5 Figure 7: (color online) Comparison of the band structure of the ARPES data and the DFT calculation results along the Γ -M cut. Note: the energy scale of the calculated band structure at the right side is 3.125 times of the energy scale of the experimental data at the left side. Figure 8: (color online) (a) Cartoon of the polarization de- pendence experiment, and the symmetry of the orbitals with respect to the mirror plane defined by sample normal and Γ - X. (b) The photoemission intensity along the Γ -X direction measured at the σ geometry, and (d) its second derivative with respect to energy. (c) The photoemission intensity along the Γ -X direction measured at the π geometry, and (e) its second derivative. Data were taken with 100 eV photons at SLS, and the temperature was 10 K. [26] were used to model the electron-ion interactions. Af- ter the full convergence test, the kinetic energy cut-off and the charge density cut-off of the plane wave basis were chosen to be 600 eV and 4800 eV, respectively. The Gaussian broadening technique was used and a mesh of 16 × 16 × 8 k-points were sampled for the irreducible Brillouin-zone integration. The internal atomic coordi- nates within a cell were determined by the energy min- imization. The doping effect upon electronic structures was studied by using virtual crystal calculations. Fig. 5 displays the calculated band structure, there are indeed three bands near $_{Γ}$, and two bands near M that cross the Fermi energy. In particular, the inner-most band near Γ does show significant dispersion along the Γ − Z direction. As a result, our calculations give five Fermi surfaces as shown in Fig. 6. The calculated band structure to a large extent resembles those of the iron- arsenide superconductors. Qualitatively, the calculated Fermi surfaces agree well with our experiments. However, there are some impor- tant quantitative discrepancies. Fig. 7 illustrates the measured band structure along $_{Γ}$-M as reproduced from Fig. 2(c), together with the calculated bands. One finds that the size of the calculated γ Fermi surface is much smaller than the measured one. However, the calculated α , β , and γ bands match the data after scaled by 3.125 and shifted down by 45 meV, except the Fermi crossings of the measured and calculated γ band are different. The scaling factor illustrates the correlation effects in this ma- terial. The experimental Fermi velocity of α , β , and γ bands are 0.62 eV Å, 0.4 eV Å, and 0.137 eV Å respec- tively. On the other hand, the measured Fermi surface around M is much smaller than the calculated ones. Simi- lar to the iron-pnictides [27], the renormalization factors of the bands vary in different regions of the Brillouin zone. We note that in order to obtain accurate band renor- malization factors, it is crucial to compare the data with the calculation conducted for the same Se doping . We have calculated the band structures of FeTe 1$_{−}$ $_{x}$Se$_{x}$ with a series of doping, and found that the band structure around Γ evolves rapidly with increasing Se concentra- tion. Similar conclusion can be drawn from the published FeSe and FeTe band structures by Subedi and coworkers [28]. For a multi-band and multi-orbital superconductor, it is crucial to understand the orbital characters of the band structure near E$_{F}$ . In photoemission, such information can be obtained to a large extent in the polarization de- pendence. Fig. 8(a) illustrates two types of experimental setup with linearly polarized light. The incident beam and the sample surface normal define a mirror plane. For the π (or σ ) experimental geometry, the electric field di- rection ( ˆ ε ) of the incident photons is in (or out of) the mirror plane. The matrix element of the photoemission V. POLARIZATION DEPENDENCE