Superconductivity and spin-density-waves in multi-band metals

TL;DR

This paper investigates the conditions under which superconductivity and spin-density waves coexist in multi-band metals, especially in iron-based pnictides, highlighting the effects of Fermi surface differences and incommensurability.

Contribution

It provides a comprehensive theoretical framework for understanding the coexistence of SC and SDW orders in two-band metals, including the influence of Fermi surface geometry and order incommensurability.

Findings

Conventional s-wave SC coexists with SDW only at very low temperatures and narrow parameter ranges.

Extended s-wave SC with sign-changing gaps coexists with SDW over wider conditions.

Incommensurate SDW enhances the coexistence region between SC and SDW.

Abstract

We present a detailed description of two-band quasi-2D metals with s-wave superconducting (SC) and antiferromagnetic spin-density wave (SDW) correlations. We present a general approach and use it to investigate the influence of the difference between the shapes and the areas of the two Fermi surfaces on the phase diagram. In particular, we determine the conditions for the co-existence of SC and SDW orders at different temperatures and dopings. We argue that a conventional s-wave SC order co-exists with SDW order only at very low $T$ and in a very tiny range of parameters. An extended s-wave superconductivity, for which SC gap changes sign between the two bands, co-exists with antiferromagnetic SDW over a much wider range of parameters and temperatures, but even for this SC order the regions of SDW and SC can still be separated by a first order transition. We show that the co-existence range becomes larger if SDW order is incommensurate. We apply our results to iron-based pnictide materials, in some of which co-existence of SDW and SC orders has been detected.