Unveiling surface and bulk contributions in temperature dependent THz emission from Bi2Te3

We report evolution of the pulsed terahertz (THz) emission from Bi2Te3 topological insulator in a wide temperature range, where an interplay between the topological surface and bulk contributions can be addressed in a distinguishable manner. A circular photogalvanic effect-induced topological surface current contribution to THz generation can be clearly identified in the signal, otherwise, overwhelmed by the hot carrier decoherence in the bulk states. With the decreasing temperature, an initial sharp increase in the topological surface THz signal is observed before it attains a constant value below ∼200 K. The scattering channels between topological surface and bulk regions via carrier-phonon scattering are dominantly active only above the bulk-Debye temperature of ∼180 K, and the temperature-independent behavior of it at lower temperatures is indicative of robust nature of topological surface states. THz emission due to ultrafast photon-drag current in the bulk states is almost independent of temperature in the entire range, while the combined photo-Dember and band-bending effects induced photocurrent is doubled at 10 K.


Introduction
Bismuth telluride (Bi 2 Te 3 ) family of three-dimensional topological insulators (3dTIs) exhibit unique electronic properties due to the existence of Dirac-like metallic surface states and insulating bulk states.The spin-momentum locked surface electrons in 3dTIs are capable of generating spin and charge currents, which are desirable in low-power spintronic devices [1].Optical excitation of these materials by ultrafast laser pulses gives rise to transient photocurrents in the bulk and on the topological surface region [2].Among the various mechanisms contributing to photocurrents in 3dTIs, the photogalvanic effect is primarily responsible for current generation on the topological surface [3,4].In the proximity of the surface of a 3dTI, the bulk photocarriers contribute to current generation due to band-bending effect and photo-Dember effect [5].Photon-drag effect, a third-order nonlinear optical process, can induce photocurrents in both the bulk and topological surface regions of 3dTIs [4,6].Recent advancements have enabled the use of ultrafast photocurrents for the generation and detection of pulsed THz radiation [7,8].The feasibility of room temperature THz direct detection using photogalvanic effect was tested recently in single crystalline Bi 2 Se 3 [7].The above processes are being exploited for the generation and manipulation of chiral THz waves from 3dTIs [9].Extensive experiments are required to fully understand the origin of and to control these photocurrents, particularly, the topological surface current, so as to enable a wide range of application potential [7,10,11].A fundamental problem concerning 3dTIs is the detection of the much weaker topological surface response in any experimental measurement.This gets more challenging with Bi 2 Te 3 and other compounds from this family due to the presence of high degree of intrinsic doping [12].Consequently, strong electron-phonon coupling in the bulk and phonon-induced scattering channels between the bulk and topological surface states can affect the topological surface response at room temperature [13].In general, the high intrinsic doping adversely affects the photocurrent generation efficiency in both the topological surface and bulk regions of these materials, which is undesirable for practical device applications [13,14].A way to circumvent this problem to some extent is to use low-temperature responses that limit the electron-phonon coupling and the phonon-induced scattering between topological surface and bulk regions.The temperature dependent carrier density and the carrier mobility play a decisive role in determining the photocurrent generation efficiency in these materials [14,15].Only a few research studies are available in the literature in this regard on semiconducting materials [2,16,17].
Time-domain THz emission spectroscopy has evolved in recent times as an alternate technique [18] which can help determine various physical properties of the carriers in condensed matter systems including the 3dTIs [3,[19][20][21] in a noncontact and non-invasive manner.It is inquisitive to determine the temperature dependent role of the ultrafast photocarriers in 3dTIs and exploit the possibility to decipher the contribution of the topological surface states in the overwhelming response from the bulk states of these systems.Here, we have performed rigorous experiments using time-domain THz emission spectroscopy in a wide temperature range, from the room temperature to near liquid helium temperature, to analyze the photocurrent generation processes occurring in the bulk and the topological surface states of a single crystalline Bi 2 Te 3 topological insulator.The ultrafast photoexcitation light helicity-dependent measurements help us to extract the topological surface contribution to THz generation even though it is nearly one order of magnitude smaller than that from the bulk states.The combined photo-Dember and band-bending effects induced surge currents are found to be dominant over the photon-drag current in the bulk, where only the prior gets enhanced at low temperatures.The circular photogalvanic effect (CPGE)-induced ultrafast injection current in the topological surface region shows a strong enhancement as we lower the sample temperature below the room temperature until it reaches a nearly constant value below ∼200 K.Such behavior is attributed to the strong decoupling of the topological surface and bulk responses due to suppression of the electron-phonon coupling and the phonon-induced scattering channels between topological surface and bulk regions at low temperatures.

