Year: 2025
Type: article
Abstract: . Incommensurate structures come from stacking the single layers of low dimensional materials on top of one another with misalignment such as a twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. This paper studies the physical observables of continuum Schrödinger operators for incommensurate systems. We characterize the density of states and local density of states in real and reciprocal spaces, and develop novel numerical methods to approximate them. In particular, we (i) justify the thermodynamic limit of the density of states and local density of states via the operator kernel characterization; and (ii) propose efficient numerical schemes based on plane wave approximation and the trapezoidal rule in reciprocal space. We present both rigorous analysis and numerical simulations to support the reliability and efficiency of our numerical algorithms.
DOI: 10.1137/23m1553650
Institutions: Beijing Normal University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, Institute of Applied Physics and Computational Mathematics, CAEP Software Center for High Performance Numerical Simulation, Louisiana State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407818698