www.nature.com/npjquantmats ARTICLE OPEN Terahertz signatures of ultrafast Dirac fermion relaxation at the surface of topological insulators S. Kovalev 1 ✉, K.-J. Tielrooij 2, J.-C. Deinert 1, I. Ilyakov1, N. Awari1, M. Chen 1, A. Ponomaryov1, M. Bawatna1, T. V. A. G. de Oliveira3,4, L. M. Eng 3,4, K. A. Kuznetsov 5 ✉, D. A. Safronenkov5, G. Kh. Kitaeva 5, P. I. Kuznetsov6, H. A. Hafez7, D. Turchinovich 7 and M. Gensch8,9 Topologically protected surface states present rich physics and promising spintronic, optoelectronic, and photonic applications that require a proper understanding of their ultrafast carrier dynamics. Here, we investigate these dynamics in topological insulators (TIs) of the bismuth and antimony chalcogenide family, where we isolate the response of Dirac fermions at the surface from the response of bulk carriers by combining photoexcitation with below-bandgap terahertz (THz) photons and TI samples with varying Fermi level, including one sample with the Fermi level located within the bandgap. We identify distinctly faster relaxation of charge carriers in the topologically protected Dirac surface states (few hundred femtoseconds), compared to bulk carriers (few picoseconds). In agreement with such fast cooling dynamics, we observe THz harmonic generation without any saturation effects for increasing incident fields, unlike graphene which exhibits strong saturation. This opens up promising avenues for increased THz nonlinear conversion efficiencies, and high-bandwidth optoelectronic and spintronic information and communication applications. 1234567890():,; npj Quantum Materials (2021)6:84 ; https://doi.org/10.1038/s41535-021-00384-9 INTRODUCTION bulk dynamics has recently been achieved at the cryogenic Nowadays, due to their unique transport properties, topological temperature of 5 K11, this is not the case at more technologically insulators (TIs) attract great attention1,2. Due to the symmetry- relevant temperatures. The main reason for this is the protected Dirac fermions with nontrivial topology on their surface, occurrence of phonon-assisted surface-to-bulk scattering above they are highly prospective as functional materials in future the Debye temperature (~180 K for Bi2Se3)7. electronic and spintronic devices3. Moreover, various optoelec- Here, we overcome these challenges by combining optical tronic and thermoelectric applications can benefit from the excitation with low photon energies and a TI sample with the combination of protected charge transport in surface states, and Fermi energy located inside the bandgap. As a result, we are able large Seebeck coefficients. For many of these applications it is to isolate the response of Dirac electrons in the surface states, crucial to understand the characteristic timescales of the without the contribution of bulk states. In particular, we use THz relaxation dynamics of excited carriers, and in particular determine pulses with photon energies below 4 meV, and verify whether the if these dynamics are different for topological surface states observed carrier dynamics originate from surface states (SSs), bulk compared to the bulk. conduction states (BCSs), or bulk valence states (BVSs), using three The carrier dynamics in TIs have been addressed using various different TI samples with the Fermi energy in the valence band pump–probe techniques4–12. However, despite these experi- (Bi2Te3), in the conduction band (Bi2Se3), and inside the bandgap mental efforts, the exact mechanism and timescale of carrier (Bi1.4Sb0.6Te1.51Se1.49, i.e. BSTS). THz excitation of bulk-conducting relaxation of the Dirac fermions in surface states of TIs are still Bi2Se3 and Bi2Te3 corresponds to intraband excitation of carriers in under debate. The reason for this is that it is challenging to the bulk and at the surface simultaneously, such that surface and experimentally disentangle excitation and relaxation channels of bulk relaxation dynamics cannot be disentangled in a straightfor- surface and bulk states. This is caused by the relatively small ward manner. However, the BCSs of the BSTS are empty while the bandgap of TIs of the bismuth and antimony chalcogenide BVSs are completely filled, so that intraband transitions in the bulk family, which is a few hundred meV13, meaning that optical of BSTS are Pauli blocked. As a result, in the BSTS sample THz excitation with near-infrared and visible light leads to interband excitation is dominated by the intraband excitation of surface transitions between the bulk bands. Thus, in order to optically states only. Using two THz-based nonlinear techniques, namely address the surface states, energetically located within the THz-pump optical-probe (TPOP) and THz high-harmonic genera- bandgap, photons in the mid-infrared or terahertz regimes are tion (THz HHG), we find that relaxation of Dirac fermions at the required. Furthermore, the Fermi energy is typically located either in the valence or the conduction band for binary TI surface of TIs occurs on a timescale of a few hundred compounds, e.g. Bi2Se3 and Bi2Te3, such that bulk states are femtoseconds, which is significantly faster than the relaxation of already populated. Whereas separating surface dynamics from bulk carriers. 