Results and discussion
THz pulses emitted from the femtosecond photoexcited Bi 2 Te 3 crystal at 800 nm that is placed inside an optical cryostat, are detected using electro-optic sampling in a nonlinear crystal as depicted in figure 1(a).Other details of the experimental setup are given in the methods section.The single crystalline Bi 2 Te 3 sample was characterized using various experimental techniques and the results are described in the supplementary information.To understand the THz emission from the crystal, we require the details of the intrinsic carrier concentration (N) and carrier mobility (µ) at each of the sample temperatures.The same is calculated from low-temperature resistivity and Hall measurements and are shown in figure 1(b).The results indicate that the mobility of the carriers in the sample increases more than twofold at low temperatures, whereas the intrinsic carrier concentration decreases by nearly 20% in the same temperature window.The time-domain signals of THz pulses are recorded for left circularly polarized (LCP) and right circularly polarized (RCP) femtosecond excitation pulses at varying sample temperatures from 10 K to 300 K.For LCP, the angle (α) of the fast axis of the quarter wave (λ/4) plate was kept at −45 • and for RCP, it was kept at +45 • with respect to incident linear polarization direction.The results for the experimentally measured THz-waveforms with the corresponding FFT spectra for the highest and the lowest temperatures are presented in figures 1(c) and (d), respectively.A noticeable difference between the THz signal strengths for LCP and RCP excitations at the two sample temperatures is seen.Such a difference was consistently verified over multiple scans and at all the temperatures during the experiments.We also find that the THz spectra of Bi 2 Te 3 at two extreme temperatures are nearly same with the bandwidth of ∼3 THz.The THz generation efficiency can be monitored by recording the peak-to-peak value of the experimentally detected THz electric field (Epp) at all the temperatures.As shown in figure 1(e), THz signal strength increases monotonically with the decreasing sample temperature for both the LCP and RCP photoexcitation.A plausible description of the excitation light helicity dependent THz emission by CPGE-induced photocurrent in 3dTIs is provided in the next paragraph.It may be noted that circular photon drag effect (CPDE)-induced photocurrent has also been considered as a contributor [4,6,22,23] as both exhibit quadratic dependence on the excitation light field.While CPGE is manifested by a third-rank tensor, CPDE involves a fourth-rank tensor owing to the involvement of the light momentum vector q, hence, enabling its occurrence even within the bulk of the material [4,6].Consequently, distinguishing CPGE-induced THz emission from that due to CPDE becomes imperative in 3dTI so as to isolate the topological surface and bulk contributions.Nevertheless, the incident angle (θ) dependent measurements help to redeem from this situation, where, phenomenologically, CPGE-induced photocurrent has been observed to scale with sinθ while CPDE-induced photocurrent scales with sin2θ.Recent experiments on other 3dTIs such as Sb 2 Te 3 and (Bi 1−x Sb x ) 2 Te 3 have revealed that CPGE contributes majorly to generate the photocurrent upon excitation by circularly polarized light [24][25][26].Therefore, we can safely ignore the CPDE-induced photocurrent over the CPGE-induced photocurrent and hence THz emission from Bi 2 Te 3 .
Circularly polarized light having specific spin-angular momentum of ±h [27] can selectively excite spin-up or spin-down electrons in a topological insulator [2], as depicted in figure 2(a).This asymmetrical excitation of electrons leads to the generation of a spin current and a net charge current on the surface of the topological insulator due to spin-momentum locked topological surface states.The generation of charge current by this surface sensitive process is due to CPGE, [3,9], which further becomes a source of THz radiation.For the LCP and RCP excitations, other than the surface sensitive CPGE contribution to the THz emission, we have a rather much stronger THz signal coming from the bulk of the sample, which however, is same for both types of circular light excitations.Therefore, the difference in the magnitudes of the THz signal for the LCP and RCP helicity light excitations, as apparent from figure 1(c), is due to CPGE.We may note that the bulk contribution to THz emission can arise because of multiple reasons, as described in the next section of the paper.At all temperatures, we distinguish between the contribution to THz emission from the CPGE-induced topological surface states and that from the bulk states by using the relation, 28,29].Correspondingly, the helicity-independent bulk-only contribution to THz emission can be deduced by using the relation, Thus, the obtained topological surface and bulk contributions to the THz generation as a function of the sample temperature are presented in figure 2(b).It can be seen that the topological surface contribution is nearly one-tenth of the bulk contribution as expected.Furthermore, we notice from figure 2(b) that with the decreasing temperature, the THz emission from the surface CPGE first increases and then quickly attains a nearly constant value at temperatures <200 K. On the other hand, the THz emission from the bulk shows a monotonic increase with the decreasing temperature in the entire temperature range.Interestingly, the temperature dependence of the bulk THz signal resembles that of the intrinsic carrier mobility µ of the sample, as noted earlier in figure 1(b).Relative to the value at the room temperature, the THz generation efficiency of the bulk states in Bi 2 Te 3 gets enhanced by a factor of ∼1.6, while the mobility increases by a factor of ∼2.2 in lowering the temperature to 10 K.At first glance, it appears from this observation that the THz generation from bulk Bi 2 Te 3 is strongly related to the corresponding carrier mobility at any given temperature.
The topological surface states region is just within a few nm underneath the surface of 3dTIs, while the bulk sample thickness, in our case, is above 120 µm.This signifies that the electrical transport properties would be dominated by the bulk carrier states.Usually, it is challenging to decipher the contribution of the topological surface states in any experiment, unlike angle-resolved photoemission spectroscopy [30].Through magneto-transport measurements, we have analyzed the weak anti-localization contribution in magnetoconductance (∆G) due to the topological surface states in Bi 2 Te 3 [31] (see supplementary information).We find that the number of conducting channels is nearly five orders of magnitude higher than unity, similar to the other reports [32].Therefore, the properties from electrical and magneto-transport measurements are overwhelmed by the bulk contribution in the entire temperature range of 10-300 K in our experiments.Consequently, the temperature dependent behavior of the bulk contribution to THz emission in figure 2(b) can be related to the temperature dependent carrier mobility in figure 1(b).THz emission from bulk carrier states in Bi 2 Te 3 mainly originates from photogenerated surge currents, which can arise from three distinct mechanisms: linear and circular photon-drag effect, band-bending effect and photo-Dember effect [9,33].As mentioned earlier, the contribution of CPDE can be safely ignored in the present case, therefore, any further reference to the photo drag effect in the rest of the current paper means the bulk contribution of the linear photon drag effect.It is also worth mentioning that THz generation through optical rectification, which occurs due to broken inversion symmetry at interfaces, is also a possibility.Nevertheless, this mechanism is comparatively negligible in our case [19].The temperature dependence of the topological surface and bulk contributions to overall THz emission from Bi 2 Te 3 is analyzed in the following subsections.

