some specific features for nuclear systems, the mechanism of pairing between nucleons in…
Pairing plays a central role in nuclear systems. The simplest model for the pairing is the constant-pairing Hamiltonian. The aim of the present paper is to include the continuum single particle level density in the constant pairing…
We study the static correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. Making use of the Algebraic Bethe Ansatz formalism, we obtain exact expressions…
The problem of the survival of superconductivity in a small super-conducting grain placed in a metal substrate is addressed. For this aim the pair correlations and super-conducting gap around and inside a negative-U impurity in one and two…
We present an extension of the pair coupled cluster doubles (p-CCD) method to quasiparticles and apply it to the attractive pairing Hamiltonian. Near the transition point where number symmetry gets spontaneously broken, the proposed…
We deal with a model for high-temperature superconductivity which maintains that in cuprates electrons running in the copper oxide layers, found in lattice of these materials, form spin-singlet bonds with electrons running in the…
We combine the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements to describe analytically how the superconducting gap depends on the size and shape of a 2d and 3d…
The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length $\xi$ is large, with two important features: the order…
We summarize previous works on the exact ground state and the elementary excitations of the exactly solvable BCS model in the canonical ensemble. The BCS model is solved by Richardson equations, and, in the large coupling limit, by Gaudin…
We deal with a model for high-temperature superconductivity which maintains that in cuprates spin-singlet bonds are formed between electrons running in the neighbouring layers of copper oxide found in lattice of these materials. This model…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
The BCS theory models electron correlations with pure zero-momentum pairs. Here we consider a family of pairing Hamiltonians, where the electron correlations are modelled with pure arbitrary-momentum pairs. We find all models in the family…
Unlike bulk superconductivity, where one energy scale, the energy gap, characterizes pairing correlations, we show that in small superconducting grains there exist two different such quantities. The first characterizes cumulative properties…
An exact-diagonalization technique on small clusters is used to study low-lying excitations and superconductivity in the two-dimensional negative-$U$ Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum, condensation…
Superconducting state is achieved through quantum condensation of Cooper pairs which are new types of charge carriers other than single electrons in normal metals. The theory established by Bardeen-Cooper-Schrieffer (BCS) in 1957 can…