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

TL;DR

This paper introduces the moiré plane wave expansion model (MPWEM), a geometry-based method for simulating STM images of incommensurate 2D heterostructures, enabling accurate and computationally efficient analysis of complex moiré patterns.

Contribution

The paper presents a novel, simple, and effective model for simulating STM images in incommensurate 2D materials, filling a gap in theoretical tools for twistronics research.

Findings

Reproduces experimental STM images with angstrom-scale accuracy

Provides a computationally friendly alternative to expensive simulations

Applicable to various structurally and electronically distinct 2D heterostructures

Abstract

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.