Final Report Summary - SCQSR (Superconductivity in quantum-size regime)
1. 1. A summary description of the project objectives
In the last decades, the quasi low-dimensional correlated electron systems have been the focus of the theoretical and experimental investigations due to their rich variety of normal and superconducting properties not found in three-dimensional materials. Amongst them layered superconductors and superconducting confined nanostructures (mostly, nanowires and films) have attracted much attention. The interplay between electronic correlations and enhanced dimensionality effects leads to a broad range of physical properties observed in these structures.
Layered organic metals are distinctive for a number of reasons. Most of them exhibit profound reduced dimensionality reflected in the very strong charge-transfer anisotropy. Moreover, organic metals are often available in highly clean single crystals that enables one to study mechanisms of superconductivity in quasi-low-dimensional electronic systems. Finally one of the most prominent property of organic layered superconductors is their robustness against high magnetic fields applied parallel to the conduction layers.
The main motivation to study the superconducting nanostructures comes from experiments recently performed with extremely small superconductors. These experimental studies became possible due to recent technological advances that resulted in the fabrication of high-quality low resistivity superconducting metallic nanofilms and nanowires being in the clean limit for the confined motion of electrons, and also single isolated metallic nanoparticles, which promises important technological applications.
The key aspect of the research project was the interplay between superconductivity and quantum confinement and the particular objectives of the project were following:
to investigate the FFLO state in the layered superconductors;
to calculate the quantum-size correction to the critical magnetic field in superconducting nanostuctures;
to study the current-carrying state in superconducting nanostructures;
to explore the possibility to qualitatively tune the superconducting characteristics by varying multilayered parameters. Hybrid structures;
to investigate the inhomogeneity of the pair condensate due to confinement and parity effects in superconducting grains. New Andreev-type states;
to discuss the influence of superconducting nanostructure size and shape on the charge and electric field distribution in order to be probed by the single-molecule technique developed in University of Bordeaux.
1. 2. A description of the work performed and main results achieved since the beginning of the project
During the project period the following research topics were studied:
1. 2. 1. FFLO state in layered superconductors: Almost 50 years ago, Fulde and Ferrell, at the same time as Larkin and Ovchinnikov, suggested that in clean superconductors at T < 0. 56 TC a paired state described by the spatially modulated order parameter becomes favourable when the spin effect of the magnetic field dominates over the orbital effect of the magnetic field. There have been observed several hints indicating the experimental realisation of the FFLO state in organic superconductors when external magnetic field is aligned along the conducting planes and in heavy fermion superconductors. Although searches for the FFLO state have been carried out exhaustively, unambiguous experimental evidence has remained elusive.
Recently an anomalous in-plane anisotropy of the onset of superconductivity in (TMTSF) 2ClO4 conductor have been reported. The behaviour is discussed in connection with the possibility of the FFLO state formation. During our research it was demonstrated that:
the anisotropy of the onset of superconductivity may change dramatically in the FFLO state as compared with the conventional superconducting phase, that permits one to suggest that the modulated phase stabilisation is at the origin of the anisotropy of Hc2 observed in the experiment.
the resonance between the period of the FFLO modulation and the period of the interlayer coupling modulation induced by the external field may lead to anomalous cusps in the field-direction dependence of the upper critical field. Their experimental observation may serve as an ambiguous evidence for the appearance of the FFLO phase in layered superconductors.
the interplay between the nodal structure of the order parameter (d-wave symmetry) and its spatial modulation results in the very peculiar angular dependence of the onset of superconductivity in the high-field regime. The principal axis of the field-direction dependence of the onset of superconductivity is tilted in the range of temperatures 0. 056 TC < T < 0. 56 TC.
It is our belief that these new results are of timely interest to the community. Our findings open the exiting perspectives to use the in-plane anisotropy as a smoking gun of the FFLO phase in layered superconductors.
1. 2. 2. Quantum-size correction to the critical magnetic field in superconducting nanostuctures: It was investigated the effect of a parallel magnetic field on the orbital motion of electrons in high-quality superconducting nanowires. It was found based on a numerical solution of the Bogoliubovde Gennes equations taking into account the spinmagnetic-field interaction, that it results in a superconductor-to-normal transition which occurs through a cascade of jumps in the order parameter as a function of the magnetic field. Investigation of the current-carrying state was performed before the project and published in Croitoru M. D. et al, Phys. Rev. B 80, 024513 (2009).
1. 2. 3. Tuning of the superconducting characteristics by varying multilayered parameters. Hybrid structures: The interplay between superconductivity (S) and ferromagnetism (F) due to their incompatible nature is one of the fundamental problems in condensed matter physics. The coexistence of s-wave superconductivity and ferromagnetism can be achieved near interface in S/F hybrid structures owing to the proximity effect that arises from the mutual influence of the superconducting and magnetic ordering in the constituent materials of the structure. Recently an experimental observation of the thermally-induced anomaly in the density-of-states of S/dilute F alloy bilayer was reported. In this project we performed a theoretical study of such bilayer and
explained the origin of the thermally-induced anomaly in the density-of-states of the SF bilayer.
investigated the upper critical field in a superconductor/ferromagnetic alloy bilayer in the limit of thin superconducting layers.
1. 2. 4. The inhomogeneity of the pair condensate due to confinement and parity effects in superconducting grains. New Andreev-type states: In our project we
focused on the effect of quantum confinement in superconducting grains that was not studied previously, i. e., spatially non-uniform pairing. It was demonstrated that this effect was very significant when single-electron levels form bunches and/or a kind of shell structure. We found that it was closely related to a QC-induced modification of the pairing-interaction matrix elements and size-dependent pinning of the chemical potential to groups of degenerate or nearly degenerate levels.
investigated how the interplay of quantum confinement and particle number-parity fluctuations affects superconducting correlations in ultra-small metallic grains. We showed that the experimentally observed anomalous increase of the coupling ratio ?E/kTC with decreasing superconducting grain size can be attributed to an enhancement of the number-parity fluctuations in ultra-small grains.
investigated 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 found that such fluctuations have a significant impact on the critical level spacing.
studied of a cigar-shaped ultracold superfluid Fermi gas. It was demonstrated here an atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantisation of the particle motion and the aggregate condensate containing both BCS and BEC-like components.
1. 3. Expected final results and their potential impact and use
The obtained results are expected to be of interest to a broad community of physicists working in the field of superconductivity as well as to technologies designing novel applications based on superconducting nanostructures. They support the interpretation of the simulations and currently available experimental data as well as to guide further experimental work