Effective continuous model for surface states and thin films of three dimensional topological insulators

TL;DR

This paper develops an effective continuous model for surface states and thin films of 3D topological insulators, capturing key features like energy gaps and wavefunction asymmetries, and applies it to experimental data on Bi2Se3 films.

Contribution

The authors derive a new effective continuous model for 3D topological insulator surface states and thin films, including effects of surface coupling and structure inversion asymmetry.

Findings

Model reproduces ARPES spectra of Bi2Se3 films.

Thin films can be in the quantum spin Hall phase.

Strong SIA destroys the quantum spin Hall state.

Abstract

Two-dimensional effective continuous models are derived for the surface states and thin films of the three-dimensional topological insulator (3DTI). Starting from an effective model for 3DTI based on the first principles calculation [Zhang \emph{et al}, Nat. Phys. 5, 438 (2009)], we present solutions for both the surface states in a semi-infinite boundary condition and in the thin film with finite thickness. An effective continuous model was derived for surface states and the thin film 3DTI. The coupling between opposite topological surfaces and structure inversion asymmetry (SIA) give rise to gapped Dirac hyperbolas with Rashba-like splittings in energy spectrum. Besides, the SIA leads to asymmetric distributions of wavefunctions along the film growth direction, making some branches in the energy spectra much harder than others to be probed by light. These features agree well with the recent angle-resolved photoemission spectra of Bi$_{2}$Se $_{3}$ films grown on SiC substrate [Zhang et al, arXiv: 0911.3706]. More importantly, we use the effective model to fit the experimental data and determine the model parameters. The result indicates that the thin film Bi$_{2}$Se$_{3}$ lies in quantum spin Hall region based on the calculation of the Chern number and the $Z_{2}$ invariant. In addition, strong SIA always intends to destroy the quantum spin Hall state.