Abstract
Topologyprotected surface transport of ultimate thinness in threedimensional topological insulators (TIs) is breaking new ground in quantum science and technology. Yet a challenge remains on how to disentangle and selectively control surface helical spin transport from the bulk contribution. Here we use the midinfrared and terahertz (THz) photoexcitation of exclusive intraband transitions to enable ultrafast manipulation of surface THz conductivity in Bi_{2}Se_{3}. The unique, transient electronic state is characterized by frequencydependent carrier relaxations that directly distinguish the faster surface channel than the bulk with no complication from interband excitations or need for reduced bulk doping. We determine the topological enhancement ratio between bulk and surface scattering rates, i.e., γ_{BS}/γ_{SS} ~3.80 in equilibrium. The ultrabroadband, wavelengthselective pumping may be applied to emerging topological semimetals for separation and control of the protected transport connected with the Weyl nodes from other bulk bands.
Introduction
The recent discovery of topologyprotected charge transport of threedimensional (3D) TIs has led to a promising platform for exploring both fundamental topological quantum phenomena and technological applications^{1,2,3,4,5,6,7}. The emergent behaviors associated with this exotic state of matter, such as spinlocking, helical spin structure, topological invariant, chiral anomaly, and dissipationless currents^{8,9,10,11,12,13}, offer new perspectives for achieving transformational technological applications in spintronics and quantum sensing, computing, and communications^{3} beyond the current technological limit. One of the current frontiers for topological phenomena lies in the fundamental challenge of how to disentangle and manipulate symmetryprotected transport from bulk conduction. On one hand, development and optimization of hot electron transistors and modulators operating at ultrahigh THz frequencies will significantly benefit from the direct probing of ultrafast THz charge transport on the surface and from a better understanding of the fundamental effects of topological spinlocking on carrier scattering. Although the existence of a helical Dirac spectrum has been well established in electrical transport^{14} and photoemission^{8,15,16}, ultrafast control of THz helical spin transport is much less known. This is due, in part, to the limitations of conventional transport characterization methods that are incapable of probing frequencydependent conductivity characterized by femtosecond (fs) in time and THz in energy scales, especially with low frequency photon pumping^{17,18,19}. On the other hand, in 3D TIs, the coexistence and mutual scattering of Dirac and bulk carriers lead to an intertwined response. Despite recent observations from static THz measurements of TI samples with significantly reduced doping and defects^{20,21}, it is still challenging to selectively control the intrinsic surface dynamics from the bulk contribution for samples that exhibit unintentional doping into bulk states.
The transport properties of 3D TIs are determined by carriers in narrowly gapped bulk bands and by gapless surface states protected by the timereversal symmetry. Although the spinmomentum locking of Dirac electrons increases the conductivity from atomicallythin surface states, its contribution can still be masked by the high density carrier conduction in static transport measurements, at either bulk or interface states, even in films with tens of nm thickness. Consequently, very few experimental techniques are capable of isolating and studying the intrinsic topological transport on the surface, especially for high Fermi energies. Sophisticated characterization and sample synthesis are involved, e.g., anisotropic magnetotransport by adjusting magnetic field directions^{14} and significantly reduced doping and thickness by thin film engineering^{20,21,22,23,24,25,26,27,28,29}. There has been considerable progress yet with complications, e.g., limited applicability or difficulty in the interpretation. For example, intrinsic Diraccones could be contaminated with possible gap opening in very thin samples. The separation of surface and bulk/interface contributions to the static THz conductivity spectra has to rely on reduced doping.
Recently, ultrafast THz conductivity has been shown to be promising by providing time resolution able to distinguish the surface from the bulk responses after suddenly driving the system outofequilibrium^{28,30}. However, the high photon frequency pumping at 1.55 eV used so far introduces interband excitations from valence to conduction and other high lying bands at both surface and bulk. Such coupling causes population transfer between surface and bulk bands and enhanced scattering between highenergy states. Selective midIR and THz pumpTHz probe spectroscopy used in this work represent powerful and versatile tools that allow us to measure and control surface transport in TIs, even for Fermi level E_{F} into the bulk bands.
