Matrix element effects in angle-resolved photoemission from ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8:$ Energy and polarization dependencies, final state spectrum, spectral signatures of specific transitions, and related issues

We have carried out extensive simulations of the angle-resolved photoemission (ARPES) intensity in Bi2212 within the one-step- and three-step-type models using a first-principles band theory framework. The focus is on understanding the behavior of emissions from the antibonding and bonding bands arising from the ${\mathrm{CuO}}_2$ bilayers around the $\overline{M}(\pi ,0)$ symmetry point. The specific issues addressed include: Dependencies of the photointensity on the energy and polarization of the incident light; character of the initial and final states involved as well as the spectrum of the relevant final states; and changes in the spectral intensity as a function of the perpendicular component $k_{\perp }$ of the momentum of the photoelectron. Considerable insight into the nature of individual transitions is adduced by examining the momentum matrix element for bulk transitions within the solid and by further decomposing this matrix element into contributions from various atomic sites and angular momentum channels. These results indicate that, via remarkable interference effects, the ARPES matrix element can in particular cases help zoom in on the properties of electrons excited from specific sites and/or angular momentum channels even in a complex material.