Resonance effects in thickness-dependent ultrafast carrier and phonon dynamics of topological insulator Bi₂Se₃

Resonance effects in the thickness-dependent ultrafast carrier and phonon dynamics of topological insulator Bi₂Se₃ are found irrespective of the kind of substrate by measuring thickness-dependent abrupt changes of pump-probe differential-reflectivity signals (ΔR/R) from Bi₂Se₃ thin films on four different substrates of poly- and single-crystalline (sc-) ZnO, sc-GaN and SiO₂. The absolute peak intensity of the ΔR/R is maximized at ∼t _C (6 ∼ 9 quintuple layers), which is not directly related to but is very close to the critical thickness below which the energy gap opens. The intensities of the two phonon modes deduced from the oscillatory behaviors superimposed on the ΔR/R profiles are also peaked at ∼t _C for the four kinds of substrates, consistent with the thickness-dependent Raman-scattering behaviors. These resonant effects and others are discussed based on possible physical mechanisms including the effects of three-dimensional carrier depletion and intersurface coupling.