Predicting topological invariants and unconventional superconducting pairing from density of states and machine learning

Flavio Noronha, Askery Canabarro, Rafael Chaves, Rodrigo G. Pereira
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Abstract

Competition between magnetism and superconductivity can lead to unconventional and topological superconductivity. However, the experimental confirmation of the presence of Majorana edge states and unconventional pairing currently poses a major challenge. Here we consider a two-dimensional lattice model for a superconductor with spin-orbit coupling and exchange coupling to randomly distributed magnetic impurities. Depending on parameters of the model, this system may display topologically trivial or nontrivial edge states. We map out the phase diagram by computing the Bott index, a topological invariant defined in real space. We then use machine learning (ML) algorithms to predict the Bott index from the local density of states (LDOS) at zero energy, obtaining high-accuracy results. We also train ML models to predict the amplitude of odd-frequency pairing in the anomalous Green's function at zero energy. Once the ML models are trained using the LDOS, which is experimentally accessible via scanning tunneling spectroscopy, our method could be applied to predict the number of Majorana edge states and to estimate the magnitude of odd-frequency pairing in real materials.
从态密度和机器学习预测拓扑不变性和非常规超导配对
磁性和超导性之间的竞争可能导致非常规和拓扑超导性。然而,实验证实马约拉纳边缘态和非常规配对的存在目前是一个重大挑战。在这里,我们考虑了一个具有自旋轨道耦合和随机分布磁性杂质交换耦合的超导体二维晶格模型。根据模型参数的不同,该系统可能显示拓扑上的琐碎边缘态或非琐碎边缘态。我们通过计算博特指数绘制出相图,博特指数是在实空间定义的拓扑不变量。然后,我们使用机器学习(ML)算法从零能量时的局部态密度(LDOS)预测 Bott 指数,获得了高精度的结果。我们还训练 ML 模型来预测零能量时反常格林函数中奇异频率配对的振幅。一旦使用 LDOS 训练出 ML 模型,我们的方法就可以应用于预测马约拉纳边沿态的数量和估计实际材料中奇频配对的幅度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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