## 3 Results and Discussion  
Figure 2 reports TARPES measurements of selected BSTS samples. Each panel shows the spectra at three illustrative pump-probe delays: before pump arrival (left, \"-\" label), at zero delay (center, \"0\" label) and one picosecond after pumping (right, \"+\" label). The linear dispersion of the TSS is clearly observed for all compounds and marked with dashed lines to guide the eye. Moving from panel (a) to panel (f) in Figure 2, the amounts of Bi and Se increase at the expenses of Sb and Te and the samples become progressively n-doped. The Dirac cone of the most p-doped sample, Sb\({}_{2}\)Te\({}_{3}\) in panel (a), is unoccupied at negative delays. Upon pumping, electrons are optically transferred above the Fermi energy (FE), filling the TSS. At the opposite extreme, the most n-doped sample, Bi\({}_{2}\)Te\({}_{0.5}\)Se\({}_{2.5}\) in panel (f), has an almost completely occupied TSS even under equilibrium conditions (negative delay). It should be noticed that the DN of the Bi\({}_{0.8}\)Sb\({}_{1.2}\)Te\({}_{3}\) sample, panel (c), has vanishing binding energy. As we will see in the next section, this feature has important consequences on the dynamics of Dirac fermions. We also point out that, regardless of the stoichiometry, at zero pump-probe delay two bulk bands (named BB1 and BB2 in Figure 2) are transiently populated, while after one picosecond most of the excess spectral weight induced by photoexcitation has been transferred from BB1 (higher energy) to BB2 (lower energy) and the TSS. Figure 1: Schematic drawing of a time- and angle-resolved photoemission spectroscopy (TARPES) system: (**a**) Yb-based laser system generating 300 fs laser pulses with photon energy \(h\upsilon=1.2\) eV (\(\lambda=1030\) nm) at repetition rate of 100 kHz; (**b**) non-collinear optical parametric amplifier (NOPA) and (**c**) sum frequency generation (SFG) stage, which produce the pump (\(h\upsilon=1.85\) eV, 30 fs) and probe (\(h\upsilon=6\) eV, 65 fs) beams, respectively; (**d**) pump delay stage; (**e**) ultrahigh vacuum chamber; (**f**) time-of-flight (ToF) analyzer equipped with a (**g**) micro channel plate (MCP) detector [29]. In order to better visualize the photo-excited band structure and dynamics reported in Figure 2, we have subtracted the equilibrium TARPES maps (panels marked with negative sign) from the pumped spectra (marked with zero and positive sign). The results are plotted in Figure 3 (same sample sequence as Figure 2). The upper and lower rows refer to the band structure at zero and at +1 ps delays, respectively. Photo-induced electronic population is represented in red, while band depletion is displayed in green. The large gray arrows connect all DN, revealing a regular 100 meV decrease of the TSS binding energy for adjacent samples. It is also interesting to observe that in the samples where the DN lies above the Fermi level (panels a and b), even one picosecond past the optical excitation (bottom row) the lower branch of the Dirac cone is not significantly populated. This dynamical behavior has been previously observed in Sb\({}_{2}\)Te\({}_{3}\)[27], but seems to be a rather general feature due to the so-called bottleneck effect related to the vanishing phase space at the DN. The electronic dynamics of each band (BB1, BB2, and TSS) were extracted by integrating the spectral intensity within the small energy-momentum boxes shown in the upper row in Figure 3: boxes 1 and 2 refer to BB1 and BB2, respectively, while boxes 3 and 4 refer to the TSS. The results are reported in Figure 4. We have followed the same color scheme used for the boxes in Figure 3: as the DN decreases in energy (i.e., p- to n-doping), the line color turns lighter. All curves are normalized to their respective maxima.