Neural-Network-Assisted Detection of Superconducting Topological Semimetals

Abstract Diagnosing nontrivial topology is one of the core pursuits of modern condensed matter physics. Up to date, a wide range of theoretical techniques have been developed for this purpose. However, the majority of these are tailored for analyzing theoretical models, rather than actual experiments. Here, we propose a machine-learning-based protocol for the identification of two-dimensional superconducting topological semimetals using superfluid stiffness data as an input. In their normal phase, these superconductors contain band touching points (BTPs) which carry nonzero topological charges, i.e., vorticities. Our method relies on detecting certain vorticity-associated patterns encoded in heat maps of the superfluid stiffness obtained by varying the chemical potential and an applied Zeeman field. We show that our neural network attains a notably high accuracy in predicting the energy-resolved total absolute vorticity of BTPs. We reach to this conclusion by testing our approach against superfluid stiffness data theoretically-obtained from suitable extended-Dirac and graphene models.