Effective theory for Cd$_3$As$_2$ thin films in the presence of magnetic fields

Recent experiments with bulk Dirac semimetals in the thin film limit have produced interesting results upon the application of magnetic fields [1,2]. We present an effective microscopic theory for Cd$_3$As$_2$ thin films, showing their transition to quantum spin Hall insulators in the thin film limit when cleaved in the (001) direction. We investigate how the band structure changes in the presence of in-plane and out-of-plane magnetic fields, showing that for sufficiently large in-plane Zeeman fields, there is a transition to a two-dimensional Weyl semimetal phase when the field is directed perpendicular to a high symmetry plane. As the field is rotated, the Weyl points become gapped, the gap changing sign as the field is rotated perpendicular to the high symmetry planes. Additionally, in the large in-plane field limit with an out-of-plane orbital field, we show that the low-energy Landau levels acquire an additional two-fold degeneracy coming from the two Weyl nodes, which is removed at higher energies. Lastly, we present a theory for the non-trivial surface states and their evolution in the presence of an in-plane Zeeman field, showing that one of the surface states vanishes in the large-field limit, leaving the system with a finite Chern number.



[1] A. C. Lygo, B. Guo, A. Rashidi, V. Huang, P. Cuadros-Romero, and S. Stemmer, Phys. Rev. Lett. 130, 046201 (2023).

[2] B. Guo, W. Miao, V. Huang, A. C. Lygo, X. Dai, and S. Stemmer, Phys. Rev. Lett. 131, 046601 (2023).