Functional Renormalization-Group Study of the Pairing Symmetry and Pairing Mechanism of the FeAs-Based High-Temperature Superconductor

We apply the fermion functional renormalization-group method to determine the pairing symmetry and pairing mechanism of the FeAs-Based materials. Within a five band model with pure repulsive interactions, we find an electronic-driven superconducting pairing instability. For the doping and interaction parameters we have examined, extended $s$ wave, whose order parameter takes on opposite sign on the electron and hole pockets, is always the most favorable pairing symmetry. The pairing mechanism is the inter-Fermi-surface Josephson scattering generated by the antiferromagnetic correlation.

Figure 1

(a) A schematic representation of the gap functions on different Fermi surfaces. The Fermi surfaces are shown in black dashed lines. The width of the region between the solid line and dashed line indicates the magnitude of the gap function, and the sign is represented by the colors. (b) Two (red and blue arrows) typical inter-Fermi-surface pair transfer (Josephson) processes that drive pairing. (c) The five Feynman diagrams contributing to the renormalization of the vertex function.

Figure 2

(a) The $N=32$ RG evolution of the scattering amplitude in the top four attractive Cooper channels for 0.1 electron doped system (6.1 electrons per site). Here ${\Lambda }_0=2.2\mathrm{eV}$ is the initial energy cutoff, and $\Lambda$ is the running energy cutoff. The constant $a=-1/\ln (0.97)$. (b) The gap function associated with the most attractive pairing channel determined from the final ($a\ln ({\Lambda }_0/\Lambda )=101$) renormalized interaction vertex function. Here $0\dots 4$ label five Fermi surfaces (see Fig. 4 for their definition). It has a full gap and exhibits significant amplitude modulation on the electron pockets (Fermi surface 2 and 3). More importantly, the sign of the gap function is different on the electron and hole packets.

Figure 3

(a) The $N=32$ RG evolution of the scattering amplitude in the top four attractive Cooper channels for 0.1 hole doped system (5.9 electrons per site), where ${\Lambda }_0=2.2\mathrm{eV}$ and $a=-1/\ln (0.97)$. (b) The gap function associated with the most attractive ($s$-wave) pairing channel determined from the final [$a\ln ({\Lambda }_0/\Lambda )=101$] renormalized interaction vertex function. It has a full gap, and exhibits significant amplitude modulation on Fermi surfaces 0, 1, 2, and 3.

Figure 4

The Brillouin zone patching scheme. Here the five disjoint Fermi surfaces are labeled from 0 to 4. The left panel is for the band with smaller hole pocket at (0,0) (FS 0). The right top panel is for the band with larger hole pocket at (0,0) (FS 1) and hole pocket at ($\pi$, $\pi$) (FS 4). The right bottom panel is for the electron pockets (FS 2 and FS 3).