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

Nonlinear optical experiments, especially 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. Importantly, by selectively tuning the polarisation of the incident laser field from linear to circular, SHG in TIs enables us to extract these explicit contributions from the band bending and metallic surface states. In this work we report the relaxation dynamics of the differential change in SHG intensity (ΔI(τ_pp)) with respect to the pump-probe delay time (τ_pp) in Bi₂Te₃ crystal, mainly emphasizing on different pump-probe polarisation configurations to provide an understanding of the temporal evolution of ΔE_dc and Δχ⁽²⁾. Upon photoexcitation, with linearly polarised pump-probe configuration, we observe two opposing contributions to ΔE_dc namely, the depletion electric field (DEF) and surface photovoltage (SPV) that arise from the spatial distribution of the bulk and surface carrier densities. However, on switching the probe polarisation from linear to circular, we show that the ΔI(τ_pp) has a predominant positive contribution from Δχ⁽²⁾ arising from the TSS. This is analytically understood by opening a band gap at the Dirac point due to the breaking of time-reversal symmetry using circularly polarised light.