PyAtoms: An interactive tool for simulating atomic scanning tunneling microscopy images of 2D materials, moiré systems and superlattices

TL;DR

PyAtoms presents an open-source, Python-based GUI for rapid, real-time STM/SPM image simulation of 2D materials, moiré systems, and superlattices using a Fourier-space lattice framework. It offers two moiré modeling approaches and a low-pass filter for efficient real-space and reciprocal-space rendering, along with real-time estimates of imaging time to assist experimental planning. The tool supports parameter exploration of lattice constants, twist angles, strain, and sublattice asymmetry across graphene, TMDCs, and CDW/BDW systems, enabling side-by-side comparison with experiments and qualitative interpretation of complex moiré patterns and QPI data. While presently qualitative in experimental matching, PyAtoms provides an accessible, extensible platform with open-source code for potential quantitative fitting and broader multilayer modeling, benefiting the quantum materials SPM community.

Abstract

We present PyAtoms, an interactive open-source software that rapidly simulates atomic-scale scanning tunneling microscopy (STM) and other scanning probe microscopy (SPM) images of two-dimensional (2D) layered materials, moiré systems, and superlattices. Rooted in a Fourier-space description of ideal atomic lattice images, PyAtoms is a Python-based graphical user interface (GUI) with robust capabilities for tuning lattice parameters (lattice constants, strain, number of layers, twist angles) and STM imaging parameters (pixels, scan size, scan angle) and provides time estimates for spectroscopic measurements. These capabilities allow users to efficiently plan time-consuming STM experiments. We provide an overview of PyAtoms' current features, describe its underlying mathematical principles, and then demonstrate simulations of several 2D materials including graphene with variable sublattice asymmetry, twisted tri-layer graphene moiré systems, and several charge- and bond-density wave systems.

Figures (7)

• Figure 1: Generalized triangular lattices. (a) PyAtoms simulated image of graphene ($a = 2.46$ Å) created with equal amplitude sublattices ($\alpha=\beta=0.5$). (b) Vertical line scan of the image in (a) connecting consecutive hollow sites. (c) Series of simulated generalized honeycomb crystals with variable amplitudes on each sublattice. (d) Experimental STM image ($V_b = -400$ mV, $I_t = 250$ pA, $T =$ 4.7 K) of graphite displaying sublattice asymmetry. (e) PyAtoms simulation of (d) ($\alpha = 0.45,\beta = 0.55$) that faithfully reproduces the sublattice asymmetry.
• Figure 2: Moiré simulations of experimental data. (a) Experimental STM image of twisted graphene-graphite with a moiré twist of $\theta=1.9^\circ$. ($V_b = -400$ mV, $I_t = 250$ pA, $T =$ 4.7 K). The height has been normalized to $[0,1]$ . (b) Simulation using the "simple" moiré model with $\theta_{12}=1.9^\circ,\eta=0.4$. (c) Same as (b) using the "log" moiré model with $\xi = 0.85$. Note the compressed color scale. (d) Linecuts between the two AA moiré sites in (a)-(c). (e-f)Same as (a-c) after low-pass filtering ($\sigma = 6$ pixels) which highlights the differences between the simulated moiré models. All images have a lateral size of 18.7 nm $\times$ 18.7 nm.
• Figure 3: PyAtoms graphical user interface. See text for brief descriptions of each labeled window.
• Figure 4: Twisted trilayer graphene simulation. (a) Cropped image of a PyAtoms simulation of unstrained twisted trilayer graphene: 2048 pixels, $a =$ 2.46 Å, $L =$ 90 nm, $\theta_{12} = 1.42^\circ$, $\theta_{23} = -1.88^\circ$, moiré 'Simple' mode. Inset: Atomic-scale zoom on AAA region. (b) (Right) Full-scale FFT of (a) and (Left) detail zoom showing the Bragg peaks for each graphene layer. (c) Low-pass filtered image of (a): $\sigma_R =$ 20 pixels ($0.88$ nm). The solid lines highlight the nearest-neighbors for the long (red) and short (yellow) moiré wavelength. (d) Zoom FFT of (c) near the origin. The circle displays the filtered region in $k$-space. (e) Same as (c) with a small strain on $G_1$ that warps the moiré pattern. (f) FFT of the strained trilayer graphene.
• Figure 5: Setting up and optimizing QPI images with PyAtoms. (a) Simulated FT-STM ($624\times 624$ pixels, 60 nm) of NbSe$_2$ with three-fold $(4\times 1)R0^\circ$ CDW domains. (b) Experimental STM topography image of NbSe$_2$ at $T = 4.7$ K with strain-induced $(4\times 1)R0^\circ$ disordered CDW domains ($V_b = 1.5$ mV, $I_t = 3$ pA). Image has optimized scan parameters from (a). Image acquisition time $\approx 90$ min. (c) FT-STM of the topography in (b) showing additional features corresponding to QPI patterns seen previously gao2018atomic.