We emphasize several strategic advantages of low frequency pumping scheme like ours, as illustrated in Fig. 1a. First, in contrast to interband photoexcitation that couples highenergy electronic states between two bands, THz and midIR photoexcitation mainly excites intraband transitions near E_{F}. Here the photon energy is below the insulating bandgap and interband transition energy, which suppresses many other charge transfer channels. This allows measurement of intrinsic scattering rates and strongly constrains the fitting parameters to scattering rates only, as discussed later. Additionally, our time resolution can separate intrinsic surface from bulk conductivity via their different hot carrier cooling times, i.e., resolve the issue directly in the timedomain. The extracted spectra fully characterize THz response functions as the complex frequencydependent conductivity. In this way we can determine the intrinsic surface electron scattering rates and their ultrafast dynamics, complimentary to commonly used transport^{14}, and photoemission^{8,16} measurements. Finally, comparison of the conductivity for wavelengthselective photoexcitations below and above the interband transition enabled by tuning the pump photon energy allows the optical control of carrier dynamics of surface and bulk bands in a selective way. However, in contrast to the several interband photoexcitation studies performed in TIs^{28,30}, midIR, and THz pumpinduced conductivity experiments have not been carried out so far in TIs.
Here we report ultrafast THz charge transport and dynamics in ntype Bi_{2}Se_{3} that arise from nonequilibrium Dirac surface and bulk transient states induced by intraband midIR and THz photoexcitation. We observe frequencydependent carrier cooling times of photoinduced THz conductivity that clearly differentiate surface from bulk contributions and allow determination of their scattering rates. We show that the topological enhancement of surface transport suppresses the surface electron scattering rate as compared to the bulk, i.e., γ_{BS}/γ_{SS}~3.80 in equilibrium. This result is consistent with surface helical spin transport in the presence of shortrange disorder^{31}. Moreover, the clear similarities between midIR and THz pumping and their distinct difference from highphotonenergy cases clearly show: (1) ultrafast manipulation of the surface and bulk THz conductivities via wavelengthselective pumping; (2) intraband vs. interband excitation mechanisms driven by low and highphotonenergy pumping. These are distinctly different from any known THz transport measurements so far, which have used either highenergy optical frequency photoexcitation or only detected timeaveraged properties. The intraband, midIR/THzinduced THz conductivity provides a powerful method for isolating the surface transport channel in TIs—unhindered by complications from interband pumping or high density doping into bulk states. The distinct spectraltemporal characteristics obtained in this way in TIs may be extended to study and understand much broader topological phenomena^{32}.
Results
Frequencydependent dynamics of THz conductivity spectra
The Bi_{2}Se_{3} thin film sample, 50 nm thick, is grown by molecular beam epitaxy on a 0.5 mm thick sapphire substrate. The static THz conductivity spectra are shown in Fig. 1b. The details about THz data analysis, sample preparation, and experimental setup are described in the Methods. We characterize the nonequilibrium THz responses of the Bi_{2}Se_{3} thin film by extracting the real parts of the transient conductivity σ_{1}(ω, Δt_{pp}) and dielectric function ε_{1}(ω, Δt_{pp}) as a function of both the frequency ω and the pumpprobe delay time Δt_{pp}. These spectra describe the dissipative and inductive parts of the response functions of quasiparticles, respectively, and are extracted from raw THz fields in timedomain.
The pumpinduced raw THz fields in Fig. 1c, d exhibit a distinctly different temperature dependence. At 300 K, the transmitted field change ΔE_{sample} has a π phase shift relative to the static field E_{sample} without any other frequency and timedependent changes. This behavior is characteristic of an absorptiondominated response, i.e., a large increase in σ_{1}(ω). On the other hand, at low temperature T = 5 K, a large inductive response ε_{1}(ω) appears in addition to the dissipative one, as manifested by a significant frequency and timedependent THz field reshaping besides the dominant π phase shift as in the 300 K case. These distinct spectraltemporal characteristics give rise to several salient features in the extracted THz response functions Δσ_{1}(ω) and Δε_{1}(ω), shown in Fig. 2a–d, that allow us to directly separate the intrinsic surface and bulk transport contributions to the conductivity from the experimental data without fitting.
