Multi-Band Superconductivity and the Steep Band/Flat Band Scenario

Abstract

The basic features of multi-band superconductivity and its implications are derived. In particular, it is shown that enhancements of the superconducting transition temperature take place due to interband interactions. In addition, isotope effects differ substantially from the typical BCS scheme as soon as polaronic coupling effects are present. Special cases of the model are polaronic coupling in one band as realized e.g., in cuprates, coexistence of a flat band and a steep band like in MgB2, crossovers between extreme cases. The advantages of the multiband approach as compared to the single band BCS model are elucidated and its rather frequent realization in actual systems discussed.

Single-gap versus two-gap scenario: Specific heat and thermodynamic critical field of the noncentrosymmetric superconductor BeAu

“…The simplest, i.e., the two-gap version of the α model, assumes the gaps are described within the weakly coupled BCS approach by following the functional form derived by Mühlschlegel [52]. The more advanced version determines temperature evolutions of the small and big gaps by solving the coupled gap equations self-consistently [41][42][43][44][45].…”

“…The important clue of these extensions to superconductivity is an interband pair scattering potential, which leads to enhanced pair scattering via exchange through an additional channel. The revised version of the model for two isotropic s-wave gaps was recently reconsidered in a series of publications by Kogan et al [41,42] and Bussmann-Holder et al [43][44][45]. Here, the approach developed in Refs.…”

“…Following Refs. [43][44][45]50,64,65], within the two-gap approach, the coupled s-wave gap equations are described as…”

“…For example, this is the case in the analysis of conventional elemental and binary superconductors within the framework of the empirical α model (see Refs. [34][35][36][37][38]) and the Eliashberg approach (see the classic reviews of Carbotte [39] and Marsiglio and Carbotte [40]) and the two-gap superconductors within the self-consistent approach using models developed by Kogan et al [41,42] and Bussmann-Holder et al [43][44][45].…”

A Lattice Litany for Transition Metal Oxides

“…Substantial Tc enhancement and tunability is possible, which is controlled by the interband coupling strengths and locations (in k-space) (e.g., [51]). Resonant coupling (e.g., Fermi resonance) is especially intriguing and is well-covered in this volume and elsewhere [52]. Clearly, the mesoscopic phase separation of lattice, charge, spin broken-and unbroken-symmetry regions described above provide environments for these scenarios, with stripes and TBs sources of flat electronic bands.…”