Pham T. Huong, Chuong V. Nguyen, Huynh V. Phuc, Nguyen N. Hieu, Bui D. Hoi and Le T.T. Phuong
The fundamental investigation of topological crystalline insulator (TCI) thin films is essential for observing interesting phenomena. In practice, a promising pathway involves the application of electric and magnetic fields to tune the topological phases of TCI thin films. To achieve this, we applied a perpendicular electric field and an in-plane magnetic field to not only tune the Dirac gap of a SnTe(001) thin film and find the phase transition but also to directly connect them with their effects on the group velocity of both massless and massive surface Dirac fermions. The TCI thin film is an inherent insulator due to the hybridization between the front and back surfaces, and it transitions to a semimetal phase at a critical perpendicular electric field due to the Stark effect. Correspondingly, the anisotropic group velocity of the upper (lower) conduction (valence) band decreases (increases) with the electric field at certain momenta. We found that when one of the in-plane Zeeman field components becomes stronger than the intrinsic hybridization potential, the anisotropic Weyl cones with opposite chiralities retrieve at the critical momenta and the corresponding group velocities become zero. Further, the isotropic in-plane Zeeman field leads to rotation of the band structure, as expected, resulting in non-zero group velocities along all directions. Finally, for the sake of completeness, the combined Stark and Zeeman effects are tracked and the results show that the system is an insulator at all fields and the group velocities are altered more than when the individual Stark and Zeeman effects are applied. Our findings may provide interesting physical insights for practical applications in nanoelectronics and spintronics.
