Quasiperiodic systems are important space-filling ordered structures, without decay and
translational invariance. How to solve quasiperiodic systems accurately and efficiently is a …

This paper presents a reduced projection method for the solution of quasiperiodic
Schrödinger eigenvalue problems for photonic moiré lattices. Using the properties of the …

We consider the problem of numerically computing the quantum dynamics of an electron in
twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are …

Because of the lack of translational symmetry, calculating the energy spectrum of an
incommensurate system has always been a theoretical challenge. Here, we propose a …

In this paper, we propose a new algorithm, the irrational-window-filter projection method
(IWFPM), for solving arbitrary dimensional global quasiperiodic systems. Based on the …

Due to quasicrystals having long-range orientational order but without translational
symmetry, traditional numerical methods usually suffer when applied as is. In the past …

Recent work of three of the authors showed that the operator which maps the local density of
states of a one-dimensional untwisted bilayer material to the local density of states of the …

In this study, we propose an extended plane wave framework to ensure that the electronic
structure calculations of twisted bilayer 2D material systems are practically feasible. Based …

Incommensurate structures arise from stacking single layers of low-dimensional materials on
top of one another with misalignment such as an in-plane twist in orientation. While these …

This paper presents a reduced algorithm to the classical projection method for the solution of
$ d $-dimensional quasiperiodic problems, particularly Schr\"{o} dinger eigenvalue …