Electric field tuning of the optical absorbance of topological insulator thin films

Abstract

In view of electro-optic modulators and switches operating in the terahertz frequency range, we study the absorbance of a topological insulator (TI) thin film subjected to a static electric field. Adopting the Hamiltonian for the three-dimensional ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ class of TIs including terms to second order in the electron wave vector and to first order in the electric field, we present an effective model for a TI thin film. We demonstrate the distinct influences of in-plane and out-of-plane external electric fields, the in-plane electric field-induced dichroism, and the electric field and chemical potential tuning of the absorbance edge. Under the influence of an out-of-plane electric field, a TI film with a thickness of about 2 nm exhibits a considerable absorbance at the absorbance edge. Of prime practical importance, the absorbance edge can be shifted about $0.3\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ with the application of moderate electric fields about $0.4\phantom{\rule{0.28em}{0ex}}\mathrm{V}{\mathrm{nm}}^{\ensuremath{-}1}$ or with chemical potential variations about $0.3\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$.