# Topological Insulator Films for Terahertz Photonics

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

_{2}Se

_{3}and Bi

_{2-x}Sb

_{x}Te

_{3-y}Se

_{y}(BSTS) topological insulators (TIs) and the generation of THz radiation in photoconductive antennas based on the TI films. The experimental results, supported by the developed kinetic theory of third harmonic generation, show that the frequency conversion in TIs is highly efficient because of the linear energy spectrum of the surface carriers and fast energy dissipation. In particular, the dependence of the third harmonic field on the pump field remains cubic up to the pump fields of 100 kV/cm. The generation of THz radiation in TI-based antennas is obtained and described for the pump, with the energy of photons corresponding to the electron transitions to higher conduction bands. Our findings open up possibilities for advancing TI-based films into THz photonics as efficient THz wave generators and frequency converters.

## 1. Introduction

^{5}cm

^{2}/V·s [5].

_{2}Se

_{3}TIs was first experimentally studied in Ref. [15]. The authors estimated the third harmonic generation efficiency as 1% for the incident field of 300 kV/cm and also observed electromagnetic transparency in the strong electric fields of the order of 1 MV/cm. A number of papers were devoted to the generation of THz radiation pulses due to the optical excitation of photocurrents in TI epitaxial films in the absence of an external bias electric field and the study of underlying mechanisms. In particular, Ref. [19] reported a circular anisotropy in the THz radiation distribution in Bi

_{2}Se

_{3}and attributed it to the circular photon drag effect. Ref. [20] presented an experimental study of the mechanisms of transient THz emission from Bi

_{2}Te

_{3}and concluded that the surface nonlinear currents dominate in the THz emission. Generation of THz radiation under the action of pulsed optical pumping has been recently investigated in TIs of double [21,22] and quaternary [23] chemical compositions. In Ref. [24], THz radiation was generated in Bi

_{2}Se

_{3}and Cu-doped Bi

_{2}Se

_{3}single crystals. The authors suggested that surface Dirac fermions are responsible for THz radiation due to the strong dependence of the radiation power on the carrier density.

## 2. Theory

#### 2.1. Kinetic Theory of THz Third Harmonic Generation

**E**and ω are the field amplitude and frequency, respectively; ${\nabla}_{p}=\partial /\partial p$; $p$ is the momentum; and $\mathrm{St}f$ is the collision integral that describes the electron gas relaxation. The approach of the kinetic equation (1) is valid provided the electron gas conductivity $\sigma \gg {e}^{2}/\hslash $ and the field frequency $\omega \ll \langle \epsilon \rangle /\hslash $, where $\hslash $ is the reduced Planck constant and $\langle \epsilon \rangle $ is the mean kinetic energy of electrons.

_{F}is the Fermi energy.

_{2}Se

_{3}, the Dirac point is close to the valence band, and the Fermi energy of surface electrons can be quite large (of the order of the band gap). According to Equation (8), the efficiency of third harmonic generation, for a given electric field amplitude E, decreases in 2D Dirac systems with large Fermi energy. At the same time, the cubic dependence ${j}_{3\omega}\propto {E}^{3}$ holds as far as the relaxation times are not affected by electron gas heating (or, alternatively, the inequality $\omega {\tau}_{1}>>1$ is fulfilled) and the distribution of surface electrons remains degenerate. The latter also suggests that the peak energy gained by an electron at the cycle of the THz field, which is estimated as $\left|ev{\tau}_{1}(\omega )\right|E$, is less than the Fermi energy. As it has been recently measured, the relaxation of hot electrons in topological surface states is very fast [16]. The reason could be the interaction with optical phonons [31,32,33] or the efficient transfer of energy between surface and bulk carriers due to Coulomb interaction [34]. For fast energy relaxation, ${\tau}_{e}~{\tau}_{1}$, and efficient dissipation of heat from the surface region, the regime ${j}_{3\omega}~{E}^{3}$ can be optimistically extended up to the electric fields $E~{E}_{F}/\left|ev{\tau}_{1}(\omega )\right|$ giving rise the current amplitude $j~e{E}_{F}^{2}/\left(v{\hslash}^{2}\right)$. This demonstrates that 2D Dirac systems with large Fermi energy and fast energy relaxation can be highly efficient for frequency multiplication in the THz spectral range.