Temperature dependence of THz generation from bulk carrier states
In Bi 2 Te 3 , the topological surface region spans just a couple of nm of thickness [34][35][36].Because the topological surface carriers and the bulk carriers in the proximity of the surface, can both contribute to THz emission, to distinguish them, the former are referred to as 'topological surface carriers' everywhere in the current paper.Figure 3(a) illustrates the microscopic mechanism of ultrafast photocurrent generation and subsequent THz emission from Bi 2 Te 3 due to the band-bending (BBe) effect.The BBe effect induces formation of a depletion layer below the topological surface region, extending into the bulk upto a certain thickness depending on the intrinsic carrier density [35,[37][38][39].Thus induced electric field is always normal to the surface [37].The photoexcited carriers get accelerated under this built-in electric field to generate a drift current that can be described as J BBe ∝ N P µ, where N P represents photoexcited carrier density, and µ is the charge carrier mobility.The direction of ⃗ J BBe depends upon the type of majority carriers in the sample.Given that we have used n-type Bi 2 Te 3 in our experiments, an upward band-bending due to the depletion of charge carriers beneath the topological surface region, is shown in figure 3(a) [40].Consequently, an outward drift current is induced, contributing THz radiation emission in the direction of detection of our experiments [5,33].Figure 3(b) shows the mechanism of the photo-Dember (PDe) effect in bulk single crystalline Bi 2 Te 3 following the excitation by an ultrafast laser pulse.In the proximity of the surface within the penetration depth, a large number of hot photocarriers are generated, which eventually diffuse to low concentration regions in the bulk [41].In low bandgap systems such as Bi 2 Te 3 , the diffusion coefficient for electrons and holes is different [42].Consequently, optically generated electron-hole pairs are spatially separated on the move leading to the formation of a transient charge current due to diffusion and hence emission of THz radiation.Like the BBe effect, the PDe effect induced transient current would depend on the photocarrier mobility and photocarrier density according to the relation, J PDe ∝ N P µ.From the above, it can be concluded that at a given sample temperature and excitation fluence, the THz generation efficiency of Bi 2 Te 3 due to PDe and BBe effects will increase in proportion with the photocarrier mobility.We may mention that for a more quantitative comparison of the relative strengths of the photo Dember effect and the band bending effect in the THz emission from 3dTIs further experiments such as the intrinsic carrier density dependent investigations would be worthwhile [43].
The THz emission from 3dTIs can also arise from photon-drag (PDr) effect whose mechanism has been schematically described in figure 3(c).Following the light absorption, either the free carriers can take away the photon momentum or the photon energy first creates free carriers, which can further acquire a directed motion along the photon wave vector.Eventually, the directed motion of the free carriers constitutes a transient photocurrent [44], the amount of which is directly proportional to the absorbed photon flux or the free carrier density N in the material.The emitted THz field strength, in this case, is related to the photon and the electron parameters via the relation [45,46], J PDr ∝ Nk µ 2 e 2 m 2 +ω 2 µ 2 , where m and e are the effective mass and the charge, respectively, of an electron, while ω and k are the angular frequency and magnitude of the wave vector, respectively, of the incident light.The effective mass of electrons in Bi 2 Te 3 is known to be very weakly temperature-dependent as opposed to the strong temperature-dependence of the electron mobility seen in figure 1(b) [47,48].Our experiments have been performed for fixed k and ω, therefore, photon-drag effect induced THz emission at any given temperature depends on the carrier mobility and the carrier concentration at that temperature.
The overall transient photocurrent in the sample, due to all the effects mentioned above, is the source of THz radiation emitted from it.The peak value of the THz field strength is directly related to the maximum change in the time-derivative of this photocurrent.Therefore, the temperature dependence of the emitted THz field strength can be analyzed using the following relation, Here, α and β are scaling parameters that are used to quantify the contributions from the photon-drag effect E PDr pp and the cumulative of the photo-Dember and the band-bending effects, i.e.E PDe pp + E BBe pp .We have used the above relation to fit the experimentally extracted THz radiation from the bulk of the Bi 2 Te 3 crystal as shown in figure 2(b).The same is reproduced again in figure 3(d) for clarity where the fit is shown by a continuous curve.From the fit, we are able to distinguish the E PDr pp and E PDe pp + E BBe pp as presented in figure 3(e).From these results on the THz emission from the bulk, it is clear that the photon-drag current is almost independent of temperature, while the photocurrent due to photo-Dember effect and band-bending effect together gets enhanced by a factor of ∼2.2 upon lowering the sample temperature to 10 K from the room temperature.