The first feature, shown in Fig. 2a, b, is that the pumpinduced THz conductivity spectra Δσ_{1}(ω) extracted from the measured timedependent THz fields exhibit a clear bipolar behavior with frequencydependent cooling times under intraband excitation (248 meV) at low temperature (5 K). Specifically, as shown by comparing three timecut spectra (whitedashed lines in Fig. 2b), Δσ_{1}(ω) at early times (Δt_{pp}<5 ps) is characterized by a strong bleaching, i.e., a negative conductivity change, in the low frequency 2–3 meV range. This changes to a strong absorption, i.e., positive conductivity change, towards high frequencies up to ~7 meV, as seen in the 1 ps trace (black dots in Fig. 2a). At Δt_{pp}>5ps, the low frequency bleaching has quickly diminished, and the transient spectra are dominated by the high frequency absorption with longer cooling times, e.g., as shown in the 5.4 ps (red dots) and 15.4 ps (blue dots) traces. The frequency cuts of the Δσ_{1}(ω) spectra from Fig. 2b are summarized in Fig. 2e (at ω = 2 meV) and 2f (at ω = 7 meV) (black dots) as a function of Δt_{pp}. Clearly, the cooling times depend on the probe frequency, i.e., the faster (slower) cooling for ultrafast THz conductivity change at low (high) frequency. The characteristic cooling time for the 2 meV probe is τ_{SS} = 1.48 ± 0.14 ps, significantly shorter than that for the 7 meV probe τ_{BS} = 5.30 ± 0.18 ps (the uncertainty is from single exponential fitting). Such a frequencydependent decay of THz electron transport is consistent with the significant THz pulse reshaping seen in Fig. 1d, which indicates more than one cooling channel of hot electrons.
Second, to understand these experimental results, we compare them with prior ultrafast THz responses from photoexcited Bi_{2}Se_{3} samples. A decrease in their thickness has been shown to induce a transition to a surfacelike, pronounced bleaching behavior that differs from a bulklike, absorption one^{30}. The latter is expected from the ionized impurity scattering in the bulk, which decreases scattering rate after pumping at low temperatures^{33} and gives rise to a positive Δσ_{1}(ω) towards zero frequency (see below for details). Therefore our results show that THz transport and dynamics of surface and bulk fermions can be selectively separated in time and measured by tuning probe frequency. Most intriguingly, upon closer scrutiny, the timedependent scattering rates of surface Dirac (red line) and bulk (green line) fermions in Fig. 2e, f match very well with the conductivity dynamics at 2 meV and 7 meV, respectively. These scattering rates are extracted by fitting the timedependent conductivity data as discussed later. This clearly shows that the experimentally obtained Δσ_{1}(ω) probed at 2 meV can be used to directly measure surface transport dynamics, distinctly different from bulk conduction (at 7 meV), without reference to theoretical models. In between 2 and 7 meV, Δσ_{1}(ω) dynamics consist of mixed responses due to competing surface and bulk states as expected.
