Hybridization and Electron-Hole Symmetry Breaking Effects on the Magento-Optical Conductivity of Sb₂Te₃ Thin-Films

The surface states residing at opposite surfaces of topological insulators (TIs) such as Bi₂Se₃ and Sb₂Te₃ hybridize if the TI thickness becomes comparable to their decay lengths, leading to a spectral gap. The TI Sb₂Te₃ has not received much attention as it is assumed that its properties are similar to Bi₂Se₃, as they belong to the same topological class. Although the same k.p Hamiltonian can describe these two TIs, their k.p parameters lead to crucial differences. These differences are prominent in their thin-films since finite-size effects and electron-hole (e-h) asymmetry play a more prominent role in the hybridization gap of Sb₂Te₃ due to longer decay lengths in this material. To discern the crucial difference between these TIs, Bi₂Se₃, and Sb₂Te₃, we study their thin-films' magneto-optical response through a self-consistent consideration of their bulk Hamiltonians, boundary conditions, and their magneto-optical conductivity. We discuss the consequences of e-h asymmetry, bulk contributions, and the Zeeman coupling on the real and imaginary parts of the optical conductivity of Sb₂Te₃ thin-films and contrast them to their Bi₂Se₃ counterpart.