Inversion Symmetry Breaking in the Probability Density by Surface-Bulk Hybridization in Topological Insulators

The probability density distribution is analyzed in a topological insulator (TI) slab of finite thickness, where the bulk and surface states are allowed to hybridize. By using an effective continuum Hamiltonian approach as a theoretical framework, the wave functions are analytically obtained for each state near the Gamma$\Gamma$-point. The results reveal that, under particular combinations of the hybridized bulk and surface states, the spatial symmetry of the electronic probability density with respect to the center of the slab can be spontaneously broken. This symmetry breaking arises as a combination of the parity of the solutions, their spin projection, and the material constants. The probability density in a topological insulator (TI) slab of thickness d, where bulk and surface states hybridize. From an effective continuum Hamiltonian, the wave functions are obtained near the Gamma$\Gamma$-point. The Author find that the spatial symmetry of the electronic probability density can be spontaneously broken as a combination of the solutions parity, spin projection, and material constants. image