Spin fluctuation dynamics and multiband superconductivity in iron pnictides

Multiband superconductivity, involving resonant pair scattering between different bands, has emerged as a possible explanation of some of the main characteristics of the recently discovered iron pnictides. A key feature of such interband pairing mechanism is that it can generate or enhance superconductivity irrespective of whether it is attractive or repulsive. The latter case typically leads to the superconducting gap switching its sign among different sections of the Fermi surface. In iron pnictides, the natural scenario is that the gap changes sign between the hole and the electron Fermi surfaces. However, the macroscopic symmetry of such an extended $s^{\prime }$-wave state still belongs to the general $s$-wave category, raising the question of how to distinguish it from an ordinary $s$ wave. In such a quest, it is essential to use experimental techniques that have a momentum space resolution and can probe momenta of order $\left(\pi ,\pi \right)$: the wave vector that separates the hole and the electron Fermi surfaces in the Brillouin zone. Here we study experimental signatures in the spin fluctuation dynamics of the fully gapped $s$- and $s^{\prime }$-wave superconducting states, as well as those of the nodal $d$ and $p$ wave states. The coupling between spin fluctuations of the incipient nearly nested spin-density wave (SDW) and the Bogoliubov-de Gennes quasiparticles of the superconducting state leads to the Landau-type damping of the former. The intrinsic structure of the superconducting gap leaves a distinctive signature in the form of this damping, allowing it to be used to diagnose the nature of iron-based superconductivity in neutron scattering and other experiments sensitive to spin fluctuations in momentum space. We also discuss the coexistence between superconductivity and SDW order.

Figure 1

An illustration of our model: a hole band $\left(c\right)$ centered at the $\Gamma$ point and an electron band $\left(d\right)$ centered at the $M=\left(\pi ,\pi \right)$ point interact via a short-range interaction $U$.

Figure 2

Fermi surfaces of inequivalent hole and electron bands. Their centers are displaced by the vector $\Delta {\vec{k}}_F$ defined in the text.

Figure 3

Coexistence of SDW and superconductivity in our model. The chemical potential $\mu$ is above the SDW gap while the superconducting gap is always pinned to $\mu$.

Figure 4

Contour plots illustrating Table , with the temperature fixed to some $T<T_c$. The damping term in the $\omega -v_{F}q$ plane is shown for perfect nesting—the brighter the shade indicates stronger damping. There is no damping for $\omega >v_{F}q$. The reader should be warned that our results become less reliable close to this boundary.

Figure 5

The illustration of the relatively mild sensitivity of the two superconducting gaps to differences in the DOSs between electron and hole bands $\left[\left(N_2-N_2\right)/N_2\right]$. The gaps were computed from Eq. (22), without retardation effects, using ${\mu }_1=0.3$ and ${\lambda }_1=0.5$, for up to 10% difference in DOSs and are measured in units of ${10}^{-2}{\omega }_C$.