The third feature is that increasing the lattice temperature leads to an induced absorption behavior over the entire frequency range measured with a frequencyindependent single cooling time, as shown in Fig. 3. Strikingly, this hightemperature behavior is opposite to the lowtemperature conductivity responses in Fig. 2. This is consistent with the different, raw THz fields ΔE_{sample} between T = 5 K and 300 K seen in Fig. 1c, d. Specifically, the pumpinduced Δσ_{1}(ω) spectra at 300 K, shown as 2D falsecolor plot in Fig. 3a, are all positive, Δσ_{1}(ω) > 0, without the negative bleaching component over the measured time and spectral range. Particularly, Δσ_{1}(ω) has similar amplitude at 5 K and 300 K as shown in Figs. 2a and 3b, but Δε_{1}(ω) at 300 K is decreased to approximately one order of magnitude smaller than its counterpart at 5 K, as shown in Figs. 2c and 3c (see also the Supplementary Note 1). This indicates large photoinduced conductive response in comparison with inductive one at the elevated temperature. Since phononmediated coupling and charge transfer between surface and bulk are activated above the Debye temperature at 182 K^{15}, the dominance of positive Δσ_{1}(ω) at 300 K is consistent with our conclusion that the bulk transport and surfacebulk charge transfer dominate at high temperatures and lead to the induced absorption. This suppresses the induced bleaching from the surface seen at 5 K in Fig. 2a. On the other hand, the frequencydependent cooling times previously seen at 5 K are no longer present at the elevated temperature. As shown in Fig. 3d the THz conductivities Δσ_{1}(ω) at ω = 2, 5, and 7 meV as a function of pumpprobe delay Δt_{pp}, now decay with the same time at 300 K. The cooling time of ~4.8 ps is similar to the bulk state cooling time τ_{BS} observed at 5 K. These observations corroborate again our claim that the low frequency conductivity at 2 meV, with faster cooling time observed at 5 K, comes from surface transport that is separated from the bulk channel. Furthermore, these distinct differences between high and low temperatures in ultrafast charge transport suggest that surfacebulk charge transfer in TIs is suppressed at low temperature.
THz spectra analysis and fitting
To put these physical pictures on a strong footing, we quantitatively simulate the experimentally determined THz response functions Δσ_{1}(ω) and Δε_{1}(ω). By extracting the temporal evolution of surface and bulk conductivity spectra, we obtain the intraband scattering rates and ultrafast dynamics of both Dirac (red line) and bulk (green line) fermions, as presented in Fig. 2e, f, respectively. A theoretical model consisting of contributions with Drude and Lorentzian lineshapes is used to reproduce the measured THz response functions. Specifically, two Drude terms account for surface state (SS) and bulk state (BS) plus one phonon oscillator centered at ω_{0} ~ 7.7 meV (1.9 THz),
where ε_{∞} is the background electrical permittivity and the plasma frequency \((\omega _{\mathrm{p}}^2)_j = ne^2/\varepsilon _0m^ \ast\) is proportional to the density of charge carriers of surface (n_{SS}, j = SS) and bulk (n_{BS}, j = BS) electrons. ω and e are the frequency and electron charge. ε_{0} and m^{*} are the vacuum electrical permittivity and carrier effective mass. γ_{j} is the scattering rate of surface (j = SS) and bulk (j = BS) carriers. In the last term of Eq. 1, F denotes the effective transition strength of the optical phonon with resonance frequency ω_{0} and scattering rate Γ. Such a composite THz response model provides an excellent agreement with the pumpinduced transient THz spectra over the entire measured pumpprobe delays and spectral range as shown in Fig. 4 (cyan lines). Such fit is achieved by only varying the scattering rates γ of surface and bulk carriers, i.e., the charge carrier densities of surface (n_{SS}) and bulk (n_{BS}) states remain constant in the fits. Please also note that the optical phonon resonance ~7.7 meV is fitted by F, ω_{0}, and Γ of the Lorentzian oscillator, which only affects locally the feature near the resonance. Examples of typical fits are shown in Fig. 4 at various time delays, Δt_{pp} = 1 ps, 9.4 ps, and 15.4 ps. The model fit (cyan lines) is divided into the sum of the surface (greendashed lines), bulk (bluedashed lines), and phonon (magentadashed lines) responses. Detailed fitting parameters are listed in the Supplementary Note 5.
