Non-Fermi-liquid transport phenomena and superconductivity driven by orbital fluctuations in iron pnictides: Analysis by fluctuation-exchange approximation

We study the five-orbital Hubbard model including the charge quadrupole interaction for iron pnictides. Using the fluctuation-exchange approximation, orbital fluctuations evolve inversely proportional to the temperature, and therefore the resistivity shows linear or convex $T$ dependence for a wide range of temperatures. We also analyze the Eliashberg gap equation, and show that an $s$-wave superconducting state without sign reversal ($s_{++}$-wave state) emerges when the orbital fluctuations dominate over the spin fluctuations. When both fluctuations are comparable, their competition gives rise to a nodal $s$-wave state. The present study offers us a unified explanation for both the normal and superconducting states.

Figure 1

(a) FSs in the unfolded zone. The dotted circles represent the cold spot given by the orbital fluctuation theory. The cold spot is composed of $xz/yz$ orbitals. (b) Phonon-mediated el-el interaction ($\widehat{V}$) for $2,3,4$ orbitals.

Figure 2

(a) $\mathit{k}$ dependence of ${\gamma }^{s\left(c\right)}$ induced by the spin (orbital) fluctuations on each FS. Note that ${\gamma }^s$ decreases with $g$ due to the suppression of ${\widehat{\chi }}^s$ by ${\gamma }^c$. (b) $T$ dependence of $S_{s\left(c\right)}={(1-{\alpha }_{s\left(c\right)})}^{-1}$. (c), (d) $T$ dependence of $\rho$. $\rho =1$ corresponds to $\left(\hslash a_c\right)/e^2\sim 300\mu$cm$\Omega$ when the interlayer distance is $a_c=0.6$ nm.

Figure 3

$T$ dependence of $S$ for (a) $U=1.2$ and (b) $U=1.8$.

Figure 4

(a) $U$-$g$ phase diagram given by solving the linearized Eliashberg equation at $T=0.015$. Nodal $s$-wave gap state is obtained in the shaded area for $n_{\mathrm{imp}}=0.02$ and 0.05, and solid lines (dotted lines) represent the boundary between fully gapped $s_{+-}$-wave ($s_{++}$-wave) state. Dashed-dotted line denotes ${\alpha }_c=0.98$. (b) $s_{++}$-wave gap (${\lambda }_{\mathrm{E}}=0.59$) for $U=0$ and $g=0.24$. (c) $s_{+-}$-wave gap (${\lambda }_{\mathrm{E}}=0.49$) for $U=1.8$ and $g=0$ and. (d) Nodal $s$-wave gap (${\lambda }_{\mathrm{E}}=0.28$) for $U=1.2$ and $g=0.15$.

Figure 5

(a) $n$ dependence of ${\lambda }_{\mathrm{E}}$ for $s_{++}$- and $s_{+-}$-wave states at $T=0.02$ and $n_{\mathrm{imp}}=0$. (b) $g$ dependence of ${\lambda }_{\mathrm{E}}$ for $s_{++}$-wave state at $T=0.015$ and $n_{\mathrm{imp}}=0$.