Constant Matrix Element Approximation to Time-Resolved Angle-Resolved Photoemission Spectroscopy

We discuss several issues associated with employing a constant matrix element approximation for the coupling of light to multiband electrons in the context of time-resolved angle-resolved photoemission spectroscopy (TR-ARPES). In particular, we demonstrate that the constant matrix element approximation -even when reasonable-only holds for specific choices of the one-electron basis, and changing to other bases, requires including nonconstant corrections to the matrix element. We also discuss some simplifying approximations, where a constant matrix element is employed in multiple bases, and the consequences of this further approximation (especially with respect to the calculated TR-ARPES signal becoming negative). We also discuss issues related to gauge invariance of the final spectra.