Hamiltonian learning with real-space impurity tomography in topological moire superconductors

TL;DR

This paper presents a machine learning approach to extract Hamiltonian parameters, including exchange and superconducting modulations, from real-space impurity spectroscopy data in topological moire superconductors, enabling detailed characterization of quantum states.

Contribution

The study introduces a novel method combining impurity spectroscopy with machine learning to infer complex Hamiltonian parameters in topological superconductors, including superconducting order features.

Findings

Machine learning can extract exchange modulations from impurity data.

Harmonic expansion with neural networks infers superconducting features.

The approach outperforms conventional architectures in certain parameter inferences.

Abstract

Extracting Hamiltonian parameters from available experimental data is a challenge in quantum materials. In particular, real-space spectroscopy methods such as scanning tunneling spectroscopy allow probing electronic states with atomic resolution, yet even in those instances extracting effective Hamiltonian is an open challenge. Here we show that impurity states in modulated systems provide a promising approach to extracting non-trivial Hamiltonian parameters of a quantum material. We show that by combining the real-space spectroscopy of different impurity locations in a moire topological superconductor, modulations of exchange and superconducting parameters can be inferred via machine learning. We demonstrate our strategy with a physically-inspired harmonic expansion combined with a fully-connected neural network that we benchmark against a conventional convolutional architecture. We show that while both approaches allow extracting exchange modulations, only the former approach allows inferring the features of the superconducting order. Our results demonstrate the potential of machine learning methods to extract Hamiltonian parameters by real-space impurity spectroscopy as local probes of a topological state.