1 Helmholtz Zentrum Dresden Rossendorf, Dresden, Germany. 2Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST and CSIC, Campus UAB, Bellaterra, (Barcelona) 08193, Spain. 3Technische Universität Dresden, Dresden, Germany. 4ct.qmat - Cluster of Excellence on Complexity and Topology in Quantum Matter, Dresden, Germany. 5 Lomonosov Moscow State University, Moscow, Russia. 6Kotelnikov IRE RAS, Moscow, Russia. 7Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany. 8DLR - Institute of Optical Sensor Systems, Berlin, Germany. 9Technische Universität Berlin, Berlin, Germany. ✉email: s.kovalev@hzdr.de; kirill-spdc@yandex.ru Published in partnership with Nanjing University S. Kovalev et al. 2 RESULTS AND DISCUSSION Samples Our three different samples, rhombohedral Bi2Se3, Bi2Te3, and Bi1.4Sb0.6Te1.51Se1.49 (BSTS) films were grown on (0001) Al2O3 substrates. Their film thicknesses are 30 nm, 490 nm, and 375 nm, respectively. The growth method is described in detail in Ref. 14. It was shown in15 that for topological insulators of the Bi2−xSbxTe3−ySey quaternary compounds, there is an optimal curve (Ren’s curve) in the composition diagram y(x). Near this curve, the properties of electronic edge states are most pronounced due to the fact that acceptors and donors mutually cancel each other. Compositions below Ren’s curve, as a rule of thumb, have predominant hole conductivity, while a composition above Ren’s curve exhibits electronic conductivity. Using THz transmission measurements, we estimate the Fermi level of Bi2Se3 to be located 26 meV above the bottom of the conduction band, and for Bi2Te3 we find it 30 meV below the top of the valence band. In case of BSTS, we find that the Fermi level is located inside the bandgap, being 110 meV below the conduction band, which is in agreement with earlier works13,15–17 (see Supplementary Fig. 13). Terahertz-pump optical-probe measurements We first measure the relaxation dynamics of these samples using transient reflectivity spectroscopy. We use laser pulses with 800 nm central wavelength and 100 fs pulse duration for probing, 1234567890():,; while single cycle THz pulses serve as a pump in THz-pump optical-probe (TPOP) experiments. As a reference, we perform optical-pump optical-probe (OPOP) measurements, where 800 nm pulses also serve as pump, instead of THz light. The experimental setups used for TPOP and OPOP measurements are described in the Supplementary information (Supplementary Fig. 1). Ultrafast pump–probe reflectivity measurements in the near- and mid- infrared ranges have been used earlier to study the dynamics of charge carriers4,8–10,18 and phonons19–21 in topological insulators. The optical reflectivity in TIs at near-IR frequencies is determined Fig. 1 Transient reflectivity spectroscopy. THz-pump optical-probe by interband transitions between the valence and conduction (TPOP) reflectivity measurements in Bi2Se3 (a), Bi2Te3 (b) and BSTS (c) bands, and depends on the number of unoccupied states in the (blue line). The intensity transient of the driving THz field is shown in conduction band10. The sign of the optical reflectivity can be both all panels (gray shaded line). The red line corresponds to the negative and positive, where the former (latter) is mostly dynamics when using optical excitation with 1.5 eV photon energy associated with carrier temperature (carrier density), see4,8–10. (OPOP). The band diagram with the Fermi level of each sample, The negative reflectivity change is most likely the effect of Pauli obtained from THz transmission experiments, is schematically blocking of interband excitations at the probe energy due to shown in the insets. carrier heating, i.e. broadening of the Fermi–Dirac distributions of the different transitions that play a role at our probe energy. The tens of nm10, thus the optical reflectivity signal does not carry probe-energy and probe-fluence dependent reflectivity of BSTS information on the dynamics at the sample-to-substrate interface. was addressed in detail in10, where a continuum consisting of the The observed dynamics are significantly different for each of the responses of transitions between different valence and conduc- three samples, and can be decomposed into several components: tion bands was shown to play a role. Similar effects likely play a ultrafast build-up, initial decay and a Raman-excited coherent role for the other TIs. phonon response. The fast rise time of the THz response In previous experiments4,8–10, however, the mid- or near-IR corresponds to the ultrafast thermalization of excited carriers pump pulses had photon energies above or close to the energy of through electron-electron scattering. As measured with optical the bandgap, such that the dynamics of bulk and surface carriers techniques and time- and