First-principle tight-binding approach to angle-resolved photoemission spectroscopy simulations: importance of light-matter gauge and ubiquitous interference effects

Angle-resolved photoemission spectroscopy (ARPES) is one of the most powerful techniques to study the electronic structure of materials. To go beyond the paradigm of band mapping and extract aspects of the Bloch wave-functions, the intricate interplay of experimental geometry, crystal structure, and photon polarization needs to be understood. In this work we discuss several model approaches to computing ARPES signals in a unified fashion. While we represent the Bloch wave-functions by first-principle Wannier functions, we introduce different approximations to the final states and discuss the implications for the predictive power. We also introduce various light-matter gauges and explain the role of the inevitable breaking of gauge invariance.Finally, we benchmark the different models for the two-dimensional semiconductor WSe$_2$, known for its strong Berry curvature, orbital angular momentum (OAM), and nontrivial orbital texture. The models are compared based on their ability to simulate photoemission intensity and interpret circular dichroism in ARPES (CD-ARPES). We show that interference effects are crucial to understanding the circular dichroism, and explain their photon-energy dependence. Our in-depth analysis provides insights into the advantages and limitations of various model approaches in clarifying the complex interplay between experimental observables and underlying orbital texture in materials.