Scaling of the superconducting gap with orbital character in FeSe

We use high-resolution angle-resolved photoemission spectroscopy to map the three-dimensional momentum dependence of the superconducting gap in FeSe. We find that on both the hole and electron Fermi surfaces, the magnitude of the gap follows the distribution of $d_{yz}$ orbital weight. Furthermore, we theoretically determine the momentum dependence of the superconducting gap by solving the linearized gap equation using a tight-binding model which quantitatively describes both the experimental band dispersions and orbital characters. By considering a Fermi surface only including one electron pocket, as observed spectroscopically, we obtain excellent agreement with the experimental gap structure. Our finding of a scaling between the superconducting gap and the $d_{yz}$ orbital weight supports the interpretation of superconductivity mediated by spin fluctuations in FeSe.

Figure 1

(a), (b) FS maps of twinned FeSe samples around the $\mathrm{\Gamma }$ point (37 eV), in both linear polarizations. (c) High-symmetry dispersions above and below $T_c$. (d) High-symmetry dispersion in LV, highlighting the shorter axis of the ellipse. (e) Schematic of the distribution of orbital weights. (f) Schematic correlation between the LEG and the $d_{yz}$ orbital character. (g), (h) EDCs integrated in small regions [cyan dashed lines in (c) and (d)] around $k_F$. (i), (j) EDCs at positions shown in (b), off the high-symmetry axes. Note that (d) and (h) are obtained with a higher resolution than other plots.

Figure 2

(a), (b) FS maps of twinned FeSe at the $A$ point (28 eV), schematically represented in (c). (d)–(g) Cuts along $k_Y$, above and below $T_c$. Analysis of the EDCs in (h)–(k) reveals a SC gap that tends to decrease further away from the center of the peanut. (l) Section of the FS used for the peak-fitting analysis; yellow circles indicate the peak positions. (m) Correlation of $d_{yz}$ peak amplitude from fitting and LEG.

Figure 3

(a) Closeup of the hole pocket (top) and electron pocket (bottom) at $k_z=0$. The color code describes the maximum orbital character and the axes are defined relative to the center of the pockets with (0,0) for the hole pocket and $(\pi ,0)$ for the electron pocket. (b) Orbital characters as a function of angle for the hole pocket (top) and electron pocket (bottom). (c) Momentum dependence of the gap structure for one hole pocket and two electron pockets with $U=0.3$ eV. (d) The same as (c) but repeated without the electron pocket located at $(0,\pi )$. The colored circles correspond to the ARPES data while the crosses are taken from quasiparticle interference experiments [16]. (e) Representation of the results of (d) around the FS.