Review: Luttinger or fermi liquids versus topological superconductivity

Abstract

Superconductors, classified by materials, embrace at least four broad groups: (i) BCS metals and alloys; (ii) heavy Fermion materials; (iii) high- T c cuprates and (some) organic compounds, and (iv) fullerides. Broadly speaking, in classes (i) and (iv), with (i) possibly embracing the recent discovery of superconductivity in MgB 2 with T c ∼ 40 K, electron liquids flow through essentially non-magnetic lattices and the electron-phonon interaction is a key component of the mechanism for Cooper pairing. In classes (ii) and (iii), plus the low- T c material Sr 2 RuO 4 , electron or hole liquids flow through assemblies with magnetic spin fluctuations. The nature of the normal state in class (iii) is not yet universally agreed, both Fermi or Luttinger liquids remaining viable to date, the former, however, with the formation of precursor 2 e Bosons somewhat above T c . Our own studies reveal some common ground between classes (ii) and (iii), involving coherence lengths and effective masses, as well as non- s -wave pairing, though the interactions leading to pairing almost certainly have different physical origins in these two groups. Finally, topological superconductivity is reviewed. It is argued that such a treatment of a topological superfluid could eventually deepen the understanding of the class (iv) fullerides. Resonating valence bond theory, used by Anderson and co-workers as an, of course, approximate strongly-correlated electron technique for high- T c cuprates, can itself be re-written in the form of topological superconductivity, as discussed especially by Wiegmann and collaborators.

Keywords:

• Fermi And Luttinger Liquids
• High- T c Cuprates
• Heavy Fermion Compounds
• Organic Superconductors
• Ruthenates
• Doped Fullerites
• Topological Superfluids