Abstract
The distribution of photoelectrons acquired in angle-resolved photoemission spectroscopy can be mapped onto the energy-momentum space of the Bloch electrons in the crystal. The explicit forms of the mapping function f depend on the configuration of the apparatus as well as on the type of the photoelectron analyzer. We show that the existence of the analytic forms of f-1 is guaranteed in a variety of setups. The variety includes the case when the analyzer is equipped with a photoelectron deflector. Thereby, we provide a demonstrative mapping program implemented by an algorithm that utilizes both f and f-1. The mapping methodology is also usable in other spectroscopic methods such as momentum-resolved electron-energy loss spectroscopy.
Highlights
INTRODUCTIONBand structures of crystals can be visualized by using angle-resolved photoemission spectroscopy (ARPES). The visualization procedure is based on the principle that the kinetic energy (εkin) and angular distribution of photoelectrons can be mapped onto energy (ω) and momentum space of Bloch electrons in the crystal. The well-established methodology makes ARPES a powerful tool to study the electronic structures of crystals
The visualization procedure is based on the principle that the kinetic energy and angular distribution of photoelectrons can be mapped onto energy (ω) and momentum space of Bloch electrons in the crystal
The explicit forms of the mapping function, or the way the angular variables appear in the function, depend on the configuration of the angle-resolved photoemission spectroscopy (ARPES) apparatus
Summary
Band structures of crystals can be visualized by using angle-resolved photoemission spectroscopy (ARPES). The visualization procedure is based on the principle that the kinetic energy (εkin) and angular distribution of photoelectrons can be mapped onto energy (ω) and momentum space of Bloch electrons in the crystal. The well-established methodology makes ARPES a powerful tool to study the electronic structures of crystals.. The analyzer equipped with a deflector can detect photoelectrons directed off the slit and achieves the so-called slit-less concept In such a setup, a new angular variable β has to be taken into account explicitly because β is independent of the angles that describe the sample orientation. We systematically investigate the derivation of the explicit forms of f 1 for a variety of setups. We provide the explicit forms for some typical setups including those illustrated in Fig. 1 and demonstrate a mapping program. In the Appendix, we summarize the analytic forms of f and f 1 for some typical setups (Appendix A) and provide some tips for the angular notation when the deflector-type analyzer is used (Appendix B). When there is no confusion, we abbreviate sine and cosine functions as follows: cos β → c β and sin β → s β
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