#### 2.2. Generation of the THz Radiation in Photoconductive Antennas

_{m}is an electric field at the location of charge carriers, and I(t) is the intensity of the laser source, determined by the expression:

_{c}is the electron capture time, τ

_{1}is the momentum relaxation time, R is the pump reflection coefficient, α is the absorption coefficient at the pump frequency, f

_{p}is the laser frequency, t

_{p}is the pump laser pulse duration, h is the Planck’s constant, e is the electron charge, and m

^{*}is an electron effective mass. The electric field at the location of the charge carriers can be found from the expression:

_{b}is the bias electric field, η is the screening coefficient, and ε is the dielectric function of the photoconductive material. At large screening factors η, the field E

_{m}becomes equal to E

_{b}so that

_{b}is the bias voltage, and W is the antenna’s gap. The relation of current density to the concentration n(t) and the velocity v(t) of charge carriers is described as $j(t)=en(t)v(t)$. In turn, the time derivative of the current density determines the strength of the emitted THz field.

_{0}and a quality factor Q. The frequency transfer function of such a resonator is well described by the shape of a Lorentzian line with a width determined by the quality factor. Then, the resulting frequency dependence of the intensity spectrum of the THz field generated by the PCA S(f) can be found by the following empirical formula:

## 3. Materials and Methods

#### 3.1. Growth and Characterization

_{2}Se

_{3}) and quaternary (Bi

_{1.9}Sb

_{0.1}Te

_{2}Se) TIs were grown on 400-µm-thick (0001) sapphire substrates with a thin (5–20 nm) ZnTe buffer layer deposited in a horizontal quartz reactor at atmospheric pressure of hydrogen. It is known that in binary systems Bi(Sb)–Se(Te) there are different phases of the homologous series mBi(Sb)

_{2·}nBi

_{2}Se(Te)

_{3,}where m and n are a number of Bi

_{2}, Sb

_{2}and Bi

_{2}Se

_{3}or Sb

_{2}Te

_{3}blocks per unit cell. In a series of works by one of the authors of this work, the phase composition of films deposited at different temperatures was studied in detail in growth systems: trimethyl bismuth (BiMe

_{3})—isopropyl selenide (iPro

_{2}Se)—hydrogen [39], trimethyl bismuth—diethyl telluride (Et

_{2}Te)—hydrogen [40] and trimethyl antimony (SbMe

_{3})—diethyl telluride—hydrogen [41] on the (0001) sapphire substrates. It was shown by methods of X-ray diffraction and energy-dispersive X-ray spectroscopy that at temperatures higher than 440 °C, rhombohedral epitaxial films of the corresponding binary compounds are deposited with m = 0 и n = 1. Therefore, to ensure the growth of films of quaternary compounds of Bi

_{2−x}Sb

_{x}Te

_{3−y}Se

_{y}stoichiometry, a temperature of 445 °C was used in this work.

_{3}, SbMe

_{3}, ZnEt

_{2}, Et

_{2}Te, and iPro

_{2}Se were used as sources of bismuth, antimony, zinc, tellurium, and selenium, correspondingly. Stainless steel bubblers with organoelement compounds BiMe

_{3}, SbMe

_{3}, ZnEt

_{2}, Et

_{2}Te, and iPro

_{2}Se were thermostated at 0, −30, 10, 25, and 27 °C, respectively. The ZnTe buffer layers were grown in a single technological cycle with TI films at the same temperature of 445 °C. The total hydrogen flow was 1.0 L/min during the deposition of ZnTe buffer layers, and 0.5 L/min during the epitaxy of TI films. The ratio of elements of the V/VI group in the vapor phase was not lower than 10, and the total partial pressure of BiMe

_{3}+SbMe

_{3}was kept close to 6 × 10

^{−5}bar.

