Terahertz signatures of ultrafast Dirac fermion relaxation at the surface of topological insulators

Topological insulators (TIs) host symmetry-protected Dirac fermions with nontrivial topology on their surfaces, offering opportunities in electronics, spintronics, optoelectronics, and thermoelectrics. A key open question for enabling such applications is whether and how the ultrafast relaxation dynamics of excited carriers in the topological surface states differ from those in the bulk. Prior pump–probe studies have not reached consensus on the mechanisms and timescales of Dirac fermion relaxation in surface states, largely because it is difficult to disentangle surface and bulk contributions. Near-IR/visible excitation typically induces interband transitions in bulk bands due to the small bulk bandgaps (few hundred meV) in bismuth and antimony chalcogenide TIs, while Fermi levels in common binaries (Bi2Se3, Bi2Te3) often lie inside bulk bands, populating bulk states. Although separation of surface and bulk dynamics has been demonstrated at 5 K, at technologically relevant temperatures phonon-assisted surface-to-bulk scattering (above the Debye temperature ~180 K for Bi2Se3) complicates isolation of surface dynamics. The authors address this by combining low-photon-energy optical excitation with a TI whose Fermi level lies within the bandgap, enabling isolation of Dirac surface-state responses using below-bandgap THz excitation. They compare three samples with different Fermi-level positions (Bi2Te3: valence band; Bi2Se3: conduction band; BSTS: within bandgap) to determine the distinct ultrafast relaxation timescales of surface versus bulk carriers.

Previous ultrafast optical and photoemission studies probed carrier and phonon dynamics in TIs using near-/mid-IR pump–probe and tr-ARPES, reporting sub-200 fs electron–electron thermalization and picosecond-scale cooling, as well as metastable states at the conduction band edge that slow population decay. However, excitation energies near/above the bandgap typically drive both bulk and surface states, preventing clear separation. THz pumping has been used for bulk-metallic TIs to study carriers and phonons, but still with mixed surface/bulk contributions. Recent work showed surface-state origin of THz HHG in Bi2Se3 by comparing to topologically trivial surfaces. The literature thus indicates: (i) fast electron–electron scattering (<200 fs) in Bi2Se3; (ii) electron–phonon cooling on few-ps scales in bulk; (iii) challenges in isolating surface dynamics at room temperature due to phonon-assisted surface–bulk scattering; and (iv) strong, often saturating THz nonlinearity in Dirac materials like graphene, with saturation linked to hot-carrier dynamics and cooling bottlenecks.

Samples: Three TI thin films grown on (0001) Al2O3: Bi2Se3 (30 nm), Bi2Te3 (490 nm), and Bi1.4Sb0.6Te1.51Se1.49 (BSTS, 375 nm). Fermi level positions estimated from THz transmission: Bi2Se3 ~26 meV above conduction band minimum; Bi2Te3 ~30 meV below valence band maximum; BSTS ~110 meV below conduction band (inside bandgap). BSTS composition chosen near Ren’s curve to minimize donors/acceptors and accentuate surface-state properties. Experimental approaches: (1) THz-pump optical-probe (TPOP): Broadband single-cycle THz pulses (photon energies <4 meV; peak fields up to ~400 kV/cm) pump; 800 nm (1.5 eV), 100 fs pulses probe transient reflectivity. Probe penetration depth: few tens of nm. (2) Optical-pump optical-probe (OPOP): Degenerate 800 nm pump and probe to compare above-bandgap excitation. (3) THz high-harmonic generation (THz HHG): Fundamental ~0.5 THz excitation with peak fields up to 140 kV/cm; electro-optic sampling of fundamental and generated harmonics (3ω and 5ω). Measurements performed in transmission geometry; polarization dependence and ellipticity tested; comparison to p-doped graphene (~10^13 cm^-2) for benchmarking nonlinearity and saturation. Data analysis: Transient reflectivity decomposed into ultrafast rise (electron–electron thermalization), initial decay (cooling/relaxation), and coherent phonon oscillations (Raman-excited). Multi-exponential fits extract timescales. HHG field scaling versus fundamental field evaluated via power-law fits (slopes near 3 for THG and near 5 for FHG indicate perturbative regime).

