Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2003-05-21
Physics
Condensed Matter
Strongly Correlated Electrons
27 pages, 10 figures, in Tobias Brandes et al.(ed.): The Anderson Transition and its Ramifications -- Localisation, Quantum In
Scientific paper
An overview is given on how superconductivity with anisotropic pairing can be realised from repulsive electron-electron interaction. (i) We start from the physics in one dimension, where the Tomonaga-Luttinger theory predicts that, while there is no superconducting phase for the repulsive case for a single chain, the phase does exists in ladders with the number of legs equal to or greater than two, as shown both by analytically (renormalisation) and numerically (quantum Monte Carlo). (ii) We then show how this pairing has a natural extension to the two-dimensional case, where anisotropic (usually d) pairing superconductivity arises mediated by spin fluctuations (usually antiferromagnetic), as shown both by analytically (renormalisation) and numerically (quantum Monte Carlo). (iii) We finally discuss how the superconductivity from the electron repulsion can be "optimised" (i.e., how $T_C$ can be raised) in 2D and 3D, where we propose that the anisotropic pairing is much favoured in systems having {\it disconnected Fermi surfaces} where $T_C$ can be almost an order of magnitude higher.
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