Effects of Coulomb interactions on the superconducting gaps in iron-based superconductors

Recent angle-resolved photoemission spectroscopy measurements of Co-doped LiFeAs report a large and robust superconducting gap on the $\mathrm{\Gamma }$-centered hole band that lies 8 meV below the Fermi level. We show that, unlike a conventional superconductor described by BCS theory, a multiband system with strong interband Coulomb interactions can explain these observations. We model LiFeAs with a five-band model in which the shallow hole band is coupled with the other bands by only Coulomb interactions. Using Eliashberg theory, we find reasonable interaction parameters that reproduce the $T_c$ and all five gaps of LiFeAs. The energy independence of the Coulomb interactions then ensures the robustness of the gap induced on the shallow band. Furthermore, due to the repulsive nature of the Coulomb interactions, the gap changes sign between the shallow band and the other hole pockets, corresponding to an unconventional $s_{\pm }$ gap symmetry. Unlike other families of iron-based superconductors, the gap symmetry of LiFeAs has not been ascertained experimentally. The experimental implications of this sign-changing state are discussed.

Figure 1

ARPES results of 3% Co-doped LiFeAs from Ref. [11]. Left: The ARPES intensity plot in the normal state, showing that the shallow hole band at the $\mathrm{\Gamma }$ point is 8 meV below the Fermi level. Middle: The same plot in the superconducting state, showing that the large gap on the shallow band is robust against the Lifshitz transition. Right: A combined plot of the shallow band's spectral weights in both the normal and superconducting states, showing significant changes between the two states even well below the Fermi level.

Figure 2

A schematic of the Fermi surfaces of LiFeAs. In our model, the deep hole bands $\left(1,2\right)$ are coupled with the deep electron bands $\left(3,4\right)$ via interactions mediated by spin fluctuations. In addition, the shallow hole band $\left(5\right)$ is coupled with the inner deep hole band $\left(1\right)$ via Coulomb interactions.

Figure 3

A plot of the energy gap against temperature for the five-band model of LiFeAs. The gaps agree with experimental measurements at low temperatures. The interaction parameters used are shown in Table 1.

Figure 4

A plot of the energy gaps against the Coulomb interactions showing Coulomb interactions inducing a large gap on the shallow hole band. Due to the energy independence of Coulomb interactions, the induced gap is robust against changes in the Fermi energy.

Figure 5

A plot showing the effects of Coulomb interactions on $T_c$. In LiFeAs, Coulomb interactions enhance the $T_c$ by a factor of $1.7$.