深度科马克：使用基于模型的数据驱动算法进行费米面断层扫描
DeepCormack: Fermi surface tomography using model-based data-driven algorithms
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中文总结 AI 辅助
研究利用电子-正电子湮灭辐射角关联重建三维双光子动量密度来研究材料费米面，提出基于数据驱动模型的深度科马克算法，通过集成深度学习模型增强传统方法，还给出合成数据方法，提高重建质量并加快采集时间。
中文摘要 AI 辅助
通过电子-正电子湮灭辐射的角关联（ACAR）对三维双光子动量密度（TPMD）进行实验重建，是研究材料费米面的一种特别有用的方法。它不依赖低温、超高真空条件或强磁场，能研究材料的自旋分辨电子结构，但仍是一个具有挑战性的逆问题。通常要测量\(10^8\)次正电子湮灭事件以获取不同角度的TPMD的3至6个投影。标准重建方法是科马克方法（MCM）的ACAR改编版，利用晶体结构的固有对称性。但信噪比差，为费米面研究收集足够质量的数据每个样本可能需要数月。我们提出了深度科马克，这是一族基于数据驱动模型的重建算法，通过在不同阶段集成监督深度学习模型（CNN、MLP和UNet）来增强MCM。为克服缺乏大型实验训练集的问题，我们提出一种利用奇异值分解和动态模式分解生成逼真合成TPMD体积的方法，仅需通过密度泛函理论计算的单个参考动量密度。在测试数据上，深度科马克在200M计数时比MCM的重建质量提高约8.5dB PSNR，在计数减少时仍保持稳定，能显著加快采集时间。对实验数据的泛化很大程度上取决于参考动量密度的训练分布与样本的匹配程度。因此，我们建议将深度科马克与目标材料的DFT计算配对以创建特定样本的训练数据。我们提出的方法能提供更高质量的重建，或能显著加快重建速度，达到几周的量级。
英文摘要
The experimental reconstruction of the 3D two-photon momentum density (TPMD) via angular correlation of electron-positron annihilation radiation (ACAR) is a particularly useful method for studying material Fermi surfaces. It does not rely on low temperatures, UHV conditions, or strong magnetic fields, and enables the study of the spin-resolved electronic structure of materials. Yet, it remains a challenging inverse problem. Typically, 10^8 positron annihilation events are measured for 3--6 projections of the TPMD at different angles. The standard reconstruction approach is an ACAR adaptation of Cormack's method (the MCM) that leverages the inherent symmetry in the crystal's structure. However, the poor signal-to-noise ratio means collecting data of sufficient quality for Fermi surface studies can take months per sample. We present DeepCormack, a family of data-driven model-based reconstruction algorithms that augments the MCM by integrating supervised deep-learning models (CNN, MLP, and UNet) at various stages. To overcome the lack of large experimental training sets, we propose a method which leverages singular value decomposition with dynamic mode decomposition to generate realistic synthetic TPMD volumes, requiring only a single reference momentum density computed via density functional theory. On test data, DeepCormack improves reconstruction quality over MCM by about 8.5 dB PSNR at 200M counts and remains stable at reduced counts, enabling significantly faster acquisition times. Generalisation to experimental data depends strongly on how well the training distribution from the reference momentum density matches the sample. We therefore recommend pairing DeepCormack with a DFT calculation of the target material to create sample-specific training data. Our proposed method offers either much higher quality reconstructions, or enables significantly faster ones, on the order of weeks.
发表机构
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge（应用数学与理论物理系，剑桥大学）
- H.H. Wills Physics Laboratory, University of Bristol（布里斯托大学HH.Wills物理实验室）
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