_{2}Se

_{3}(Bi-Mα and Se-Lα), Sb (Sb-Lα), ZnS (Zn-Lα), PbTe (Te-Lα), and Al

_{2}O

_{3}(Al-Kα) crystals and O-Ka). Measurement of standards and analysis of samples were carried out under the same conditions at an accelerating voltage of 10 kV and an electron probe current of 1.4 nA. The spectrum accumulation time was set to 100 s. Under such conditions, the detection thresholds for all analyzed elements was 0.03–0.05 wt. %. As expected, in all BSTS films studied in this work, the ratio of elements of the V/VI groups was close to 2:3 and was within the limits of the detection thresholds. It should be emphasized that the composition of quaternary solid solutions cannot be determined from XRD spectra, and EDS analysis is required here.

_{2}Se

_{3}sample was obtained by atomic force microscopy (AFM) via a NT-MDT INTEGRA Prima scanning probe microscope (LLC “NT-MDT”, Moscow, Russia) operating in the semi-contact mode. Sample BSTS was studied by AFM AIST-NT Smart SPM with AIST-NT SPM Control software. Nanosensors PointProbePlus PPP-NCh-20, designed to operate in the semi-contact mode, were used. The radius of curvature of the tip end was 5–10 nm, and the oscillation amplitude of the free end of the cantilever far from the sample’s surface was chosen to be 15–20 nm. Before measurements, the samples were washed in isopropyl alcohol in an ultrasonic bath for 5 min and dried. In addition, for the samples without overhead electrodes, the side that was examined by AFM was studied by measuring the electrical conductivity. The resulting images were processed using the NT-MDT Image Analysis software. The results were used both to analyze the surface morphology and to obtain information about the surface roughness and film thickness. Note that our films were not thin enough for the surface Dirac states to completely disappear. As shown in Ref. [42], the Dirac cone of surface states disappears at 5 quantile thicknesses and less, while our TI samples are much thicker. Thus, topologically protected states exist on the film surface, and TI films can be treated as bulk samples.

_{2}Se

_{3}film surface is shown in Figure 1a. From the analysis of the cross sections of the AFM images, it can be concluded that the “effective thickness” of the TI film is about 20 nm. In this case, the film itself is not completely continuous but contains a relatively small number of pores, the depth of which is equal to the film thickness. No crystallites with noticeable faceting were found on the surface; to characterize the quality of the surface, the roughness parameters were measured over an area of 16 μm

^{2}. The average roughness was 2.5 nm. The histogram of the distribution of surface heights in the same area was close to the normal distribution.

^{2}is 7.4 nm. The surface of the “islands” has a nm-size height terraces. The terraces have low contrast, because next to them there are the borders of the “islands”, the height of which is an order of magnitude greater. Further film deposition proceeds according to the two-dimensional (2D) growth regime. Upon transition to the 2D growth regime, only protrusions about 1 nm high are present on the surface, which are formed by five-layer Ch-Bi-Ch-Bi-Ch-Bi, where Ch is Te or Se. The surface roughness over the area of ~4 μm

^{2}is 0.41 nm.

_{2}Se

_{3}sample. This fact is associated with a high concentration of bulk charge carriers due to the location of the Fermi level in the conduction band (Bi

_{2}Se

_{3}) [45]. On the contrary, in the BSTS sample, the bulk transfer is strongly suppressed, since the chemical composition is close to the Ren curve [45], and the Fermi level is located in the bulk bandgap. Although thicker films were studied in Ref. [45], our results for BSTS nano-films with compositions close to the Ren curve are in good agreement with the static resistivity data from Ref. [46].

