Highly Anisotropic and Twofold Symmetric Superconducting Gap in Nematically Ordered ${\mathrm{FeSe}}_{0.93}{\mathrm{S}}_{0.07}$

FeSe exhibits a novel ground state in which superconductivity coexists with a nematic order in the absence of any long-range magnetic order. Here, we report on an angle-resolved photoemission study on the superconducting gap structure in the nematic state of ${\mathrm{FeSe}}_{0.93}{\mathrm{S}}_{0.07}$, without the complications caused by Fermi surface reconstruction induced by magnetic order. We find that the superconducting gap shows a pronounced twofold anisotropy around the elliptical hole pocket near $Z$ (0, 0, $\pi$), with gap minima at the end points of its major axis, while no detectable gap is observed around $\mathrm{\Gamma }$ (0, 0, 0) and the zone corner ($\pi$, $\pi$, $k_z$). The large anisotropy and nodal gap distribution demonstrate the substantial effects of the nematicity on the superconductivity and thus put strong constraints on current theories.

Figure 1

(a) Fermi surfaces in the two-Fe Brillouin zone of FeSe in the nematic state measured by ARPES [36]. (b) Fermi surface mapping around $Z$ with linear-horizontal (LH) polarized photons. The corresponding momenta are indicated by the purple square in (a). (c) Orbital character of pocket $\alpha$ (the solid ellipse) and its counterpart from twin domains (${\alpha }^{\prime }$, the dashed ellipse). (d) Same as (b), but around $A_2$ with circular-right (CR) polarized photons. (e) Photoemission intensity along $\mathrm{\Gamma }-M_1$. $E_{\text{nematic}}$ indicates the band splitting due to nematic ordering. (f) Symmetrized photoemission intensity along cut No1, as indicated in (c). (g) Energy distribution curves (EDCs) above and below $T_c$ at the momentum $k_1$ in (f). The width of the superconducting quasiparticle peak is indicated. (Inset) The leading edge shift resulting from the gap opening. (h) Temperature dependent symmetrized EDCs at the momentum $k_1$. (i) Superconducting gap size as a function of temperature fits to the Bardeen-Cooper-Schrieffer formula.

Figure 2

(a) Illustration of hole pockets $\alpha$ and ${\alpha }^{\prime }$ around the $Z$ point. (b) Symmetrized photoemission intensity along cut No2, as indicated in (a). (c) Symmetrized EDCs (the red dots) on the pocket $\alpha$, and superconducting spectra (the black curves) obtained following the standard fitting procedure [32, 33, 40]. The insets define the in-plane angle $\theta$. (d) Symmetrized EDCs (the blue dots) on the pocket ${\alpha }^{\prime }$ and fitted superconducting spectra (the black curves). (e) Polar plot of the superconducting gap as a function of $\theta$ along the pockets $\alpha$ and ${\alpha }^{\prime }$. (f) EDC at the pocket $ϵ$ indicated by the red circle. (g) Symmetrized EDCs on the electron pockets $ϵ$ (the red solid curves) and ${ϵ}^{\prime }$ (the blue dashed curve) around the $A_1$ point.

Figure 3

(a) Illustration of pockets $\alpha$ and ${\alpha }^{\prime }$ around the $\mathrm{\Gamma }$ point. (b) Photoemission intensity along cut No3, as indicated in (a). (c) The EDC at momentum $k_7$. (d) Symmetrized EDCs on the pocket ${\alpha }^{\prime }$. The inset defines the in-plane angle $\theta$. (e) Symmetrized EDCs on the pocket $\alpha$. Quasiparticle peaks from band ${\alpha }^{\prime }$ are indicated. (f) EDCs divided by the resolution-convolved Fermi-Dirac function near the upper Fermi crossings of cut No4 in (a). (g) Same as (f) but near the upper Fermi crossings of cut No3.

Figure 4

(a) Angular dependence of the superconducting gap on the $\alpha$ pocket and fitting results by cosine series, ${\mathrm{\Delta }}_{s\pm ,s\pm }$, ${\mathrm{\Delta }}_{d,s\pm }$, and ${\mathrm{\Delta }}_{s\pm ,s++}$. (b) Overlapping of the pockets $ϵ$ (the dashed curves) and $\alpha$ (the solid curves) in the case of antiferromagnetic folding. (c)–(e) The gap forms obtained by the fitting results in (a). (f) The gap structure on the pocket $\alpha$ according to the theory of Ref. [46].