Observation of two distinct $d_{xz}$/$d_{yz}$ band splittings in FeSe

We report the temperature evolution of the detailed electronic band structure in FeSe single crystals measured by angle-resolved photoemission spectroscopy (ARPES), including the degeneracy removal of the $d_{xz}$ and $d_{yz}$ orbitals at the $\mathrm{\Gamma }$/Z and M points, and the orbital-selective hybridization between the $d_{xy}$ and $d_{xz/yz}$ orbitals. The temperature dependences of the splittings at the $\mathrm{\Gamma }$/Z and M points are different, indicating that they are controlled by different order parameters. The splitting at the M point is closely related to the structural transition and is attributed to orbital ordering defined on Fe-Fe bonds with a $d$-wave form in the reciprocal space that breaks the rotational symmetry. In contrast, the band splitting at the $\mathrm{\Gamma }$/Z points remains at temperature far above the structural transition. Although the origin of this latter splitting remains unclear, our experimental results exclude the previously proposed ferro-orbital ordering scenario.

Figure 1

(a) FS mapping at 10 K along the $\mathrm{Z}(0,0,\pi )\text{−}\mathrm{A}(\pi ,0,\pi )$ direction, recorded with unpolarized He $\mathrm{I}\alpha$ photons (21.212 eV). (b) FS mapping at 22 K along the $\mathrm{\Gamma }(0,0,0)$-Z direction obtained in the $\sigma$ geometry. The red dashed lines indicate the $k_z$ dispersion. The intensity in (a) and (b) have been integrated in the $\pm 5$ and $\pm 20$ meV energy ranges, respectively. (c)–(e) Band structure at $\mathrm{\Gamma }$, Z, and $\mathrm{M}(\pi ,0,0)$ along $\mathrm{\Gamma }$-M or Z-A, recorded in the $\sigma$ geometry, with $T$ = 22 K, 22 K, and 45 K, respectively. (f)–(h) 2D curvature of (c)–(e). The red, blue, and black lines indicate the dispersions of the $d_{yz}$, $d_{xz}$, and $d_{xy}$ orbitals, respectively. The thick and thin lines in (h) correspond to 2 different domains. (i)–(k) EDC plots of (c)–(e). The black dots indicate the EDC peaks.

Figure 2

(a)–(e) ARPES intensity plots of the band structure at $\mathrm{\Gamma }$ at different temperatures. The intensity in each plot is the sum of data acquired with ${\mathrm{C}}^{+}$ and ${\mathrm{C}}^{-}$ polarized photons. (f)–(j) EDC curvatures of (a)–(e). (k)–(o) ARPES intensity plots of the band structure at the M point at different temperatures, recorded in the $\sigma$ geometry. (p)–(t) MDC curvatures of (k)–(o). (u) EDCs of (a)–(e) at $k_x=0$. The blue dashed line is the second derivative of the blue solid line with an extra minus sign. The two dashed black lines indicate the peak positions. (v) EDCs of (k)–(o) at $k_x=0$. The black dashed lines correspond to the EDC peaks. In all the intensity plots, the red lines represent the $d_{yz}$ orbitals, while the blue/cyan ones represent the $d_{xz}$ orbitals, and they are parabolic fittings of EDC and MDC peaks together. All cuts are along the $\mathrm{\Gamma }$-M or the Z-A high-symmetry direction. All the intensities are divided by Fermi function at the corresponding temperatures.

Figure 3

(a) Summary of the $d_{xz}$/$d_{yz}$ splittings at $\mathrm{\Gamma }$, Z, and M as a function of temperature. The splitting at M disappears at a slightly higher temperature than $T_s$, which might be caused by short-range ordering or fluctuations above the transition. (b) Draft of band structure extracted from experimental data and fitted with a tight binding model. The $d_{xy}$, $d_{xz}$, and $d_{yz}$ symbols are for $T>T_s$ only since the orbital characters will change along $\mathrm{\Gamma }\text{−}{\mathrm{M}}_1$ and $\mathrm{\Gamma }\text{−}{\mathrm{M}}_2$. (c)–(d) Band structure of onsite and bond orbital order, calculated from a tight binding model (see SM Part II for the details).