#### 3.2. Experimental Techniques

_{1}(Figure 3a) was installed after the crystal, which separated THz radiation at a fundamental frequency of 0.5 THz. The peak strength of the THz field was about of 100 kV/cm. To vary the THz pump field strength, a pair of wire grid polarizers (WG

_{1}and WG

_{2}) was used; one of them was rotated on a motorized platform to control the transmitted power, and the other was fixed so that the polarization would be vertical. A band-pass filter F

_{2}was installed after the TI sample, which suppressed THz radiation at the fundamental frequency and transmitted only its third harmonic at a frequency of 1.5 THz. The amplitude of the THz pump pulses and the third harmonic was measured electro-optically with a 2-mm-thick ZnTe crystal, using probing laser pulses of 100 fs duration (EOS).

_{1}in the operating mode was about 15 mW. The detection of THz radiation was performed by the antenna A

_{2}Tera8-1 product (Menlo Systems); the signal from this was directed to the input of a lock-in amplifier. Parabolic mirrors M

_{1}and M

_{2}were used to collimate THz radiation. Instead of a typical beam chopper, we used the meander-shaped bias voltage modulation U

_{b}at a frequency of f

_{m}= 20 kHz.

## 4. Results and Discussion

#### 4.1. Generation of the Third THz Harmonic

_{2}Se

_{3}and BSTS samples on the fundamental radiation field strength [16]. For comparison, we show also the results of measurements of p-doped graphene with a charge carrier concentration of about 10

^{13}cm

^{−2}. Nowadays, graphene is the best material with the highest third harmonic conversion efficiency, reaching 1% and higher [47,48,49]. In our experiment, the highest field conversion efficiency in graphene is about 0.5%. The conversion efficiencies in the TIs Bi

_{2}Se

_{3}and BSTS at 100 kV/cm are 0.03% and 0.08%, respectively. The amplitude of the third harmonic field in BSTS is about three times larger than that in Bi

_{2}Se

_{3}. The enhanced conversion efficiency in BSTS, where the Fermi energy of surface electrons is smaller, is in accordance with the theoretical result; see Equation (8) and the subsequent discussion.

_{2}Se

_{3}and BSTS films is still lower than that in graphene, the TIs, in contrast to graphene, exhibits a purely cubic dependence of the third harmonic field on the pump field. This indicates that THz-induced nonlinear processes are far from saturation up to the pump fields of 100 kV/cm. We attribute these qualitatively different behaviors to a large difference in the relaxation times of carriers in graphene and TIs. In graphene, the energy dissipation is rather slow because of inefficient direct electron–phonon interaction and weak heat transfer from graphene to substrate [50,51]. In contrast, the energy relaxation of surface carriers in TIs occurs much faster, at the timescale of few hundred picoseconds, as was recently demonstrated for Bi

_{2}Te

_{3}by means of THz pump-probe spectroscopy [16]. As follows from the theoretical considerations in Section 2.1, faster relaxation suggests larger range of the validity of the cubic law ${E}_{3\omega}\propto {E}_{\omega}^{3}$ and the possibility of reaching higher conversion efficiency. Therefore, one can expect that, at high values of the pumping field, the efficiency of conversion to the third harmonic of the TI will be comparable or even exceed that of graphene.

_{2}Se

_{3}and BSTS would reach that of graphene, we extrapolated the pure cubic dependence ${E}_{3\omega}\propto {E}_{\omega}^{3}$ for Bi

_{2}Se

_{3}and BSTS to higher fields. The validity of such an extrapolation is also supported by recent experiments by the Kovalev group [52], in which the cubic dependence is confirmed over the wide range of pump intensities. To approximate the saturating dependence of the third harmonic field strength in graphene, we use the empirical expected expression ${E}_{3\omega}\propto \frac{{E}_{\omega}^{3}}{1+{E}_{\omega}^{2}/{E}_{S}^{2}}$, where ${E}_{S}$ is the saturation strength of the cubic susceptibility. Extrapolating the theoretical dependences to the region of high pump field strengths ${E}_{\omega}>>100$ kV/cm, we estimate the intersection of these curves at the field strength ${E}_{\omega}^{c}=430$ kV/cm and ${E}_{\omega}^{c}=390$ kV/cm for Bi

_{2}Se

_{3}and BSTS, respectively. Thus, we expect that TIs can be highly efficient frequency-converters of terahertz radiation in strong fields. By varying the chemical composition of TIs based on bismuth and antimony chalcogenides, one can tune the Fermi level and optimize the parameters of harmonic converters.