We like to emphasize three key observations from the quantitative fitting. First, while the static THz spectra, shown in Fig. 1b, can be fitted equally well with either single or multiple Drude components, the transient THz spectra, shown in Fig. 4, can only be fitted by the twoDrude model. This is the case because the strong constraint imposed by the requirement to simultaneously describe both the conductivity Δσ_{1}(ω) and the dielectric function Δε_{1}(ω) over broad temporal and spectral ranges, shown in Fig. 2a–d, instead of just fitting the lineshape as in the static case. Second, an even stronger constraint comes from the intraband, midIR/THz excitation scheme that most likely conserves the number of surface and bulk quasiparticles after the photoexcitation, i.e., carrier densities of both surface and bulk states are kept constant in the fitting, Δn_{SS} = 0 and Δn_{BS} = 0 (more details and discussions in Fig. 5). Remarkably, by simply varying the surface and bulk scattering rates we are able to consistently reproduce the experimental results, as shown in Fig. 4, and extract the scattering rates (or inverse transport lifetimes that should not be confused with hot carrier cooling times) γ_{SS} (red line), γ_{BS} (green line), and their cooling dynamics in Fig. 2e, f. On the flip side, this excellent agreement implies that midIR/THz photoexcitation creates a unique nonequilibrium state of hot, yet mostly conserved, Dirac fermions and bulk carriers in their respective bands. Third, the equilibrium surface and bulk scattering rates, γ_{SS} and γ_{BS} extracted before the photoexcitation, are 0.84 THz and 3.18 THz, respectively, which reveal an enhancement ratio, γ_{BS}/γ_{SS} ~3.8. Remarkably, this value matches very well with the topological enhancement factor, 4, for protected, helical spin transport of noninteracting fermions in the presence of shortrange disorder such as structural defects and surface or interface roughness. In the presence of long range, Coulomb disorder, this enhancement decreases from 4 to 2 due to increase of screening^{31}. Furthermore, as shown in Fig. 2e, f, the scattering rates of the surface Dirac and bulk fermions nearly coincide with the frequencydependent decay of Δσ_{1}(ω) for 2 meV and 7 meV probe, respectively. This corroborates again that tuning the THz probe frequency under midIR/THz pump can be used to disentangle the distinct symmetryprotected transport from the bulk conduction and measure their dynamics without reference to theoretical models. In between 2 and 7 meV, it consists of competing responses from surface and bulk, e.g., Δσ_{1}(ω) at 3 meV consists of THz conductivity contributions from both states with a similar strength.
Wavelengthselective pumping from THz to visible
Figure 5 highlights ultrabroadband, wavelengthselective pumping that extends from THz and midIR to nearIR and visible. This data show that our THz conductivities following 4 meV (Fig. 5a) and 248 meV (Fig. 5b) pump have similar bipolar lineshape. In contrast, highpump photon energy, e.g., 950 meV (Fig. 5d) and 1550 meV (Fig. 5e), show an overall positive conductivity change down to 2 meV. The clear similarities between midIR and THz pumping and their distinct difference vs. highenergy pumping allow us to distinguish two excitation channels, i.e., intraband (interband) excitations with low (high) photon energy pumping. Importantly, the data obtained for THz and midIR pumping can be wellfitted without changing carrier densities. In sharp contrast, the data for highphotonenergy pumping cannot be fitted in this way. Specifically, our good fittings obtained in Fig. 5a, b indicate that the pumpinduced bulk components (dashed blue lines) have nearly identical amplitude and lineshape. This implies that the bulk responses following 4 meV and 248 meV pump are very similar, which indicate a possible transition from filled surface to empty bulk states following 248 meV pump cannot be a major channel, or at least any such contribution is much smaller in our probed THz spectral region than the main intraband signals. Additionally, it is fully consistent that the negative surface response (dashed green lines) is greater following 4 meV pump than 248 meV and 354 meV pump (still below but closer to the bulk bandgap) in the linear Dirac dispersion. In strong contrast, for highphotonenergy pumping we can see that the THz conductivities are positive in the probe range and much larger. Importantly, they cannot be fitted by the model with conserved carrier density any more, see Fig. 5d, e. Instead, they can be fitted decently only with Δn_{SS} > 0 and Δn_{BS} > 0, as shown in Fig. 5f, g. Their bulk (dashed blue lines) and surface (dashed green lines) components are both larger than their counterparts following low energy pump, which gives the overall positive THz conductivity change in the probed range, indicative of the bulkdominant response. Moreover, please note that the fittings are faithful, because it only needs to change two scattering rates, which leads to distinctly different THz lineshapes that uniquely converge. We also rule out the possibility that two different sets of scattering rates, which differ from each other by >2%, can fit the same data. These results clearly demonstrate the control of THz conductivity by ultrabroadband, wavelengthselective pumping from THz to visible.
