Seeing the Invisible: Machine learning-Based QPI Kernel Extraction via Latent Alignment

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. In this work, we propose the first AI-based framework for QPI kernel extraction. 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 even 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, and improved generalization to unseen kernels.

• The paper presents a two-step AI framework that separates kernel representation and observation-to-kernel inference to address challenges in QPI extraction.
• It leverages a variational autoencoder to capture scattering dynamics, achieving up to a 23% reduction in RMSE compared to one-step methods.
• The approach enhances precision in quantum material analysis and paves the way for advanced AI applications in condensed matter physics.

AI-Based Framework for QPI Kernel Extraction via Latent Alignment

Quasiparticle Interference (QPI) imaging stands as a potent method for examining the electronic structures of quantum materials, yet it poses challenges, notably the extraction of single-scatterer QPI patterns from multi-scatterer images. In addressing this inverse problem, the paper presents an innovative AI-based framework that leverages machine learning techniques to achieve QPI kernel extraction through a method called latent alignment.

Methodological Approach

The proposed solution consists of a two-step learning strategy which separates the process of kernel representation learning from observation-to-kernel inference. In the initial step, a variational autoencoder (VAE) is employed to establish a compact latent space for scattering kernels. The VAE architecture, well-suited for high-dimensional data tasks, is integral in capturing the complex kernel dynamics. The second step involves aligning the latent representation of QPI observations with those of the established kernels through a dedicated encoder. This separation into two stages mitigates the complexity inherent in inferring kernels within entangled scattering scenarios.

Dataset and Evaluation

The authors developed a comprehensive and physically realistic QPI dataset containing 100 unique kernels that reflect a wide range of scattering environments. Each kernel in this dataset is characterized through simulated QPI images incorporating various impurity configurations. The two-step approach demonstrated a substantial improvement in inference accuracy when evaluated against a direct one-step baseline, with notable gains shown in metrics such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE).

Numerical Results

Quantitatively, the two-step method achieved extraction accuracy up to a 23% reduction in RMSE compared to traditional approaches. This highlights the model's capacity for accurate kernel inference even under the complexities of multi-scattering environments. The results showcase the method's robustness and its potential to generalize better to unseen kernels in out-of-domain settings.

Implications and Future Prospects

The proposed framework represents a significant advancement in applying AI to quantum material analysis. The insights provided by this paper lay the groundwork for integrating machine learning more profoundly into the field of condensed matter physics. Practically, this methodology may enhance the precision of understanding electronic structures in quantum materials, potentially influencing further development in areas like superconductivity.

The future of AI in quantum materials research may involve refining models such as this one to improve their understanding of kernel symmetry features, boosting the precision of inferred kernel structures. There is significant potential for this framework to evolve beyond simulation environments, becoming applicable in real-world QPI imaging scenarios.

In conclusion, this paper presents a compelling AI approach to address a challenging inverse problem in condensed matter physics, offering substantial improvements in kernel extraction accuracy and paving the way for more sophisticated AI applications in the field.