Time-resolved ARPES signal in pumped semiconductors within the dynamical projective operatorial approach

In this manuscript, after discussing in detail the internals of our recently developed method, the dynamical projective operatorial approach (DPOA), we provide the framework to apply this method to pumped semiconductor lattice systems and, in particular, to study and analyze their electronic excitations and TR-ARPES signal. The expressions for relevant out-of-equilibrium Green's functions and TR-ARPES signal are given within the DPOA framework and, defining a retarded TR-ARPES signal, it is shown that it is possible to obtain an out-of-equilibrium version of the fluctuation-dissipation theorem. We clarify how single- and multiphoton resonances, rigid shifts, band dressings, and different types of sidebands emerge in the TR-ARPES signal. We also propose protocols for evaluating the strength of single- and multiphoton resonances and for assigning the residual excited electronic population at each crystal momentum and band to a specific excitation process. Hamiltonians, where intra- and interband transitions are selectively inhibited, are defined and used to analyze the effects on the TR-ARPES signal and the residual electronic excited population. Three relevant cases of light-matter coupling are examined within the dipole gauge: only a local dipole, only the Peierls substitution in the hopping term, and both terms at once. The transient and residual pump effects are studied in detail, including the consequences of the lattice symmetries at different crystal momenta on the TR-ARPES signal. A detailed study of the dependence of the TR-ARPES signal on the probe-pulse characteristics is also reported. To provide a guideline for understanding the complex effects and interplays and the variety of possible physical phenomena without being limited by the characteristics of a single particular real material, we have chosen to study a prototypical pumped two-band semiconductor lattice system.