- Isolated surface-state dynamics with below-bandgap THz excitation in BSTS (Fermi level in bandgap) show ultrafast relaxation on a few hundred femtosecond timescale, with negligible slow component immediately after excitation. - Bulk-conducting TIs exhibit slower dynamics: Bi2Se3 shows a fast decay 1.45–1.9 ps (electron–phonon cooling) and a slow decay ~190 ps; Bi2Te3 shows non-oscillatory decay within ~2 ps, followed by a monotonic increase to a plateau at ~15 ps and a very slow decay ~600 ps. - Coherent optical phonons are observed as oscillations, more pronounced and slightly red-shifted in Bi2Te3 relative to Bi2Se3. - OPOP (1.5 eV) excites both bulk and surface states; for Bi2Se3 and Bi2Te3, OPOP and TPOP dynamics are similar (bulk-dominated). In BSTS, OPOP reveals an additional picosecond-scale component, while TPOP remains purely fast, indicating surface-state specificity of the THz-driven response. - THz HHG: Clear third-harmonic generation (THG) observed (e.g., THG at ~1.5 THz for 0.5 THz fundamental, 100 kV/cm). In TIs (Bi2Se3, Bi2Te3, BSTS), THG scales cubically with fundamental field across 15–140 kV/cm without saturation. In BSTS, fifth-harmonic generation (FHG) shows slope 5.2 ± 0.3 (perturbative regime) up to 140 kV/cm. - Graphene benchmark exhibits strong saturation: THG scaling exponent decreases from ~3 at low fields (<10 kV/cm) to ~1.06 ± 0.08 at highest fields (60–100 kV/cm), with ~2.3 at 15–25 kV/cm, consistent with saturable absorption, sub-linear heating (temperature-dependent heat capacity), and hot-phonon bottleneck. - Reported maximum field conversion efficiencies: THG in Bi2Te3 ~0.13%, BSTS ~0.08%, Bi2Se3 ~0.03%; FHG in BSTS ~0.014% at 140 kV/cm. Although lower than graphene (~0.5%), the absence of saturation in TIs suggests potential for higher efficiencies at increased fields. - Interpretation: Sub-picosecond surface-state cooling in TIs prevents heat accumulation during multi-ps THz pulses, maintaining perturbative nonlinearity and avoiding saturation; lower Fermi velocity than graphene may further delay saturation onset.

The study directly addresses whether surface-state Dirac fermions in TIs exhibit distinct ultrafast relaxation compared to bulk carriers. By using below-bandgap THz excitation and a BSTS sample with the Fermi level inside the gap, the authors isolate surface-state intraband dynamics and measure a few-hundred-femtosecond relaxation, much faster than the picosecond-scale bulk cooling observed in Bi2Se3 and Bi2Te3. This supports a picture where efficient electron–phonon coupling and phonon-assisted surface-to-bulk scattering at room temperature facilitate rapid energy dissipation from surface carriers. The absence of THz HHG saturation up to 140 kV/cm in all three TIs, contrasted with strong saturation in graphene, is consistent with these ultrafast cooling dynamics that prevent heat accumulation over the THz pulse duration. The results imply that TI-based THz nonlinear photonics could achieve higher conversion efficiencies by increasing the driving field, with device-level enhancements (e.g., metamaterials) further boosting performance. The findings refine understanding of TI carrier dynamics at room temperature and highlight differences with cryogenic behavior (e.g., longer surface-state decay ~1.5 ps at 5 K), emphasizing the role of phonons and surface–bulk scattering channels.

The work isolates and quantifies ultrafast relaxation of Dirac fermions in TI surface states, demonstrating few-hundred-femtosecond decay at room temperature under below-bandgap THz excitation, much faster than bulk-carrier dynamics. Consistently, THz HHG in TIs remains in the perturbative regime (cubic/fifth-power scaling) up to 140 kV/cm without saturation, unlike graphene. These insights suggest TIs can sustain higher THz nonlinear conversion efficiencies at elevated fields and are promising for high-bandwidth optoelectronic and spintronic applications. Future research could optimize material composition and Fermi level placement, engineer phonon interactions and surface–bulk coupling, and employ field-enhancing architectures to further increase HHG efficiency and explore higher-order harmonics and ultrafast device operation.

- In bulk-conducting samples (Bi2Se3, Bi2Te3), simultaneous population of bulk and surface states prevents unambiguous separation of their contributions under THz excitation; isolation of surface-state dynamics is achieved only in BSTS with Fermi level in the gap. - Transient reflectivity at 1.5 eV probes only to a depth of a few tens of nm and does not access the sample–substrate interface dynamics. - THz HHG measured in transmission geometry can include contributions from both front (air–TI) and back (TI–substrate) surfaces, complicating precise attribution of the harmonic source region. - Detailed microscopic pathways (relative roles of direct electron–phonon cooling versus phonon-assisted surface–bulk scattering) are inferred but not fully disentangled within the experiments presented.