Effects of gap fluctuations on the pair-transfer correlation function in nanometer-scale superconducting grains (original) (raw)
Related papers
Journal of Physics: Condensed Matter, 2012
Superconducting correlations in an isolated metallic grain are governed by the interplay between two energy scales: the mean level spacing δ and the bulk pairing gap 0 , which are strongly influenced by the position of the chemical potential with respect to the closest single-electron level. In turn superconducting correlations affect the position of the chemical potential. Within the parity projected BCS model we investigate the probability distribution of the chemical potential in a superconducting grain with randomly distributed single-electron levels. Taking into account statistical fluctuations of the chemical potential due to the pairing interaction, we find that such fluctuations have a significant impact on the critical level spacing δ c at which the superconducting correlations cease: the critical ratio δ c / 0 at which superconductivity disappears is found to be increased.
Pair correlations and the survival of superconductivity in and around a superconducting impurity
Physical Review B, 2007
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 dimensions is calculated, in a discrete tight-binding model and a continuous model. Using a mean-field decomposition, it is shown that finite pairing in the grain develops when the system has a degeneracy between successive number of electron pairs, and thus may oscillate as a function of the chemical potential. For finite pairing in the island, pair correlations in the normal part exhibit a cross-over from being long-ranged to exponentially decaying, depending on the strength of interaction in the grain. It is shown analytically that there is a minimal island size under-which pairing vanishes which is different than that given by Anderson's criterion, and that it scales as a power-law with island size, rather then exponentially as in isolated grains.
Two pairing parameters in superconducting grains
Physical Review B, 2003
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 of the grain, such as the condensation energy, and the second single-particle properties. To describe these two energy scales, we define two corresponding pairing parameters, and show that although both reduce to the bulk gap for large grains, this occurs at different size scales.
Quantum fluctuations in superconducting dots at finite temperature
We study the thermodynamics of ultrasmall metallic grains with level spacing delta\deltadelta comparable or smaller than the pairing correlation energy, at finite temperatures, TgsimdeltaT \gsim \deltaTgsimdelta. We describe a method which allows to find quantum corrections to the effect of classical fluctuations. We present results for thermodynamic quantities in ordered grains and for the reentrant odd susceptibility in disordered grains.
Superconducting correlations in ultra-small metallic grains
Europhysics Letters (EPL), 2000
To describe the crossover from the bulk BCS superconductivity to a fluctuationdominated regime in ultrasmall metallic grains, new order parameters and correlation functions, such as "parity gap" and "pair-mixing correlation function", have been recently introduced. In this paper, we discuss the small-grain behaviour of the Penrose-Onsager-Yang off-diagonal long-range order (ODLRO) parameter in a pseudo-spin representation. Relations between the ODLRO parameter and those mentioned above are established through analytical and numerical calculations.
Pairing dynamics in strongly correlated superconductivity
Physical Review B, 2009
Confirmation of the phononic origin of Cooper pair formation in superconductors came with the demonstration that the interaction was retarded and that the corresponding energy scales were associated with phonons. Using cellular dynamical mean-field theory for the two-dimensional Hubbard model, we identify such retardation effects in d-wave pairing and associate the corresponding energy scales with short-range spin fluctuations. We find which frequencies are relevant for pairing as a function of interaction strength and doping and show that the disappearance of superconductivity on the overdoped side coincides with the disappearance of the low-energy feature in the antiferromagnetic fluctuations, as observed in neutron-scattering experiments.
Exact study of the effect of level statistics in ultrasmall superconducting grains
Physical Review B, 2000
The reduced BCS model that is commonly used for ultrasmall superconducting grains has an exact solution worked out long ago by Richardson in the context of nuclear physics. We use it to check the quality of previous treatments of this model, and to investigate the effect of level statistics on pairing correlations. We find that the ground state energies are on average somewhat lower for systems with non-uniform than uniform level spacings, but both have an equally smooth crossover from the bulk to the few-electron regime. In the latter, statistical fluctuations in ground state energies strongly depend on the grain's electron number parity.
Small Superconducting Grain in the Canonical Ensemble
Physical Review Letters, 1998
By means of the Lanczos method we analyze superconducting correlations in ultrasmall grains at fixed particle number. We compute the ground state properties and the excitation gap of the pairing Hamiltonian as a function of the level spacing delta\deltadelta. Both quantities turn out to be parity dependent and universal functions of the ratio delta/Delta\delta/\Deltadelta/Delta ($\Delta$ is the BCS gap). We then characterize superconductivity in the canonical ensemble from the scaling behavior of correlation functions in energy space.
Pairing Fluctuation Effects on the Single-Particle Spectra for the Superconducting State
Physical Review Letters, 2004
Single-particle spectra are calculated in the superconducting state for a fermionic system with an attractive interaction, as functions of temperature and coupling strength from weak to strong. The fermionic system is described by a single-particle self-energy that includes pairing-fluctuation effects in the superconducting state. The theory reduces to the ordinary BCS approximation in weak coupling and to the Bogoliubov approximation for the composite bosons in strong coupling. Several features of the single-particle spectral function are shown to compare favorably with experimental data for cuprate superconductors.