Abstract
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.
Highlights
Time-resolved and angle-resolved photoemission spectroscopy (TR-ARPES) is emerging as one of the powerful tools in ultrafast optics used to probe the nonquilibrium behavior of quantum materials and how they recover back to a quasiequilibrium state
Introducing the time-reversed low-energy electron diffraction (TRL) states, as described in Reference [18], we find the total photocurrent for a particular probe pulse is given by hJd i =
We helped clarify a number of subtle points associated with TR-ARPES studies when the number of low-energy bands is larger than one
Summary
Time-resolved and angle-resolved photoemission spectroscopy (TR-ARPES) is emerging as one of the powerful tools in ultrafast optics used to probe the nonquilibrium behavior of quantum materials and how they recover back to a quasiequilibrium state. It is common to invoke a “constant matrix element approximation”, wherein its dependence on its various arguments is entirely neglected, within theoretical calculations of photoemission spectra. This is not necessarily because the matrix elements are known to be constant, but because explicitly determining the matrix elements is extremely challenging for quantum materials, so employing a constant matrix element is a good first step in modeling such systems. We discuss different options one has for invoking the constant matrix element approximation within TR-ARPES, paying particular attention to the issues of gauge invariance and non-negativity of the spectra. We discuss implications for time-resolved photoemission spectroscopy (TR-PES), where the momentum dependence has been integrated over
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