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

TL;DR

This paper examines the validity and implications of using a constant matrix element approximation in time-resolved ARPES, highlighting basis dependence, potential inaccuracies, and gauge invariance concerns.

Contribution

It clarifies the conditions under which the constant matrix element approximation is valid and explores its limitations across different bases in TR-ARPES.

Findings

Constant matrix approximation holds only in specific coordinate representations.

Using multiple bases with constant matrix elements can lead to nonphysical negative signals.

Gauge invariance considerations are crucial for accurate TR-ARPES spectra.

Abstract

We describe different approximations associated with employing a constant matrix element 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 approximation only holds for one of the coordinate representations, 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 TR-ARPES signal no longer being nonnegative). We also discuss issues related to gauge invariance of the final spectra.