Evidence for a $\cos (4\phi )$ Modulation of the Superconducting Energy Gap of Optimally Doped ${\mathrm{FeTe}}_{0.6}{\mathrm{Se}}_{0.4}$ Single Crystals Using Laser Angle-Resolved Photoemission Spectroscopy

We study the superconducting-gap anisotropy of the $\Gamma$-centered hole Fermi surface in optimally doped ${\mathrm{FeTe}}_{0.6}{\mathrm{Se}}_{0.4}$ ($T_c=14.5\mathrm{K}$), using laser-excited angle-resolved photoemission spectroscopy. We observe sharp superconducting (SC) coherence peaks at $T=2.5\mathrm{K}$. In contrast to earlier angle-resolved photoemission spectroscopy studies but consistent with thermodynamic results, the momentum dependence shows a $\cos (4\phi )$ modulation of the SC-gap anisotropy. The observed SC-gap anisotropy strongly indicates that the pairing interaction is not a conventional phonon-mediated isotropic one. Instead, the results suggest the importance of second-nearest-neighbor electronic interactions between the iron sites in the framework of $s_{\pm }$-wave superconductivity.

Figure 1

(a), (b) FS intensity map of ${\mathrm{FeTe}}_{0.6}{\mathrm{Se}}_{0.4}$ measured at 25 K with right- and left-circularly polarized light, respectively. The integration energy window is $\pm 5\mathrm{meV}$ from $E_F$. (c) FS map image obtained by summing up the spectra in (a) and (b) and symmetrized by taking into account the tetragonal crystal symmetry. The symbols indicate the $k_F$ positions where the SC gap was measured. The solid line corresponds to the FS shape deduced from fitting the $k_F$ positions to the model function with fourfold symmetry. The definition of FS angle $\phi$ is indicated. (d) FSs of the pure FeTe given by the band-structure calculation. Solid and dashed lines indicate those at $k_z=0$ ($\Gamma \mathrm{\text{−}}X\mathrm{\text{−}}M$) plane and $k=\pi (Z\mathrm{\text{−}}R\mathrm{\text{−}}A)$ plane, respectively. The innermost FS around the $\Gamma$ point is closed around this point and does not exist around the $Z$ point due to its three dimensionality. The other two FSs around the $\Gamma$ point are nearly two dimensional. The solid square corresponds to the region displayed in (c) [36].

Figure 2

(a) EDCs and (b) symmetrized EDCs with respect to $E_F$ at $k_F$ measured below $T_c$ (2.5 K) and above $T_c$ (25 K). To cancel out the effect of the Fermi-Dirac cutoff, these EDCs are symmetrized with respect to $E_F$, and the results are shown in Fig. 2b. Color of each EDC and symmetrized EDC corresponds to that of the $k_F$ positions in Fig. 1c. The FS angle of each EDC is indicated in Fig. 2b. The solid lines are the fitting functions using the BCS spectral function.

Figure 3

FS-angle dependence of the SC-gap size obtained from fitting to the BCS spectral function. Solid circles are the SC-gap sizes obtained from fitting of the spectra in (a) and open circles are symmetrized by taking into account the tetragonal symmetry of the structure. Color of each symbol corresponds to that of the $k_F$ positions in Fig. 1c. The solid line is a fitting result using the model SC-gap function $\Delta (\phi )=|\Delta [1+A\cos (4\phi )]|$, where $\phi$ is the FS angle.