Superconductivity from the repulsive electron interaction -- from 1D to 3D

TL;DR

This paper reviews how anisotropic superconductivity can emerge from repulsive electron interactions, spanning from 1D ladders to 3D systems, highlighting the role of disconnected Fermi surfaces in enhancing transition temperatures.

Contribution

It provides a comprehensive overview of the mechanisms enabling superconductivity from repulsive interactions across different dimensions, emphasizing the importance of disconnected Fermi surfaces for higher $T_C$.

Findings

Superconductivity with repulsive interactions appears in multi-leg ladders.

Anisotropic (d-wave) pairing mediated by spin fluctuations extends to 2D.

Disconnected Fermi surfaces can significantly increase $T_C$.

Abstract

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.