Scalable Machine Learning Models for Predicting Quantum Transport in Disordered 2D Hexagonal Materials

TL;DR

The paper addresses predicting quantum transport in disordered 2D hexagonal materials by predicting the transmission $T(E)$ and average-$LDOS$ using ML. It combines a tight-binding Hamiltonian with the NEGF formalism to generate a large, diverse dataset across graphene, germanene, silicene, and stanene and introduces a geometry-driven feature space that enables cross-material generalization. Random Forest regression emerges as the most accurate approach for continuous targets, outperforming classification, and polynomial feature expansion further improves performance; however extrapolation to unseen configurations shows substantial degradation, revealing limitations of tree-based methods. The work enables high-throughput screening for nanoelectronic and spintronic device design, while pointing to physics-informed or graph-based models as promising avenues to improve generalization beyond the trained domain, with data and code publicly available for reuse.

Abstract

We introduce scalable machine learning models to accurately predict two key quantum transport properties, the transmission coefficient T(E) and average local density of states (Average-LDOS) in two-dimensional (2D) hexagonal materials with magnetic disorder. Using a tight binding Hamiltonian combined with the Non-Equilibrium Green's Function (NEGF) formalism, we generate a large dataset of over 400,000 unique configurations across graphene, germanene, silicene, and stanene nanoribbons with varying geometries, impurity concentrations, and energy levels. A central contribution of this work is the development of a geometrydriven, physically interpretable feature space that enables the models to generalize across material types and device sizes. Random Forest regression and classification models are evaluated in terms of accuracy, stability, and extrapolation ability. Regression consistently outperforms classification in capturing continuous transport behavior on in-domain data. However, extrapolation performance degrades significantly, revealing the limitations of tree-based models in unseen regimes. This study highlights both the potential and constraints of scalable ML models for quantum transport prediction and motivates future research into physics-informed or graph-based learning architectures for improved generalization in spintronic and nanoelectronic device design.

Figures (8)

• Figure 1: Schematic of the two terminal device. Red color region represent leads and The unit cell is highlighted in blue.
• Figure 2: The transmission (T) and average local density of states (LDOS) are plotted as a function of energy (eV) for three random magnetic configurations of a graphene nanoribbon (width: 9.83 nm, length: 9.23 nm).
• Figure 3: Comparison of T(E) and Average-LDOS for materials with equal number of sites $N=48$ and $nm=4$ used in the training dataset.
• Figure 4: Flowchart of how we train and evaluate models
• Figure 5: Regression model performance. Comparing the predicted vs. true values for Average-LDOS and Transmission ($T$). The dashed red line represents the ideal prediction ($y=x$), and the shaded area shows the $95\%$ Prediction Interval (PI).