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weight is mostly located around Γ and M. In order to resolve the details of the Fermi crossings, Fig. 2(c) shows the photoemission intensity along the cut #1 in the Γ $_{−}$M direction, several bands could be resolved. For a better visualization of the bands, Fig. 2(d) shows the second derivative with respect to energy for the data in Fig. 2(c). Three bands, α , β , and γ , could be clearly identified. The top of the α band is very close to the Fermi energy, but it is hard to judge whether it crosses E$_{F}$ based on the energy distribution curves (EDC’s) in Fig. 2(f). By judging from the momentum distribution curves (MDC’s) in Fig. 2(g) near $_{Γ}$, one finds that it crosses the Fermi level with a very small-sized Fermi surface. In order to check whether the spectral weight around M represents band crossings, the data in Fig. 2(c) is renormalized by its angular integrated spectrum and shown in Fig. 2(e). In this way, another band, δ , is resolved. The MDC’s in the boxed region are shown in Fig. 2(h), where one observes an electron-pocket type of dispersion. This is similar to the BaFe 2 As 2 [23], the δ band is quite weak in such an experimental geometry due to the strong orbital-dependence of the matrix element [22]. Similarly, Figs. 2(i) and (j) show the photoemission intensity and its second derivative plot along the $_{Γ}$-X direction, where α , β , and γ bands are observed. Therefore, there are totally three bands near the $_{Γ}$-point, and they all cross the Fermi surface and form three hole pockets. Based on the identified band dispersions, the Fermi crossings are determined and shown in Fig. 2(b). We note because of symmetry constraints, only crossings for one elliptical Fermi surface could be observed around M or M’ [22]. The experimen- tal Fermi surfaces are determined by fitting the Fermi crossings with symmetry in consideration. Assuming the β , γ , and δ Fermi surfaces to be cylindrical, one could estimate the electron concentration based on the 

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Luttinger theorem. We obtained 0.08 holes per unit cell. This is not inconsistent with the chemical formula, considering variations of the Fermi surface volume caused by k$_{z}$ dispersion of the band structure. 

To further illustrate the behavior of the α band, Fig. 3 shows three nearby cuts taken with 22 eV photons. When approaching ( k$_{x}$ = 0 , k$_{y}$ $_{= 0)}$, the α band disperses rather rapidly with its top in each cut moving towards E$_{F}$ . Based on the peak positions in the MDC’s [Fig. 3(j)], one could observe a Fermi crossing of the α band very close to ( k$_{x}$ = 0 , k$_{y}$ $_{= 0)}$, giving a small hole-like Fermi surface. However, this Fermi crossing is not observed at several other photon energies such as 50 eV and 100 eV (Fig. 4). Since these momentum cuts sample through ( k$_{x}$, k$_{y}$ ) = (0 , 0) at different k$_{z}$ , the α Fermi surface is thus a closed pocket. Moreover, in Figs. 4(j-l), the EDC’s have been divided by the temperature-broadened Fermi- Dirac distribution, where both the α and β bands appear to be degenerate within the experimental resolution at 22 eV. Based on the calculations below, it suggests that this data cut should be very close to the zone center, $_{Γ}$. 

## IV. ELECTRONIC BAND STRUCTURE CALCULATION 

To understand the data, we have calculated the electronic band structure for FeTe 0 . 66 Se 0 . 34 . In the calculations the plane wave basis method was used [24]. We adopted the generalized gradient approxima- tion of Perdew-Burke-Ernzerhof [25] for the exchange- correlation potentials. The ultrasoft pseudopotentials 

