Time-Resolved Second-Harmonic Generation in Topological Insulator Bi₂Te₃: Competing Contributions from Dirac Surface States, Surface Photovoltage, and Band Bending

Abstract

Nonlinear optical experiments, especially the second-harmonic generation (SHG) of topological insulators (TIs) such as Bi2Te3 and Bi2Se3, provide significant insights into the second-order nonlinear susceptibility (χ(2)) of the topological surface states (TSS) and the DC electric field (E dc), formed by the intrinsic band bending between the surface and bulk states. Importantly, by selectively tuning the polarization of the incident laser field from linear to circular, second-harmonic measurements in TIs enable us to extract these explicit contributions from the band bending (E dc) and metallic surface states (χ(2)), respectively. In this work, we report the relaxation dynamics of the differential change in SHG intensity (ΔI(τpp) = I shg pump on(τpp) – I shg pump off) with respect to the pump–probe delay time (τpp) in Bi2Te3 crystal, mainly emphasizing on different pump–probe polarization configurations to provide an understanding of the temporal evolution of ΔE dc(τpp) and Δχ(2)(τpp). Upon photoexcitation, ΔI(τpp) with linearly polarized pump–probe configuration, we observe two opposing contributions to ΔE dc, namely, the depletion electric field (DEF) and surface photovoltage (SPV) that effectively determine the spatial distribution of the bulk and surface carrier densities. However, on switching the probe polarization from linear to circular, we show that the SHG response has a predominant contribution from χ(2), thereby extracting the time evolution of Δχ(2) arising from the TSS after photoexcitation, observed as an additional positive enhancement of ΔI(τpp). This is analytically understood by opening a band gap of ∼48 meV at the Dirac point due to the breaking of time reversal symmetry using circularly polarized light.