Topology of Bi2Se3 nanosheets

Recently, the quantum spin-Hall edge channels of two-dimensional colloidal nanocrystals of the topological insulator Bi2Se3 were observed directly. Motivated by this development, we reconsider the four-band effective model which has been traditionally employed in the past to describe thin nanosheets of this material. Derived from a three-dimensional k <middle dot> p model, it physically describes the top and bottom electronic surface states at the I' point that become gapped due to the material's small thickness. However, we find that the four-band model for the surface states alone, as derived directly from the three-dimensional theory, is inadequate for the description of thin films of a few quintuple layers and even yields an incorrect topological invariant within a significant range of thicknesses. To address this limitation we propose an eight-band model which, in addition to the surface states, also incorporates the set of bulk states closest to the Fermi level. We find that the eight-band model not only captures most of the experimental observations, but also agrees with previous first-principles calculations of the Z2 invariant in thin films of varying thickness. The band inversion around the I' point, which endows the surfacelike bands with topology, is shown to be enabled by the presence of the additional bulklike states without requiring any reparametrization of the resulting effective Hamiltonian.