Symmetry analysis of possible superconducting states in K${}_x$Fe${}_y$Se${}_2$ superconductors

A newly discovered family of Fe-based superconductors is isostructural with the so-called 122 family of Fe pnictides but has a qualitatively different doping state. Early experiments indicate that superconductivity is nodeless, yet prerequisites for the $s_{\pm }$ nodeless state (generally believed to be realized in Fe superconductors) are missing. It is tempting to assign a $d$-wave symmetry to the new materials, and it does seem, at first glance, that such a state may be nodeless. Yet a more careful analysis shows that it is not possible, given the particular 122 crystallography. If indeed superconductivity in this system is nodeless, the possible choice of admissible symmetries is severely limited: it is either a conventional single-sign $s_{+}$ state or another $s_{\pm }$ state, different from the one believed to be present in other Fe-based superconductors.

Figure 1

(Color online) A cartoon showing a generic 3D Fermi surface for an AFe${}_2$Se${}_2$ material in the unfolded (1 Fe/cell) Brillouin zone. Different colors show the signs of the order parameter in a nodeless $d$-wave state, allowed in the unfolded zone. The $\Gamma$ point is in the center (no Fermi surface pockets around $\Gamma$), and the electron pockets are around the $\overline{X},\overline{Y}$ points.

Figure 2

(Color online) A cartoon showing a folded 3D Fermi surface for an AFe${}_2$Se${}_2$ material, assuming a finite ellipticity, but 0 $k_z$ dispersion. Different colors show the signs of the order parameter in a $d$-wave state. Wherever the two colors meet, turning on hybridization due to the Se potential creates nodes in the order parameter.

Figure 3

(Color online) Same as Fig. 2, but assuming a moderated $k_z$ dispersion. The plane at $k_z=\pi /2c$ is shown, and one of the Fermi surfaces is clipped above this plane and below the $k_z=0$ plane, to show how the nodal points move away from their high-symmetry positions.

Figure 4

(Color online) Same as Fig. 3, but assuming a very strong $k_z$ dispersion.

Figure 5

(Color online) Cuts of the Fermi surfaces calculated for K${}_{0.8}$Fe${}_2$Se${}_2$ using the LAPW band structure in the virtual crystal approximation, and the experimental lattice parameter and atomic positions. (a) $k_z=0$. (b) $k_z=\pi /2c$ (halfway between $\Gamma$ and $Z$).

Figure 6

Fixed spin moment calculations for the uniform (ferromagnetic) susceptibility in KFe${}_2$Se${}_2$. The line is the first (quadratic) term in the total energy expansion, as explained in the text. Inset: The same for large moments; here the line is a guide for the eye.