Machine Learning Reconstruction of High-Dimensional Electronic Structure from Angle-Resolved Photoemission Spectroscopy

Abstract

The emergent behavior of quantum materials is governed by their electronic structure, which can be experimentally probed by photoemission spectroscopy techniques that generate a four-dimensional dataset of energy and momentum. However, the quantitative extraction of Hamiltonian parameters from these high-dimensional spectra remains a significant challenge, currently relying on labor-intensive, expert-dependent analysis rather than standardized workflows. Here, we introduce a deep learning framework based on implicit neural representations to accelerate the retrieval of Hamiltonian parameters in two types of transition-metal oxides: perovskite nickelates and manganites. Our approach outperforms traditional analytical fitting procedures, yielding superior agreement with experimental Fermi surface topologies and energy-momentum dispersions. This work highlights the potential of deep learning tools to bridge the gap between theory and experiment, paving the way for high-throughput, autonomous discovery pipelines in quantum materials.

Figures (4)

• Figure 1: a. Crystal structure of Nd$_{1-x}$Sr$_x$NiO$_3$ with the corresponding electronic configuration of Ni$^{3+}$. b. Architecture of the SIREN model: five hidden layers are placed between the inputs (three tight-binding parameters and $\mathbf{k}$) and the output (spectral intensity $I_{ML}$). c. Fermi surface obtained from the trained machine learning model (left) and from the tight-binding model (right).
• Figure 2: a. Our machine learning workflow to obtain the materials parameters. An initial guess of the tight-binding parameters is fed into the well-trained SIREN model. The parameters are iteratively updated using the gradient $\frac{\partial L}{\partial t_i}$ until convergence. b. Visualization of the loss landscape at $\mu = 1.9t_1$. A grid of 30 sampled values was employed for both $t_1$ and $t_2$. The color map represents the loss calculated by the trained ML model for the corresponding tight-binding parameters. Red and yellow points indicate the results from the ML fitting method and grid search (30$\times$30), respectively.
• Figure 3: Fermi surface and $E_k$ dispersion for perovskite nickelates. Comparison between ARPES data (1$^{st}$ Row) and ML predictions (2$^{nd}$ Row) uses ML-fitted parameters with $t_1=0.31eV$, $t_2/t_1=0.05$, $\mu/t_1=1.94$. The blue values on each graph represent the photon energy used during measurement.
• Figure 4: a. La$_{1-x}$Sr$_x$MnO$_3$ ($x=0.33$) ARPES Fermi surface measurements (top row) and ML predictions (bottom row) with parameters $t_1=0.42eV$, $t_2/t_1=0.06$, $\mu/t_1=1.23$. b. ARPES band dispersion (left panel) and ML predicted band dispersion (right panel). The blue values in the upper right corner of each panel in a and b represent the photon energy used during ARPES measurements. c. Visualization of the loss landscape at $\mu = 1.2t_1$ with 101$\times$101 grid for both $t_1$ and $t_2$. Both the Fermi surface and band dispersion ARPES data in a and b are utilized during the ML procedure.