#### 4.2. Photoconductive THz Antenna

_{c}, the dynamics of excitation with energies above the bandgap were studied using the degenerate optical pump-optical probe spectroscopy (OPOP) scheme. The photon energy of optical pulses in OPOP was 1.5 eV, as in the experiment on THz generation in the photoconductive antenna. Results of the OPOP experiment are shown in the inset to Figure 5a, which shows the time dependence of the normalized induced change in the reflectance. Neglecting slower contributions, a single-exponential approximation yields the value for the capture time τ

_{c}= 0.93 ps. This is very close to the time scattering of photoexcited carriers into the surface states and lower bulk conduction band [53]. The following parameters were taken in further modeling of THz generation: τ

_{c}= 0.93 ps, τ

_{1}= 0.1 ps, τ

_{p}= 0.1 ps, R = 0.31, α = 120,000 cm

^{−1}, U

_{b}= 15 V, f

_{p}= 3.8 × 10

^{14}Hz, $\tilde{\epsilon}$ = 14, and m* = 0.21 m

_{e}[54]. In order to find the quality factor of a dipole antenna with the parameters length L = 240 μm, gap W = 20 μm, and electrode width d = 40 μm, and according to Ref. [55], we find Q = 1.1. The calculation results are shown in Figure 5a,b by dashed lines. A fairly good agreement between the experimental data and predictions of the simplest THz generation model can be seen there.

