Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials (Communications in Computational Physics, 2024)
In this paper, we apply the effective potentials in the localization landscapetheory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of theincommensurate systems. We uniquely develop a plane wave framework for the effective potentials of the incommensurate systems. And utilizing the effective potentialsrepresented by the plane wave, the location of the electron density can be inferred.Moreover, the spectral distribution can be obtained from the effective potential versionof Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool forinvestigating the localization and spectral properties of the incommensurate systems,without solving the eigenvalue problem explicitly.