Quasiparticle Interference Kernel Extraction with Variational Autoencoders via Latent Alignment

TL;DR

The paper tackles the ill-posed problem of extracting a single-scatterer QPI kernel $\mathcal{A}$ from multi-scatterer STM images $\mathcal{Y}$ by introducing a two-step variational autoencoder with latent alignment. Step 1 learns a compact kernel latent space via a kernel VAE, and Step 2 trains an observation encoder to map $(\mathcal{Y},\mathcal{M})$ into that space, enforcing $\mathbf{h}_y \approx \mathbf{h}_A$. A 100-kernel synthetic dataset (50k samples) with noise augmentation is developed and validated on real Ag and FeSe data, showing superior accuracy and generalization over a one-step baseline. Ablation studies demonstrate the value of symmetric losses, pre-trained VAEs, and noise augmentation in improving robustness. This data-driven framework provides a scalable, physically informed approach to inverse problems in quantum materials and enables efficient kernel extraction and benchmarking.

Abstract

Quasiparticle interference (QPI) imaging is a powerful tool for probing electronic structures in quantum materials, but extracting the single-scatterer QPI pattern (i.e., the kernel) from a multi-scatterer image remains a fundamentally ill-posed inverse problem, because many different kernels can combine to produce almost the same observed image, and noise or overlaps further obscure the true signal. Existing solutions to this extraction problem rely on manually zooming into small local regions with isolated single-scatterers. This is infeasible for real cases where scattering conditions are too complex. In this work, we propose the first AI-based framework for QPI kernel extraction, which models the space of physically valid kernels and uses this knowledge to guide the inverse mapping. We introduce a two-step learning strategy that decouples kernel representation learning from observation-to-kernel inference. In the first step, we train a variational autoencoder to learn a compact latent space of scattering kernels. In the second step, we align the latent representation of QPI observations with those of the pre-learned kernels using a dedicated encoder. This design enables the model to infer kernels robustly under complex, entangled scattering conditions. We construct a diverse and physically realistic QPI dataset comprising 100 unique kernels and evaluate our method against a direct one-step baseline. Experimental results demonstrate that our approach achieves significantly higher extraction accuracy, improved generalization to unseen kernels. To further validate its effectiveness, we also apply the method to real QPI data from Ag and FeSe samples, where it reliably extracts meaningful kernels under complex scattering conditions.

Figures (10)

• Figure 1: Illustration of the QPI Kernel Extraction Problem
• Figure 2: Top: The proposed two-step training framework. Step 1 (blue box): training a VAE for kernel $\mathcal{A}$ reconstruction using the losses $\mathcal{L}_{\text{MSE}}$ and $\mathcal{L}_{\text{SYM}}$. Step 2 (red box): training the observation–activation encoder via aligning $\mathbf{h}_A$ and $\mathbf{h}_y$ (the kernel encoder is frozen). Bottom: The inference process.
• Figure 3: Illustration of the symmetric loss $\mathcal{L}_{\text{SYM}}$: the reconstructed image is rotated by $180^\circ$, $120^\circ$, $90^\circ$, or $60^\circ$ when there are $2$-, $3$-, $4$-, or $6$-fold symmetries, respectively. Only the values in the red box are taken into consideration.
• Figure 4: Comparison of noise-free and noisy datasets in a $20\times20\;\mathrm{nm}$ observation window, illustrating kernels with 2-, 3-, 4-, and 6-fold rotational symmetry.
• Figure 5: Examples of experimental observation denoised with different methods (1st row-Gaussian, 2nd row-Median, 3rd row-Box) at different intensities (1st column-original, 2nd column-light, 3rd column-heavy)