angle-resolved photoemission spectro- both contribute to the observed signals. The description of excited scopy (tr-ARPES), the electron-electron scattering time constant carrier dynamics in TIs is further complicated by the formation of has been determined to be lower than 200 fs for Bi2Se37. The metastable states at the conduction band bottom5,6. The slow relaxation dynamics of Bi2Se3 (Fig. 1a, TPOP) can be decomposed population decay in these states can compete with the faster into two different exponential decays. The faster decay rate varies carrier cooling. In a few pump–probe studies, THz light was used from 1.45 to 1.9 ps under excitation with 280 and 400 kV cm−1 as the pump, in order to study carriers11, and phonons21,22. fields (see Supplementary Fig. 8) and can be attributed to carrier However, in both cases bulk-metallic TIs were used. Therefore, the carrier relaxation dynamics observed in all of those studies always cooling via electron–phonon scattering5,7,8,11. The slow decay contained contributions from both the surface and bulk electronic component shows a time constant of about 190 ps (see systems. Supplementary Fig. 7). The presence of a slow relaxation upon In Fig. 1 we show normalized optical-probe reflectivity changes sub-bandgap excitation in Bi2Se3 was observed previously using for the three topological insulators investigated in our work after tr-ARPES23 and was attributed to thermal excitation of the carrier excitation by broadband THz radiation with 400 kV cm−1 peak population. As mentioned before, due to the coexistence of field strength. We point out that the sign of the observed partially filled BCS and gapless Dirac SS24, it is not possible to reflectivity variations for all three cases is negative, in agreement separate relaxation processes occurring in bulk and surface states with8,10. The penetration depth of the 1.5 eV probe pulse is few based on these measurements. npj Quantum Materials (2021) 84 Published in partnership with Nanjing University S. Kovalev et al. 3 Measurements performed on the Bi2Te3 sample are presented Terahertz harmonic generation in Fig. 1b. The Raman-excited optical phonon25, seen as periodic In order to obtain additional insights into the relaxation dynamics of oscillation, is more pronounced than in Bi2Se321 and slightly red- Dirac fermions in TI surface states, we study THz high-harmonic shifted due to the heavier Te atoms (Supplementary Fig. 10). After generation (HHG). Strong THz high-harmonic generation (HHG) has a sharp increase in reflectivity variation, the non-oscillatory part been observed in a number of Dirac materials: in graphene29–31, in decreases within 2 ps via electron–phonon scattering and then the 3D Dirac semimetal Cd3As232,33, and in the prototypical TI monotonously increases again reaching a plateau at a Bi2Se334. Comparing the nonlinear THz response of samples with pump–probe delay of 15 ps. At longer delays, the reflectivity nontrivial (Bi2Se3) and trivial ((Bi0.9In0.1)2Se3) topology at the surface, variation slowly decreases with a decay timescale of about 600 ps it was shown that THz HHG originates from the surface states of the (shown in Supplementary Fig. 7). Such dynamics are very similar to TI34. those observed for 3 eV pump excitation25 that was attributed to The underlying mechanism for THz HHG by Dirac fermions can the interplay between free carrier absorption and the band filling be described by a thermodynamic nonlinearity mechanism that effect. relies crucially on the ultrafast modulation of the THz absorption. In comparison with Bi2Te3 and Bi2Se3, the carrier dynamics in This mechanism is enabled by efficient heating and subsequent BSTS (Fig. 1c) show a much faster decay after the ultrafast build- cooling of the electronic system on fs to ps timescales upon up caused by THz excitation. The slow response observed in the interaction with strong THz fields29,30,35. Therefore, the THz HHG other samples immediately after pump excitation is almost behavior is intricately related to the characteristic timescales of negligible. The relaxation time in BSTS is short—a few hundred carrier dynamics of Dirac fermions. In particular, we point out that fs—which is very different compared to Bi2Se3, Bi2Te3 and also when cooling takes several picoseconds, this leads to a reduction with respect to the dynamics in BSTS observed in studies of the nonlinearity coefficient and strong saturation effects for employing above-bandgap excitation10,26. In all these cases, a increasing incident field strengths, as observed recently for pronounced initial relaxation component with a timescale of a graphene under strong THz excitation31 (see also Supplementary few picoseconds is present. We ascribe the observed fast Fig. 12). dynamics to the isolated response of Dirac fermions in the In Fig. 2, we show measurements of fundamental and third- surface states of our TI system. We suggest that these fast harmonic (THG) fields measured by electro-optic sampling for surface-state