Temperature dependence of THz generation from topological surface states
The low temperature evolution of CPGE-induced surface photocurrent, which is responsible for THz emission from the topological surface states in Bi 2 Te 3 , is analyzed here.The temperature dependent behavior of the topological surface THz signal is reproduced in figure 4(a).As can be seen here, with the decreasing temperature, an initial sharp increase in the THz signal is followed by a large plateau region below the temperature of ∼200 K.This kind of behavior indicates the existence of a strong scattering between the bulk conduction band and the topological surface states in Bi 2 Te 3 down to a certain temperature from the room temperature.In 3dTIs, the topological surface charge carriers within just a couple of nm underneath the surface [36] are physically separated from the bulk carriers as shown schematically in figure 4(b).Since the penetration depth of 800 nm centered pulsed excitation light is ∼25 nm [20], charge carriers in both the topological surface and bulk regions are excited.As mentioned above, the topological surface carriers emit THz radiation via ultrafast CPGE.At the same time hot electrons created in the bulk region can scatter into the topological surface via phonon and impurity mediated scattering processes as indicated schematically in figure 4(b).Such scattering processes can affect the mobility of the topological surface carriers and hence would hamper the probability of topological surface electrons emitting coherent THz radiation.
Phonon mediated scattering channels between topological surface and bulk regions for the electrons are at task mainly above the Debye temperature [49].This situation is alleviated by the increased number of thermally generated carriers at high temperatures (figure 1(b)).Therefore, due to an enhanced number of bulk carriers and strong scattering between the bulk conduction band and the topological surface states, the THz generation efficiency of the topological surface electrons gets reduced as we go above the Debye temperature of Bi 2 Te 3 [50].The bulk and surface Debye temperatures for Bi 2 Te 3 are at ∼165 K and ∼80 K, respectively [50,51].Only above the bulk Debye temperature, the topological surface carriers are influenced strongly by the coupling between the bulk conduction band and the topological surface states via electron-phonon scattering.For below the bulk Debye temperature, the inter layer scattering channels between topological surface and bulk regions get diminished more and more and hence the topological surface electron dynamics remains governed by a weak electron-phonon and electron-impurity scattering in the topological surface region [51,52].Therefore, nearly temperature-independent THz emission below the bulk-Debye temperature in figure 4(a) may be regarded as a signature of the robust nature of topological surface states in Bi 2 Te 3 .This robustness, which strictly prohibits backscattering of topological surface electrons against any nonmagnetic impurities, originates from the time-reversal symmetry protected spin-momentum-locked helical surface transport of these Dirac fermions [53].This observation aligns with the recently reported findings that the charge-impurity scattering in the topological surface of Bi 2 Te 3 family of 3dTIs exhibits weak temperature-dependence at low temperatures [54].

