Correlation-Enhanced Odd-Parity Interorbital Singlet Pairing in the Iron-Pnictide Superconductor LiFeAs

The rich variety of iron-based superconductors and their complex electronic structure lead to a wide range of possibilities for gap symmetry and pairing components. Here we solve in the two-Fe Brillouin zone the full frequency-dependent linearized Eliashberg equations to investigate spin-fluctuations mediated Cooper pairing for LiFeAs. The magnetic excitations are calculated with the random phase approximation on a correlated electronic structure obtained with density functional theory and dynamical mean field theory. The interaction between electrons through Hund’s coupling promotes both the intraorbital $d_{xz(yz)}$ and the interorbital magnetic susceptibility. As a consequence, the leading pairing channel, conventional $s^{+-}$, acquires sizable interorbital $d_{xy}-d_{xz(yz)}$ singlet pairing with odd parity under glide-plane symmetry. The combination of intra- and interorbital components makes the results consistent with available experiments on the angular dependence of the gaps observed on the different Fermi surfaces.

Figure 1

Partial spectral weight, $A_{ll}(\mathbf{k},0)$, of Fe $t_{2g}$- orbitals on the FS in the $k_x\text{−}{k}_y$ plane with $k_z=0$ (left) and $k_z=\pi /c$ (right) obtained from the $\mathrm{LDA}+\mathrm{DMFT}$ calculation. Here the $d_{xy}$, $d_{xz}$, and $d_{yz}$ orbitals are illustrated by green, blue, and red colors, respectively. The ${\alpha }_1$ pocket crosses the Fermi level only in close vicinity to the $\mathrm{\Gamma }$ point (not visible on this scale).

Figure 2

Several components of the pairing interaction of LiFeAs at $k_{B}T=0.01\mathrm{eV}$ in the particle-hole channel. There are two sets of screened interaction parameters yielding the same magnetic Stoner factor, namely, $J_s=0.1U_s$, $U_s=2.4\mathrm{eV}$ on the top and $J_s=0.3U_s$, $U_s=1.68\mathrm{eV}$ on the bottom. The legend for the color coding is spread over both figures.

Figure 3

Real part of the several intrasublattice components of the generalized particle-particle bare susceptibility at the lowest fermionic and bosonic Matsubara frequency.

Figure 4

Top panels: The real part of the $d_{xy}$ (left) and $d_{xz}$ (right) in-plane intraorbital components of the SC gap function at the lowest Matsubara frequency with the largest eigenvalue in the orbital representation for $J_s/U_s=0.3$ and $k_{B}T=0.01\mathrm{eV}$. The imaginary part can be obtained from $\mathrm{Im}{\mathrm{\Delta }}_{ll}=-\mathrm{Re}{\mathrm{\Delta }}_{ll}$. Bottom panels: The real or imaginary part of the interorbital components of the SC gap function on sublattice $A$ in the orbital representation, ${\mathrm{\Delta }}_{l_1{l}_2}^{AA}$. The corresponding components on sublattice $B$ are out of phase with the displayed components, i.e., ${\mathrm{\Delta }}_{l_1{l}_2}^{BB}=-{\mathrm{\Delta }}_{l_1{l}_2}^{AA}$. The lines show one quarter of the Fermi surfaces.

Figure 5

For $J_s/U_s=0.3$, the SC gap magnitude (in units of the average gap magnitude on the ${\alpha }_1$ pocket) as a function of the angle $\theta$ measured at the $\mathrm{\Gamma }$ and $M$ points with respect to the $x$ axis for $k_z=0$ FSs.