Discussion
To highlight the difference between the intraband excitation scheme used in this work and the interband excitation found in previous literature, Fig. 6a, b compare the ultrafast THz dynamics under 390 meV (3.18 μm) and 248 meV (5 μm) pumping, respectively. The former resonantly excites interband transitions in our bulk Bi_{2}Se_{3} sample (Fig. 1a). Here, for simplicity, we show the THz field change ΔE_{sample} by fixing the gate time t_{gate} at the peak of the static THz field as a function of pumpprobe delay Δt_{pp}, similar to previous studies^{28,30}. Unlike the aboveobtained frequencydependent conductivity Δσ_{1}(ω) dynamics that closely follows the pumpinduced change of surface/bulk scattering rates, ΔE_{sample} measured at a fixed gate time originates from frequencyintegrated responses within the measured spectral range ~2–10 meV. This frequency average leads to more complicated dynamics that may come from all relaxation channels of opposite signs as shown in Fig. 2. Nevertheless, Fig. 6 shows that there is still a distinct difference between the interband (Fig. 6a) and intraband (Fig. 6b) pump excitation schemes. On the one hand, with resonant interband pump excitation at 390 meV (inset, Fig. 6a), ΔE_{sample} at several pump fluences shows two main decay features: (1) a dominant, fast overshoot, which exhibits fluencedependent amplitude and quickly diminishes within ~4 ps; (2) a slow, hundreds of ps component, which is fluence independent, i.e., the ΔE_{sample} for all fluences merge and decay together after ~100 ps. On the other hand, with intraband excitation at 248 meV (inset, Fig. 6b), the fast overshoot component is absent in the THz responses at low fluences ≤12 μJ cm^{−2}, the fluence used for midIR pumping in Figs. 1–4. A distinct difference is clearly visible between interband and intraband pumping with low fluence, e.g., the 7 μJ cm^{−2} (cyan) and 9.5 μJ cm^{−2} (green) traces. Interestingly, increasing the midIR pump fluence to 19 μJ cm^{−2} (red line in Fig. 6b) leads to a transition to a decay profile, where a fast overshoot component now appears similar to the interband photoexcitation, e.g., the 390 meV excitation scan at 1.6 μJ cm^{−2} (pink line in Fig. 6a). For a better comparison, this pink curve is also plotted in Fig. 6b as a filled gray curve, which resembles the 248 meV excitation scan at 19 μJ cm^{−2}, unlike for the lower fluences. This reveals the same relaxation mechanism between the two, which can be attributed to the two photon absorption (TPA) present in the high fluence, midIR pumping case. This excites interband transitions in our sample in spite of below gap pump photon energy. The dynamics of Bi_{2}Se_{3} under highphotonenergy pumping have been extensively studied recently and the few ps relaxation component is mainly from bulksurface charge transfer and/or decay that can give the overshoot feature after interband carrier injection^{16}. The absence of such process in the midIR pumping below ~12 μJ cm^{−2} is consistent with the intraband excitation channel and its similarity with THz (few meV) pumping.
Although the optical transition from filled surface state to empty bulk state with 248 meV midIR pump is potentially allowed, our results show that the relative strength of this channel and its contribution to the THz conductivity are, however, still an open question. The similarity between THz (few meV) and midIR pump implies that this channel is relatively weak for THz and midIR pumping when compared to the intraband excitation channel, unlike in the case of optical pump, which warrants further studies. In addition, our fitting is faithful because it only needs to change two parameters, which are the two timedependent scattering rates directly seen in distinctly different timeresolved THz lineshapes. Since the fitting result is already uniquely converging with the two fitting parameters, additional parameters only relax the constraint and add uncertainty, which is hard to be physically meaningful. The midIR/THz pump spectroscopy experiment like ours reveals ultrafast manipulation of surface and bulk THz conductivity via wavelengthselective pumping and underpin the difference of intraband vs. interband pumping, shown in Fig. 5, without reference to any model and/or assumption for fitting. The observation of frequencydependent hot carrier cooling times is shown in Fig. 2a–d, which directly distinguish the faster surface channel from the slower bulk in the raw data. These ultrafast conductivity dynamics of surface states are absent in the prior static THz and timeaveraged probes.
