Extraction of the electron self-energy from angle-resolved photoemission data: Application to ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$

The self-energy $\Sigma (\mathbf{k},\omega ),$ the fundamental function that describes the effects of many-body interactions on an electron in a solid, is usually difficult to obtain directly from experimental data. In this paper we show that by making certain reasonable assumptions, the self-energy can be directly determined from angle-resolved photoemission data. We demonstrate this method on data for the high-temperature superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$ in the normal, superconducting, and pseudogap phases.