Moir\'e plane wave expansion model for scanning tunneling microscopy simulations of incommensurate two-dimensional materials

• Main Authors: Ster, Maxime Le, Dabrowski, Paweł, Krukowski, Paweł, Rogala, Maciej, Lutsyk, Iaroslav, Ryś, Wojciech, Märkl, Tobias, Brown, Simon A, Sławińska, Jagoda, Palotás, Krisztián, Kowalczyk, Paweł J
• Format: Journal Article
• Language: English
• Published: 10-10-2023
• Subjects: Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.2310.06535

Incommensurate heterostructures of two-dimensional (2D) materials, despite
their attractive electronic behaviour, are challenging to simulate because of
the absence of translation symmetry. Experimental investigations of these
structures often employ scanning tunneling microscopy (STM), however there is
to date no comprehensive theory to simulate an STM image in such systems. In
this paper, we present a geometry-based method to generate STM images in
incommensurate van der Waals (vdW) heterostructures, which we call the moir\'e
plane wave expansion model (MPWEM). We generate the STM images using a weighted
sum of three image terms: the non-interacting STM images of (1) the substrate
layer, (2) the adsorbate layer, and (3) a semi-empirical Fourier expansion of
the moir\'e wavevectors obtained analytically which results from the
interaction of (1) and (2). We illustrate and benchmark the model using
selected vdW 2D systems composed of structurally and electronically distinct
crystals, and show that the method reproduces experimental STM images down to
angstrom-scale details. The MPWEM, thanks to its simplicity, can serve as an
initial prediction tool prior to more computationally expensive calculations
which are often limited by the number of atoms and the requirement of periodic
supercells, and thus offers a promising class of computationally-friendly STM
simulations, of high relevance in the growing field of twistronics.