Finally, we note that the assignment of THz conductivity of these two decay channels is justified by the distinctly different THz spectrum lineshapes and dynamics of the surface and bulk states, respectively. First, only the TI surface state could give rise to a photoexcited negative THz conductivity in Fig. 2e and intraband decay of Dirac spectrum at the surface is much faster than the bulk. Second, the other channel, i.e., photoexcited positive THz conductivity that we have assigned to bulk in Fig. 2f, exhibits a decrease in the scattering rate. This is well explained by the reduced ionized impurity scattering which leads to a decrease in scattering rate and an increase in THz conductivity at low frequency after photoexcitation. Third, a decrease in Bi_{2}Se_{3} thickness has been shown to induce a transition from a bulklike, positive conductivity to a surfacelike, negative THz conductivity^{30}.
In conclusion, we have provided the measurement and insights into the intraband, midIR, and THz pumpinduced quantum transport in TIs. We achieve this by suppressing all interband transitions that mask the processes of main interest. The conclusions from this advanced spectroscopy are the demonstration of another tuning knob for both controlling THz conductivity and isolating the surface contribution from the bulk contribution, by using low photon energy pumping and comparing them to optical pumping. This scheme enables a clear observation of enhanced surface transport, which provides evidence for helical spin structure of surface (Dirac) electrons that suppresses backscattering. The pump photon energy tuning achieved in this way also allows us to control the surface transport optically in a selective way. Our experiments may evolve into a benchmark characterization method for high frequency topological transport in TIbased device development, and motivate fundamental quantum phase discovery and control at the boundaries of topology, magnetism^{34}, and other broken symmetry states^{35,36,37}.
Methods
Experimental schemes
Our midIR/THz pump and THz probe spectrometer is driven by a 1 kHz Ti:sapphire regenerative amplifier, which has 800 nm central wavelength and 40 fs pulse duration^{38}. The majority of the output is used to pump either an optical parametric amplifier to generate midIR pulses tunable from 3–15 μm (or 83–413 meV) or a lithium niobate crystal to generate strong THz pulses centered at 4 meV^{39} allowing for selective intraband and interband photoexcitation. The other part of the output is used to generate and detect phaselocked THz electric fields in timedomain via optical rectification and electrooptic sampling in a 1 mm thick ZnTe crystal, respectively. THz fields with a bandwidth from 0.5 to 2.5 THz (2.1–10.3 meV) are used as a probe beam. The measurement scheme is briefly illustrated in Fig. 1a, in which midIR (red) or THz (yellow) pump photoexcites the sample and THz pulse (light blue) probes photoinduced responses of the sample. The transmitted THz probe containing spectral amplitude and phase information of the sample is directly measured in timedomain using an optical gate pulse. The setup is enclosed in a N_{2} gas purge box.
Sample preparation and characterization
The Bi_{2}Se_{3} thin film sample, 50 nm thick, is grown by molecular beam epitaxy on a 0.5 mm thick sapphire substrate. The sample is mounted together with a 0.5 mm thick pure sapphire substrate, used as a reference, into a cryostat with temperatures down to T = 5 K. Two copper mounts with the same aperture are placed directly in front of the sample and reference to ensure uniform photoexcitation and accurate comparison of their THz transmission.
