Mechanism for Explaining Differences in the Order Parameters of FeAs-Based and FeP-Based Pnictide Superconductors

We put forward a scenario that explains the difference between the order-parameter character in arsenide (As) and phosphorous (P) iron-based superconductors. Using functional renormalization group to analyze it in detail, we find that nodal superconductivity on the electron pockets (hole pocket gaps are always nodeless) can naturally appear when the hole pocket at $(\pi ,\pi )$ in the unfolded Brillouin zone is absent, as is the case in LaOFeP. There, electron-electron interactions render the gap on the electron pockets softly nodal (of $s^{\pm }$ form). When the pocket of $d_{xy}$ orbital character is present, intraorbital interactions with the $d_{xy}$ part of the electron Fermi surface drives the superconductivity nodeless.

Figure 1

Band structure for LaOFeAs (a) and LaOFeP (b). (Inset: Brillouin zone.) The tight-binding model for LaOFeAs is given in 5; the parameters are varied for LaOFeP according to the different pnictogen height parameter [25]. The dashed horizontal lines denote the undoped Fermi level. The major difference between (a) and (b) is the $d_{X^2-Y^2}$ dominated band crossing the Fermi level in (a), but not in (b).

Figure 2

Five pocket scenario for LaOFeAs. (a) Plot of the SC form factor gap $f^{\mathrm{SC}}(k)$ versus the patching indices (momenta) shown in (b). The gap on the outer $h$ pocket at $\Gamma$ is smaller than that of the inner $h$ pocket and of the same order as the $M$-pocket gap. The gap on the $e$ pockets is very anisotropic but nodeless and of opposite sign. (c1)–(c3) Orbital weight distribution on the different pockets [inner $h$ pocket at $\Gamma$ is similar to (c2) shifted by 90°]. Dashed arrows indicate relevant intraorbital scatterings. (d) Leading orbital SC instability eigenvalues $c_{i,(a,b)}^{\mathrm{SC}}({\Lambda }_c)$ from (3). $d_{XZ,YZ}$ and $d_{X^2-Y^2}$ scattering dominates. (e) Flow of leading instability eigenvalues [charge density wave (CDW), Pomeranchuk instability (PI), SDW, and SC]. The leading instability is $s^{\pm }$ SC at ${\Lambda }_c\approx 0.03\mathrm{eV}$, $B_{1g}$ $d$-wave SC and SDW diverge closely (hardly distinguishable on the log scale).

Figure 3

Four pocket scenario for LaOFeP. (a) $s^{\pm }$ SC form factor, with FS patches given in (b); the $d_{X^2-Y^2}$-dominated $h$ pocket at $M$ is absent. The $h$ pockets at $\Gamma$ are gapped and isotropic. The $e$ pockets show strong anisotropy, being nodal on the pocket tips indicated in Fig. 2b by dashed arrows. (c) Relevant pair scattering and intraorbital processes between different $e$ pockets [orbital weights of the pockets are shown in (f1) and (f2)]. (d) Orbital decomposition of the SC instability: large $d_{XZ,YZ}$ and less relevant $d_{X^2-Y^2}$ contribution. (e) Flow of leading instability eigenvalues [notation as in Fig. 2e]; ${\Lambda }_c\approx 0.002\mathrm{eV}$ is smaller than in Fig. 2.