relaxation dynamics we unveiled are the result of Bi2Te3, together with the respective amplitude spectra. The details the efficient coupling of carriers to phonons5,27 and ultrafast of the THz HHG experimental setup are shown in the Supple- surface-to-bulk scattering7, and could hence be a general property of this material class. These fast dynamics are likely mentary information. We observe a clear third-harmonic signal related to the carrier temperature that can exceed 1000 K for the fluence we used (~100 μJ cm−2), according to Ref. 7. We note that the observed decay is significantly faster than the decay of surface-state carriers reported at 5 K, which was ~1.5 ps11. The reason for faster decay at room temperature than at 5 K is most likely related to phonons—either because of cooling directly to phonons, or because of phonon-assisted surface-bulk scattering that becomes faster at room temperature. Optical-pump optical-probe measurements To verify independently that the ultrafast relaxation in BSTS originates from intraband dynamics within the topological SS, we have performed degenerate optical pump–probe measurements using pump pulses with a photon energy of 1.5 eV (Fig. 1c). The experimental setup is described in the Supplementary Informa- tion. This scheme leads to the simultaneous excitation of bulk and surface states in all samples. In the case of Bi2Te3 and Bi2Se3 (Fig. 1a, b), we see almost identical relaxation dynamics for optical and THz excitation, confirming that the dominant contribution to the dynamics originates from bulk states in bulk-metallic TIs. For BSTS we, in contrast to the below bandgap THz excitation, observe also a much slower dynamic on picosecond timescales in agreement with earlier observations for above bandgap excitation28. The significantly faster decay after photoexcitation with below- bandgap THz photons, in comparison with excitation with above-bandgap photons, clearly suggests that the hot surface- state Dirac fermions have a much shorter lifetime. Apart from an initial decay, the OPOP measurements in Bi2Te3, Bi2Se3 and BSTS yield qualitatively very different results. This can be attributed to different ways in which the temperature and population relaxation can compete with each other, depending on the material’s band structure and wavelength of the probe pulse10. For example, in the case of BSTS, depending on the probe wavelength, the photo- induced reflectivity variations change the sign for probe energies Fig. 2 THz third-harmonic generation in Bi2Te3. Time-domain below 0.95 eV, and not for higher energies, such as the 1.5 eV that waveforms of the fundamental radiation electric field (a) and the we used10. Note that for all investigated TIs both TPOP and OPOP third-harmonic field generated in Bi2Te3, and the Al2O3 substrate for measurements show negative photo-induced reflectivity at 1.5 eV reference (b). Amplitude spectra of the fundamental radiation and probe energy. THG in Bi2Te3 and substrate (c). Published in partnership with Nanjing University npj Quantum Materials (2021) 84 S. Kovalev et al. 4 These observations for graphene are in agreement with earlier publications29,31,33. The strong saturation at the highest field strengths has been ascribed to a combination of effects: the first reason for this is the occurrence of saturable absorption: if the carrier temperature increases, the graphene conductivity decreases and the absorption of THz light is reduced. Eventually, the carrier temperature can become too high such that no incident THz light is absorbed. In that case, further increasing of the field strength will not lead to any additional generation of a higher harmonic signal. The second reason for saturation is that the increase of temperature scales sub-linearly with the incident THz power36,37, because the heat capacity scales with tempera- ture. This sub-linearity also gives rise to saturation. The third reason is that at elevated temperatures cooling slows down, because of a hot phonon bottleneck effect. With slower cooling, the heating-cooling dynamics oscillate with a smaller amplitude, thus giving rise to saturation in the HHG. Compared to graphene, the TI samples show fundamentally different behavior: all topological insulators demonstrate a clear cubic dependence of the third-harmonic field across the whole accessible field regime meaning that THz-induced nonlinear processes are far away from the saturation regime. In order to verify this perturbative behavior further, we show in Fig. 3b the field strength of the fifth harmonic as a function of the fundamental field strength for the BSTS sample. Using a power- law fit, the fifth-harmonic (FHG) fields scale with an exponent of 5.2 ± 0.3 as a function of fundamental field, which is clear evidence that the FHG process is also in the perturbative regime. This purely perturbative behavior all the way up to incident field strengths of 140 kV cm−1 can be ascribed (partially) to the sub- picosecond cooling dynamics we observed in