The sample studied has a Fermi energy E_{F} ~ 60 meV from the bulk conduction band edge (Fig. 1a), as estimated from the measured plasma frequency in the static THz conductivity spectra shown in Fig. 1b. The gray lines are theoretical fittings that are discussed in Results. The estimated Fermi energy is consistent with the difference between the separately measured, interband optical transition onset E_{inter} ~ 390 meV using our wavelengthdependent pumpinduced THz field change data (see Supplementary Note 1) and the bulk insulating bandgap E_{g} ~ 332 meV, which yields a similar E_{F} = E_{inter} − E_{g} ~ 58 meV. Please note that the exact value of the gap size is not critical for our scheme, nor does it change our conclusion, as long as the interband transition gap in our sample is larger than our pump photon energy, e.g., 4 meV and 248 meV used.
THz data analysis
Raw THz field transients are measured as a function of gate time t_{gate} after transmission through (i) the reference bare substrate E_{ref}(t_{gate}), (ii) the unexcited sample E_{sample}(t_{gate}), and (iii) as pumpinduced change ΔE_{sample}(t_{gate}, Δt_{pp}) at pumpprobe delay Δt_{pp}. Figure 1c,d shows the 2D falsecolor plots of ΔE_{sample}(t_{gate}, Δt_{pp}) after below gap photoexcitation at 248 meV (5 μm) for high (300 K) and low (5 K) temperatures, respectively. Also plotted in the above figures are the corresponding E_{sample}(t_{gate}) (green curves) and pumpinduced change ΔE_{sample}(t_{gate}) at Δt_{pp} = 1 ps (blue curves). For the unexcited sample, through the fast Fourier transformation and Fresnel equation, the static THz conductivity, shown in Fig. 1b, is directly obtained from the experimentally measured complex transmission coefficient \(\tilde t(\omega )\) with spectral amplitude and phase information extracted by comparing the fields transmitted through sample and reference, i.e., \(\tilde t(\omega ) = E_{{\mathrm{sample}}}(\omega )/E_{{\mathrm{ref}}}(\omega )\), similar to the method reported in ref. ^{29} (see also Supplementary Note 5). For the excited sample at Δt_{pp}, the complex transmission coefficient is obtained by \(\tilde t_{{\mathrm{excited}}}(\omega ) = [{\mathrm{\Delta }}E_{{\mathrm{sample}}}(\omega ) + E_{{\mathrm{sample}}}(\omega )]/E_{{\mathrm{ref}}}(\omega )\) and is used to extract the photoexcited transient THz conductivity. Afterwards, the pumpinduced conductivity change \({\mathrm{\Delta }}\tilde \sigma (\omega ) = \tilde \sigma _{{\mathrm{excited}}}(\omega )  \tilde \sigma (\omega )\) is calculated. The corresponding dielectric function can be calculated by the equation \(\tilde \sigma (\omega ) = i[1  \tilde \varepsilon (\omega )]\omega \varepsilon _0\). The simultaneously obtained real parts of transient conductivity change Δσ_{1}(ω) and dielectric function change Δε_{1}(ω) as a function of Δt_{pp} are presented in the study, which allow us to quantitatively describe the ultrafast dynamic evolution of the photoexcited Dirac and bulk fermions and their intrinsic scattering processes.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering (Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. DEAC0207CH11358) (science driver, THz spectroscopy experiment and theory). Sample development was supported by National Science Foundation DMR 1400432. Terahertz spectroscopy instrument was supported in part by National Science Foundation EECS 1611454. Additional analysis by I.E.P and M.M was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DESC0019137.
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L.L. and X.Y. performed the experimental measurements and collected the data. They analysed the results and developed the model with the help of J.W., Z.L., C.V., D.C., M.M., X.Z., Y.Y., C.Z.W., K.M.H. and I.E.P. Thin film growth and basic characterizations are done by X.L., M.D. and J.K.F. at University of Notre Dame. J.W. and L.L. wrote the paper with help from all authors. J.W. supervised the study.
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Luo, L., Yang, X., Liu, X. et al. Ultrafast manipulation of topologically enhanced surface transport driven by midinfrared and terahertz pulses in Bi_{2}Se_{3}. Nat Commun 10, 607 (2019). https://doi.org/10.1038/s41467019085596
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DOI: https://doi.org/10.1038/s41467019085596
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