Convergence of the Planewave Approximations for Quantum Incommensurate Systems
arxiv(2022)
摘要
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 structures are of significant
physical interest, they pose many theoretical challenges due to the loss of
periodicity. In this paper, we characterize the density of states of
Schrödinger operators in the weak sense for the incommensurate system and
develop novel numerical methods to approximate them. In particular, we (i)
justify the thermodynamic limit of the density of states in the real space
formulation; and (ii) propose efficient numerical schemes to evaluate the
density of states based on planewave approximations and reciprocal space
sampling. We present both rigorous analysis and numerical simulations to
support the reliability and efficiency of our numerical algorithms.
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