拓扑绝缘体表面态量子输运的物理约束神经网络建模与退相干机制研究

Physics-Informed Neural-Network Modeling of Quantum Transport and Decoherence Mechanisms in Topological-Insulator Surface States

摘要: 拓扑绝缘体表面态具有自旋–动量锁定、时间反演对称保护和弱反局域化等特征，是研究低维量子输运、相干调控和自旋电子器件的重要平台。然而在真实器件中，表面态电导同时受到费米能级漂移、非磁性无序、磁性杂质、有限尺寸、接触电阻以及电子–电子、电子–声子相互作用的共同影响，传统解析模型和逐点数值模拟难以在多参数空间中快速识别主导退相干机制。本文提出一种面向拓扑绝缘体表面态输运的物理约束神经网络框架，将表面Dirac哈密顿量、Landauer-Büttiker电导、时间反演互易关系和弱反局域化修正嵌入损失函数，并以电导、磁电导修正、相干长度和Hikami-Larkin-Nagaoka系数为多任务学习目标。在规范化数值样本上，物理约束网络相较于普通多层感知机降低了电导误差和互易性违背度，同时给出可解释的退相干通道分解。结果表明，将拓扑保护规律与数据驱动学习结合，可为复杂样品的快速表征、退相干来源判别和器件参数反演提供有效途径。

Abstract: The surface states of topological insulators, characterized by spin-momentum locking, time-reversal symmetry protection, and weak antilocalization, serve as a prominent platform for investigating low-dimensional quantum transport, coherent manipulation, and spintronic devices. In realistic devices, however, the surface-state conductance is concurrently influenced by Fermi-level drifting, nonmagnetic disorder, magnetic impurities, finite-size effects, contact resistances, as well as electron-electron and electron-phonon interactions. Conventional analytical models and point-by-point numerical simulations struggle to efficiently identify the dominant decoherence mechanisms across a multidimensional parameter space. To address this challenge, we propose a physics-constrained neural network framework tailored for transport in topological insulator surface states. The surface Dirac Hamiltonian, Landauer-Büttiker conductance formalism, time-reversal reciprocity relations, and weak antilocalization corrections are explicitly embedded into the loss function, while the conductance, magnetoconductance corrections, coherence length, and Hikami-Larkin-Nagaoka coefficient are formulated as multi-task learning targets. On standardized numerical samples, the proposed physics-constrained network achieves reduced conductance errors and lower reciprocity violations compared to a conventional multilayer perceptron, while also providing interpretable decomposition of decoherence channels. Our results demonstrate that integrating topologically protected transport laws with data-driven learning offers an effective pathway for rapid characterization of complex samples, identification of decoherence origins, and inversion of device parameters.