Impact of static disorder on quasiparticle spectra: Debye-Waller, mean free path, and potential fluctuation effects

Angle-resolved photoemission spectroscopy (ARPES) is a widely used characterization technique in condensed matter physics, providing direct access to the single-electron spectral function of crystals, including their electronic band structure and Fermi surface. Measuring the band structure of novel quantum materials has been fundamentally important for determining, for example, nontrivial band topology, as in topological insulators, Weyl semimetals, and Dirac semimetals, or for identifying new classes of materials, such as altermagnets. A key challenge with these emerging quantum materials is that their initial crystalline quality is rarely optimized, which directly affects the spectra measured by ARPES. Here, we present a theoretical framework and experimental evidence addressing two common consequences of static disorder in photoemission experiments: the loss of coherent spectral weight and the broadening of spectral features. ARPES spectra can be understood as a sum of coherent and incoherent intensities, with their relative contributions controlled by atomic disorder and electron correlation effects. For disorder caused by phonons, the coherent intensity is exponentially suppressed as temperature increases, a phenomenon analogous to the Debye-Waller factor in diffraction, where Bragg peaks diminish in favor of diffuse scattering as disorder increases. In this work, we report a soft-x-ray study of the deliberately disordered (via Ar ion sputtering) InAs(110) surface, characterized by scanning tunneling microscopy, scanning tunneling spectroscopy, and low-energy electron diffraction. We introduce a framework that enables quantification of coherent photoemission intensity loss with increasing disorder, allowing both thermal and static disorder to be treated within a unified approach. Additionally, we identify a second major effect of disorder beyond lifetime broadening: inhomogeneous spectral broadening arising from local potential fluctuations. We show that such fluctuations increase the linewidths of the spectra of localized and delocalized states and contribute to the suppression of ARPES intensity from states near the Fermi level. The concepts and analysis methods presented should make ARPES useful for direct diagnosis of disorder effects on electronic states, for science as well as engineering.