Unconventional Anisotropic $s$-Wave Superconducting Gaps of the LiFeAs Iron-Pnictide Superconductor

We have performed high-resolution angle-resolved photoemission spectroscopy on Fe-based superconductor LiFeAs ($T_c=18\mathrm{K}$). We reveal multiple nodeless superconducting (SC) gaps with $2\Delta /k_B{T}_c$ ratios varying from 2.8 to 6.4, depending on the Fermi surface (FS). We also succeeded in directly observing a gap anisotropy along the FS with magnitude up to $\sim 30\%$. The anisotropy is fourfold symmetric with an antiphase between the hole and electron FSs, suggesting complex anisotropic interactions for the SC pairing. The observed momentum dependence of the SC gap offers an excellent opportunity to investigate the underlying pairing mechanism.

Figure 1

(a) Plot of the ARPES intensity at $E_F$ of LiFeAs ($T_c=18\mathrm{K}$) as a function of the two-dimensional wave vector measured with the He $I\alpha$ line ($h\nu =21.218\mathrm{eV}$). The intensity is obtained by integrating the spectra within $\pm 5\mathrm{meV}$ with respect to $E_F$. (b) ARPES spectra along the $\Gamma –M$ high-symmetry line. (c) and (d) Intensity plot and second-derivative intensity plot of (b), respectively, as a function of binding energy and wave vector. (e) ARPES intensity plot at $T=50\mathrm{K}$ divided by a Fermi-Dirac function measured along cut 1 in (a), and (f) corresponding energy distribution curves. (g) ARPES intensity plot at 20 K along cut 2 and (h) corresponding momentum distribution curves. Blue dots in (f) and (h) are guides for the eye to trace the band dispersion.

Figure 2

(a) and (b) High-resolution ARPES spectra in the SC state (8 K) measured along cut 1 and 2 in (c), respectively. The ARPES spectra at $k_F$ points are indicated by blue curves. Dots are guides for the eye to trace the band dispersion. (c) Schematic FS and $k$ location of the cuts. (d) Symmetrized ARPES spectra in the SC state measured at $k_F$ points of the $\alpha$, $\beta$, $\gamma$, and $\delta$ bands.

Figure 3

(a) Schematic FS and definition of the FS angle ($\theta$). (b)–(e) Symmetrized ARPES spectra in the SC state measured at various $k_F$ points of the $\alpha$, $\beta$, $\gamma$, and $\delta$ bands. Dashed lines and dots are guides for the eye.

Figure 4

(a) and (b) Polar plots of the SC gap size for the $\alpha$, $\beta$ and the $\gamma$, $\delta$ FSs, respectively, as a function of $\theta$ defined in Fig. 3a. Filled circles are the original data, and open circles are the folded data which take into account the fourfold symmetry. Error bars in (a)–(c) originate from the fitting uncertainty on $\Delta$, as well as experimental uncertainties in determining the energy position of $E_F$ and the momentum location of $k_F$ (less than 0.1 and 0.2 meV, respectively). Solid curves show the fitting results with $\Delta (\theta )={\Delta }_0+{\Delta }_1\cos [4(\theta +\varphi )]$. (c) Plot of the SC gap size as a function of $\mid \cos k_x\cos k_y\mid$. The fitting result assuming the gap function $\mid \Delta \mid ={\Delta }_0\mid \cos k_x\cos k_y\mid$ is indicated by a black dashed line.