Methods
In the THz emission time-domain experiments, we have used a Ti:sapphire based femtosecond regenerative amplifier (Astrella, Coherent Inc. USA) providing femtosecond pulses of full width at half maximum duration of ∼35 fs, central wavelength of 800 nm and pulse repletion rate of 1 kHz.A collimated excitation beam diameter of ∼2 mm was used in our experiments that corresponds to an excitation fluence of ∼100 micro-Joules cm −2 .Freshly exfoliated single crystal of Bi 2 Te 3 sample of thickness ∼120 µm and lateral size of 3 mm × 5 mm was optically excited by the femtosecond pulses and THz pulsed emission was collected in the reflection geometry by using a 15 cm focal length 90-degree off-axis parabolic mirror.A similar parabolic mirror was used to guide the THz beam along with a collinearly propagating optical gating beam towards a thin ZnTe crystal for THz pulse detection by electro-optic sampling.More details about the detection can be found elsewhere [55].The linearly polarized light from the laser was converted to LCP and RCP by using an achromatic quarter-wave plate having AR coating in the range of 690-1200 nm.The temperature dependent measurements were carried out on the sample by mounting it on the cold finger copper sample holder of an optical cryostat (Janis, SI4-2-XG).All the experiments reported in the manuscript have been carried out at the above mentioned fixed value of excitation fluence and at a fixed crystal orientation (azimuthal angle) corresponding to the maximum signal from the sample [19] so as to determine the explicit role of the other conditions with the polarization state of the excitation light or the sample temperature and so on.High quality single crystalline samples of Bi 2 Te 3 with purity >99.995% were purchased from HQ Graphene, Netherlands.These were characterized using different experimental techniques as described in our previous work [19].

