Topological insulators (TIs) are attracting significant attention due to their unique transport properties stemming from symmetry-protected Dirac fermions on their surface. These properties make them promising candidates for applications in spintronics, optoelectronics, and photonics. Understanding the relaxation dynamics of excited carriers, particularly distinguishing between surface and bulk behavior, is crucial for realizing these applications. Previous studies using various pump-probe techniques have investigated carrier dynamics in TIs, but disentangling surface and bulk contributions has proven challenging due to the relatively small bandgap of TIs in the bismuth and antimony chalcogenide family. Optical excitation with near-infrared or visible light leads to interband transitions in the bulk, obscuring the surface state response. To address this, mid-infrared or terahertz photons are needed to selectively excite surface states located within the bandgap. Furthermore, the Fermi energy is often within the valence or conduction bands, leading to population of bulk states. While separation of surface and bulk dynamics has been achieved at cryogenic temperatures (5K), this isn't feasible for technologically relevant temperatures above the Debye temperature. This work addresses these challenges by combining low-energy optical excitation (THz pulses) with TI samples exhibiting varying Fermi level positions, enabling isolation of the surface state response without significant contribution from bulk states.

Numerous studies have explored carrier dynamics in topological insulators using pump-probe techniques. However, these investigations often struggle to differentiate the contributions of surface and bulk states to the observed dynamics due to experimental limitations. The small band gap of common TI materials (Bi2Se3 and Bi2Te3) means that near-infrared and visible light excitation creates both bulk and surface state carriers, making it difficult to isolate the surface state response. Prior work has attempted to overcome this limitation by using THz excitation, but this often involved bulk metallic TIs, making it difficult to separate surface and bulk effects. Furthermore, the formation of metastable states at the conduction band bottom complicates analysis of relaxation dynamics. Studies at cryogenic temperatures have yielded some success in separating surface and bulk dynamics, but this is not representative of practical, room-temperature operation. The present work aims to provide a more complete and practical understanding by employing a more refined approach.

This study utilizes three different TI samples: Bi2Se3 (Fermi level above the conduction band), Bi2Te3 (Fermi level below the valence band), and Bi1.4Sb0.6Te1.51Se1.49 (BSTS, Fermi level within the bandgap). These samples were grown as thin films on Al2O3 substrates. The Fermi level positions were determined using THz transmission measurements. The research employs two THz-based nonlinear techniques: THz-pump optical-probe (TPOP) and THz high-harmonic generation (THz HHG). In TPOP measurements, single-cycle THz pulses served as the pump, while 800nm, 100fs laser pulses were used as probes. Optical-pump optical-probe (OPOP) measurements, using 800nm pulses for both pump and probe, served as a control. The reflectivity changes were measured as a function of the pump-probe delay. THz HHG measurements were conducted to gain further insights into carrier relaxation dynamics. Electro-optic sampling was used to measure the fundamental and harmonic signals. The fluence dependence of the THz HHG was analyzed to assess the saturation behavior, which is highly sensitive to carrier relaxation times and Fermi velocity. The experimental setups for both TPOP and OPOP measurements, as well as THz HHG, are detailed in the supplementary information.

TPOP measurements revealed significantly different relaxation dynamics for the three samples. Bi2Se3 and Bi2Te3 showed slower relaxation times (picosecond timescale), attributed to carrier cooling via electron-phonon scattering. In contrast, BSTS exhibited significantly faster relaxation (few hundred femtoseconds), attributed to the isolated response of Dirac fermions in the surface states. OPOP measurements confirmed the ultrafast relaxation in BSTS was primarily due to intraband dynamics within the topological surface states. They contrasted with the results obtained through THz excitation. THz HHG measurements further corroborated the ultrafast relaxation. Unlike graphene, which exhibited strong saturation effects at high fields, the TIs showed a purely perturbative behavior with no saturation, maintaining cubic scaling for the third harmonic and scaling with exponent of 5.2 for the fifth harmonic. This absence of saturation is consistent with the ultrafast relaxation observed in TPOP. The maximum conversion efficiencies for the third harmonic were 0.13%, 0.08%, and 0.03% for Bi2Te3, BSTS, and Bi2Se3, respectively. The maximum fifth-harmonic conversion efficiency for BSTS was around 0.014%. Although lower than graphene at its optimal field, the purely perturbative nature of the harmonic generation in TIs suggest that higher conversion efficiency than graphene might be achievable at higher incident fields. The absence of saturation in THz harmonic generation up to 140 kV/cm supports the observed ultrafast relaxation times.

The observed ultrafast relaxation of Dirac fermions in the surface states of TIs (few hundred femtoseconds) is significantly faster than the bulk carrier relaxation (few picoseconds). This is likely due to efficient phonon-assisted scattering, either through surface intraband or surface-to-bulk interband transitions. The absence of saturation effects in THz harmonic generation, unlike in graphene, strongly suggests that the ultrafast cooling dynamics prevents heat accumulation. This has significant technological implications, as it indicates the potential for higher nonlinear conversion efficiencies compared to graphene by increasing the incident field strength. The results contribute significantly to the understanding of ultrafast carrier dynamics in TIs, offering valuable insights for designing and optimizing devices for THz applications and ultrafast spintronics.

This study successfully isolated and characterized the ultrafast relaxation dynamics of Dirac fermions in the surface states of topological insulators. The observed sub-picosecond relaxation times, contrasting with the slower bulk carrier relaxation, open new avenues for highly efficient THz nonlinear devices and ultrafast spintronic applications. The absence of saturation effects at high fields in THz harmonic generation suggests that significantly higher conversion efficiencies are achievable with increased incident fields, exceeding the potential of graphene. Future research could explore metamaterial integration to enhance electric fields further for optimizing conversion efficiency and expanding the scope of applications.

The study primarily focuses on thin-film samples, and the results may not directly translate to bulk materials. The specific growth methods and parameters could influence the observed carrier dynamics. Furthermore, while the study successfully separates the surface state response from the bulk, complexities introduced by the different layers of the heterostructures might influence the absolute values of the relaxation times and nonlinearities. Finally, further investigation into the precise mechanisms of phonon-assisted scattering is needed to refine the understanding of the relaxation processes.