Modeling of Weyl semimetals via Automatic Differentiation

Topological materials often exhibit characteristic energy bands that are not observed in conventional materials. A representative example is the Weyl semimetal, characterized by a cone-shaped energy band. In the analysis of realistic Weyl semimetals, Wannier functions constructed from first-principles calculations are widely used. However, these Wannier functions are often complex, making their physical interpretation difficult. Moreover, from the viewpoint of computational cost, an effective low-energy model that captures the essential physics is often more suitable. On the other hand, the quantitative accuracy of such effective models is sometimes questionable.

In this study, we propose the construction of accurate and effective models using automatic differentiation (AD), a modern numerical differentiation technique emerging from AI and machine learning. Although model design methods based on AD have been proposed [1], they have not yet been applied to enhance the quantitative accuracy of effective models.

In this talk, we focus on the compensated ferrimagnetic Weyl semimetal Ti₂MnAl [2] and demonstrate model construction using AD. By applying AD to a 4×4 tight-binding model, we successfully constructed an effective model that reproduces the high-symmetry line band structure close to the first-principles calculation results.

[1] K. Inui and Y. Motome, Commun. Phys. 6, 37 (2023)

[2] W. Shi et al., Phys. Rev. B 97, 060406 (2018)