Size quantization in high-temperature superconducting cuprates and a link to Einstein's diffusion law |
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| Institution: | 1. Département d''Immuno-Hématologie, Inserm U. 1016, Institut Cochin, Paris, France;2. Service d''Hématologie et d''Immunologie, Hôpital Ambroise Paré, Boulogne, France;3. UFR Sciences de la Santé, Université de Versailles SQY, Versailles, France;4. Service d''Orthopédie, Hôpital Ambroise Paré, Boulogne, France;5. Service de Réanimation, Hôpital Georges Pompidou, Paris, France;6. Université Paris Descartes, Paris, France;7. Division of Medicine, Center for Cardiovascular Biology and Medicine, University College, London, UK |
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| Abstract: | Optimum doping of high-temperature superconductors (HTSC) defines a superconducting unit volume for each HTSC. For a single-mode HTSC, e.g., a cuprate with one CuO2 plane, the volume is given by Vsc=cx2, where c is the unit cell height and x the doping distance. The experimental resistivity at Tc is connected to the structure by ρ(exp)≈c×h/(2e2). Combining this result with the classical definition of resistivity leads to an equation similar to Einstein's diffusion law x2/(2τ)=h/(2Meff)=D, where τ is the relaxation time, Meff=2me and D the diffusion constant. It has also been shown that the mean free path d=x. The Einstein–Smoluchowski diffusion relation D=μkBTc provides a connection to Tc. |
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