Conclusion
In conclusion, temperature dependent investigations on ultrafast photocurrent in single crystalline Bi 2 Te 3 via coherent THz emission has revealed the role of temperature in modulating carrier dynamics in both the bulk and the topological surface states.The dominant role of photo-Dember effect and band-bending effect-induced surge currents in the bulk, particularly at low temperatures, has been uncovered in our findings.Conversely, we discovered that the transient current induced by the photon-drag effect in the bulk shows minimal change with the temperature variation.With the decreasing temperature below the room temperature, a gradual enhancement in the CPGE-induced ultrafast injection current on the topological surface takes place until it attains a nearly constant value below temperature of ∼200 K.This experimental observation suggests strong decoupling of the topological surface and the bulk states at low temperatures.A complete suppression of the scattering between the bulk conduction band and the topological surface states takes place below the surface Debye temperature.The nearly constant THz emission yield from the surface region due to CPGE below 200 K is indicative of the robust nature of the topological surface states in Bi 2 Te 3 .

Figure 1 .
Figure 1.(a) Schematic of the time-domain THz emission measurement setup integrated with a low-temperature optical cryostat for varying the sample temperature from room temperature down to a few Kelvin (K).By using a quarter wave plate (λ/4), linear polarized excitation light is converted to left and right circular polarized light.The single crystalline bulk Bi2Te3 sample is characterized by various experimental techniques as discussed in the supplementary information.(b) Intrinsic carrier concentration and carrier mobility at all the temperatures.(c) Real-time THz scans measured at 10 K and 300 K sample temperatures for LCP and RCP femtosecond optical pulse excitations and (d) the corresponding fast Fourier transform spectra.(e) Temperature-dependence of the THz generation efficiency for LCP and RCP excitations from the behavior of the peak-to-peak value of the THz electric field.

Figure 2 .
Figure 2. (a) Schematics of the optical excitation by left and right circularly polarized, and THz emission from spin selected photoexcited electrons on the surface of a 3dTI via circular photogalvanic effect.The topological surface and bulk contributions to THz emission can be distinguished from these experiments, as discussed in the text.(b) Extracted values of the THz amplitude contributed by both the topological surface and the bulk states as a function of the sample temperature for Bi2Te3.

Figure 3 .
Figure 3. Transient photocurrent generation mechanisms in the bulk of a femtosecond pulse excited Bi2Te3 sample.(a) Schematic representation of the band-bending effect and subsequent THz emission by the transient drift current.The valence and conduction bands of the material and the depletion region below the topological surface are indicated.(b) Illustration of the photo-Dember effect indicating how ultrafast laser excitation induces a transient current by carrier diffusion and hence emission of a THz pulse.(c) Depiction of the photon-drag effect, resulting from the transfer of photon momentum to free carriers, constitutes a transient charge current along the light propagation direction and hence emission of a THz pulse.The possible processes of photon momentum transfer to intrinsic free carriers and the photogenerated carriers are indicated by dashed arrows.The horizontal dashed line in the conduction band is drawn to indicate the Fermi level and the metallic nature of the Bi2Te3 sample.(d) Experimentally extracted bulk THz emission and its temperature dependence fitted using equation (1).(e) Components of the emitted THz field strength, E PDr pp and E PDe pp + E BBe pp due to bulk photon-drag (PDr) effect and the photo-Dember + Band-bending (PDe + BBe) effects, respectively.

Figure 4 .
Figure 4. Temperature-dependence of CPGE induced photocurrent generated THz radiation from the topological surface states in Bi2Te3.(a) THz signal from the topological surface reproduced from figure 2(b).A horizontal dashed line is drawn to indicate the region of nearly constant THz emission.The surface and bulk Debye temperatures of Bi2Te3 crystal are marked by vertical arrows.(b) Schematic illustration of distinction between the optical excitation of topological surface and bulk carriers, and the interband transitions due to phonon and impurity scattering in physical and momentum space.The curved arrows are only for representation to indicate that the carriers may go through either a single or multiple scattering processes involving phonons during their transition from bulk to topological surface states.