Subgap tunneling via quantum-interference effect: insulators and charge density waves

A quantum interference effect is discussed for subgap tunneling over a distance comparable to the coherence length, which is a consequence of ``advanced-advanced'' and ``retarded-retarded'' transmission modes [Altland and Zirnbauer, Phys. Rev. B 55, 1142 (1997)]. Effects typical of disorder are obtained from the interplay between multichannel averaging and higher order processes in the tunnel amplitudes. Quantum interference effects similar to those occurring in normal tunnel junctions explain magnetoresistance oscillations of a CDW pierced by nanoholes [Latyshev et al., Phys. Rev. Lett. 78, 919 (1997)], having periodicity h/2e as a function of the flux enclosed in the nanohole. Subgap tunneling is coupled to the sliding motion by charge accumulation in the interrupted chains. The effect is within the same trend as random matrix theory for normal metal-CDW hybrids [Visscher et al., Phys. Rev. B 62, 6873 (2000)]. We suggest that the experiment by Latyshev et al. probes weak localization-like properties of evanescent quasiparticles, not an interference effect related to the quantum mechanical ground state.Comment: 13 pages, 11 figures, article rewritten, new section on wave-function matchin

Non local Andreev reflection in a carbon nanotube superconducting quantum interference device

We investigate a superconducting quantum interference device (SQUID) based on carbon nanotubes in a fork geometry [J.-P. Cleuziou {\it et al.}, Nature Nanotechnology {\bf 1}, 53 (2006)], involving tunneling of evanescent quasiparticles through a superconductor over a distance comparable to the superconducting coherence length, with therefore ``non local'' processes generalizing non local Andreev reflection and elastic cotunneling. Non local processes induce a reduction of the critical current and modify the current-phase relation. We discuss arbitrary interface transparencies. Such devices in fork geometries are candidates for probing the phase coherence of crossed Andreev reflection.Comment: 13 pages, 8 figures, revised versio

Thouless energy of a superconductor from non local conductance fluctuations

We show that a spin-up electron from a normal metal entering a superconductor propagates as a composite object consisting of a spin-down hole and a pair in the condensate. This leads to a factorization of the non local conductance as two local Andreev reflections at both interfaces and one propagation in the superconductor, which is tested numerically within a one dimensional toy model of reflectionless tunneling. Small area junctions are characterized by non local conductance fluctuations. A treatment ignoring weak localization leads to a Thouless energy inverse proportional to the sample size, as observed in the numerical simulations. We show that weak localization can have a strong effect, and leads to a coupling between evanescent quasiparticles and the condensate by Andreev reflections ``internal'' to the superconductor.Comment: 11 pages, 12 figures, revised manuscrip

Dephasing of Andreev pairs entering a charge density wave

An Andreev pair from a s-wave superconductor (S) entering a conventional gapless charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length, not by the Fermi wave-length.Comment: 8 pages, 2 figures, revised manuscrip

Performance Scores in General Practice: A Comparison between the Clinical versus Medication-Based Approach to Identify Target Populations

CONTEXT: From one country to another, the pay-for-performance mechanisms differ on one significant point: the identification of target populations, that is, populations which serve as a basis for calculating the indicators. The aim of this study was to compare clinical versus medication-based identification of populations of patients with diabetes and hypertension over the age of 50 (for men) or 60 (for women), and any consequences this may have on the calculation of P4P indicators. METHODS: A comparative, retrospective, observational study was carried out with clinical and prescription data from a panel of general practitioners (GPs), the Observatory of General Medicine (OMG) for the year 2007. Two indicators regarding the prescription for statins and aspirin in these populations were calculated. RESULTS: We analyzed data from 21.690 patients collected by 61 GPs via electronic medical files. Following the clinical-based approach, 2.278 patients were diabetic, 8,271 had hypertension and 1.539 had both against respectively 1.730, 8.511 and 1.304 following the medication-based approach (% agreement = 96%, kappa = 0.69). The main reasons for these differences were: forgetting to code the morbidities in the clinical approach, not taking into account the population of patients who were given life style and diet rules only or taking into account patients for whom morbidities other than hypertension could justify the use of antihypertensive drugs in the medication-based approach. The mean (confidence interval) per doctor was 33.7% (31.5-35.9) for statin indicator and 38.4% (35.4-41.4) for aspirin indicator when the target populations were identified on the basis of clinical criteria whereas they were 37.9% (36.3-39.4) and 43.8% (41.4-46.3) on the basis of treatment criteria. CONCLUSION: The two approaches yield very "similar" scores but these scores cover different realities and offer food for thought on the possible usage of these indicators in the framework of P4P programmes