our TPOP experi- ments: the ultrafast surface-state relaxation of the TI samples prevents heat accumulation effects within the comparably long Fig. 3 Fluence dependence of the THz HHG. a The peak values of duration (several picoseconds) of the THz excitation pulse. An third-harmonic fields generated in topological insulators and graphene obtained for different driving fields of fundamental additional reason for the extended perturbative regime for the radiation at 500 GHz central frequency (dots). Solid lines are linear tested TIs could be the lower nonlinearity, which is likely due to fits providing the scaling law: 1.06 ± 0.08 for graphene at highest the lower Fermi velocity compared with graphene38. This allows field and 2.3 at lowest fields, 3.08 ± 0.03 for Bi2Te3, 2.99 ± 0.06 for for driving the TI samples with higher fields before saturation is BSTS, and 2.98 ± 0.07 for Bi2Se3. b Fields of fifth harmonic generated observed. The influence of both relaxation times and the Fermi in BSTS, the slope of the linear fit is 5.2 ± 0.3; The inset shows velocity on the THz THG saturation is shown in the Supplemen- amplitude spectra of fundamental and fifth harmonic. tary information (Supplementary Fig. 15). According to the thermodynamic model, both relaxation and Fermi velocity from Bi2Te3 at 1.5 THz (Fig. 2b) upon driving the sample with the determine the THz HHG saturation. Long relaxation and high 0.5 THz fundamental with a peak field strength of 100 kV cm−1. In Fermi velocity are required to have high THz nonlinearity at low Fig. 2c the resulting amplitude spectra of the fundamental beam driving fields, while at driving fields above 100 kV cm−1 ultrafast and the THG in both TI and substrate are shown. In these cooling is the most critical parameter to reach high THz experiments, the THG polarization is collinear with the polarization HHG yield. of the linear fundamental beam polarization. The third-harmonic The observation of perturbative HHG in TIs is highly interesting, field strength scales down linearly with fundamental beam because it could mean that a higher conversion efficiency can be ellipticity reaching zero in the case of circularly polarized pump obtained for increased incident field strengths. We observe that (see Supplementary Figs. 5, 6). As we investigated the THz THG in the highest overall conversion efficiency for graphene is about transmission geometry, the observed harmonics can originate 0.5% in the field, which is consistent with other studies29,31. from both front (air–TI interface) and back surfaces (TI–substrate However, saturation effects at high fields may impose an interface) of the sample. efficiency limit. For the TI samples, we observe maximum third- In Fig. 3a, we show the peak field strengths of the third- order conversion efficiencies of 0.13, 0.08, and 0.03% in the field harmonic signal generated in Bi2Se3, Bi2Te3 and BSTS as a for Bi2Te3, BSTS, and Bi2Se3, respectively. A maximum conversion function of the field strength of the fundamental radiation. For efficiency for the fifth harmonic generation of around 0.014% at comparison we show THz third-harmonic signal measurements 140 kV cm−1 fundamental field strength is observed. These from p-doped graphene with around 1013 cm−2 charge carrier efficiencies are lower than the one obtained for graphene. concentration. For fundamental field strengths between 60 and However, the purely perturbative scaling indicates that higher 100 kV cm−1 the third-harmonic signal from graphene exhibits conversion efficiencies than for graphene are achievable by clear saturation behavior and begins to scale linearly with the further increasing the incident field, which is of great technolo- fundamental field, rather than the expected cubic scaling for gical interest. third-harmonic generation in the perturbative regime. Even in the lowest range of driving fields, between 15 and 25 kV cm−1, third-harmonic generation in graphene shows a power law PERSPECTIVE AND SUMMARY scaling with an exponent of 2.3, indicating that the perturbative In conclusion, we experimentally isolated the dynamical response regime is only maintained at driving fields below 10 kV cm−1. of Dirac fermions in surface states of TIs that are excited by THz npj Quantum Materials (2021) 84 Published in partnership with Nanjing University S. 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Lett. 92, 011108 (2008). Open Access funding enabled and organized by Projekt DEAL. Published in partnership with Nanjing University npj Quantum Materials (2021) 84 S. Kovalev et al. 6 COMPETING INTERESTS Open Access This article is licensed under a Creative Commons The authors declare no competing interests. Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative ADDITIONAL INFORMATION Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless Supplementary information The online version contains supplementary material indicated otherwise in a credit line to the material. 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