The idea of superconductivity without the mediating role of lattice vibrations (phonons) has a long history. It was realized soon after the publication of the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity 50 years ago that a full treatment of both the charge and spin degrees of freedom of the electron predicts the existence of attractive components of the effective interaction between electrons even in the absence of lattice vibrations—a particular example is the effective interaction that depends on the relative spins of the electrons. Such attraction without phonons can lead to electronic pairing and to unconventional forms of superconductivity that can be much more sensitive than traditional (BCS) superconductivity to the precise details of the crystal structure and to the electronic and magnetic properties of a material.

1. School of Physics,
   
2. Centre for Science at Extreme Conditions, University of Edinburgh, Edinburgh EH9 3JZ, UK
   
3. G756 Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
   
4. Institute for Complex Adaptive Matter and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
   
5. Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK

Correspondence to: G. G. Lonzarich⁵ Correspondence and requests for materials should be addressed to G.G.L. (Email: GGL1@phy.cam.ac.uk).