_{1}conduction band to another C

_{2}[56] band, which is located higher in the energy diagram. The signal from the TI antenna turned out to be comparable in amplitude with the signal from an antenna thicker by an order of magnitude based on the InGaAs/InAlAs semiconductor heterostructure. This indicates that TI antennas are promising as commercial THz emitters, with laser pumping in the visible range.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Volkov, B.A.; Pankratov, O.A. Two-dimensional massless electrons in an inverted contact. JETP
**1985**, 42, 178–181. [Google Scholar] - Hasan, M.Z.; Kane, C.L. Colloquium. Topological insulators. Rev. Mod. Phys.
**2010**, 82, 3045. [Google Scholar] [CrossRef][Green Version] - Ando, Y. Topological insulator materials. J. Phys. Soc. Jpn.
**2013**, 82, 102001. [Google Scholar] [CrossRef][Green Version] - Dziom, V.; Shuvaev, A.; Pimenov, A.; Astakhov, G.V.; Ames, C.; Bendias, K.; Böttcher, J.; Tkachov, G.; Hankiewicz, E.M.; Brüne, C.; et al. Observation of the universal magnetoelectric effect in a 3D topological insulator. Nat. Commun.
**2017**, 8, 15197. [Google Scholar] [CrossRef][Green Version] - Kozlov, D.A.; Kvon, Z.D.; Olshanetsky, E.B.; Mikhailov, N.N.; Dvoretsky, S.A.; Weiss, D. Transport Properties of a 3D Topological Insulator based on a Strained High-Mobility HgTe FilmD. Phys. Rev. Lett.
**2014**, 112, 196801. [Google Scholar] [CrossRef] - He, M.; Sun, H.; He, Q.L. Topological insulator: Spintronics and quantum computations. Front. Phys.
**2019**, 14, 43401. [Google Scholar] [CrossRef] - Fan, Y.; Wang, K.L. Spintronics Based on Topological Insulators. SPIN
**2016**, 6, 1640001. [Google Scholar] [CrossRef] - Zhang, X.; Wang, J.; Zhang, S.-C. Topological insulators for high-performance terahertz to infrared applications. Phys. Rev. B
**2010**, 82, 245107. [Google Scholar] [CrossRef][Green Version] - Egorova, S.G.; Ryabova, L.I.; Skipetrov, E.P.; Yashina, L.V.; Danilov, S.N.; Ganichev, S.D.; Khokhlov, D.R. Detection of highly conductive surface electron states in topological crystalline insulators Pb
_{1−x}Sn_{x}Se using laser terahertz radiation. Sci. Rep.**2015**, 5, 11540. [Google Scholar] [CrossRef] [PubMed][Green Version] - Durnev, M.V.; Tarasenko, S.A. High-Frequency Nonlinear Transport and Photogalvanic Effects in 2D Topological Insulators. Ann. Phys.
**2019**, 531, 1800418. [Google Scholar] [CrossRef][Green Version] - McIver, J.W.; Hsieh, D.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N. Control over topological insulator photocurrents with light polarization. Nat. Nanotechnol.
**2012**, 7, 96–100. [Google Scholar] [CrossRef] [PubMed] - Olbrich, P.; Golub, L.E.; Herrmann, T.; Danilov, S.N.; Plank, H.; Bel’kov, V.V.; Mussler, G.; Weyrich, C.; Schneider, C.M.; Kampmeier, J.; et al. Room-temperature high-frequency transport of Dirac fermions in epitaxially grown Sb
_{2}Te_{3}− and Bi_{2}Te_{3}− based topological insulators. Phys. Rev. Lett.**2014**, 113, 096601. [Google Scholar] [CrossRef][Green Version] - Dantscher, K.M.; Kozlov, D.A.; Olbrich, P.; Zoth, C.; Faltermeier, P.; Lindner, M.; Budkin, G.V.; Tarasenko, S.A.; Bel’kov, V.V.; Kvon, Z.D.; et al. Cyclotron-resonance-assisted photocurrents in surface states of a three-dimensional topological insulator based on a strained high-mobility HgTe film. Phys. Rev.
**2015**, 92, 165314. [Google Scholar] [CrossRef][Green Version] - Dantscher, K.M.; Kozlov, D.A.; Scherr, M.T.; Gebert, S.; Bärenfänger, J.; Durnev, M.V.; Tarasenko, S.A.; Bel’kov, V.V.; Mikhailov, N.N.; Dvoretsky, S.A.; et al. Photogalvanic probing of helical edge channels in two-dimensional HgTe topological insulators. Phys. Rev.
**2017**, 95, 201103. [Google Scholar] [CrossRef][Green Version] - Giorgianni, F.; Chiadroni, E.; Rovere, A.; Cestelli-Guidi, M.; Perucchi, A.; Bellaveglia, M.; Castellano, M.; di Giovenale, D.; di Pirro, G.; Ferrario, M.; et al. Strong nonlinear terahertz response induced by Dirac surface states in Bi
_{2}Se_{3}topological insulator. Nat. Commun.**2016**, 7, 11421. [Google Scholar] [CrossRef][Green Version] - Kovalev, S.; Tielrooij, K.J.; Deinert, J.C.; Ilyakov, I.; Awari, N.; Chen, M.; Ponomaryov, A.; Bawatna, M.; de Oliveira, T.V.A.G.; Eng, L.M.; et al. Terahertz signatures of ultrafast Dirac fermion relaxation at the surface of topological insulators. Npj Quantum Mater.
**2021**, 6, 84. [Google Scholar] [CrossRef] - Burford, N.M.; El-Shenawee, M.O. Review of terahertz photoconductive antenna technology. Opt. Eng.
**2017**, 56, 10901. [Google Scholar] [CrossRef] - Ponomarev, D.S.; Lavrukhin, D.V.; Zenchenko, N.V.; Frolov, T.V.; Glinskiy, I.A.; Khabibullin, R.A.; Katyba, G.M.; Kurlov, V.N.; Otsuji, T.; Zaytsev, K.I. Boosting THz photoconductive antenna-emitter using optical light confinement behind a high refractive sapphire fiber-lens. Opt. Lett.
**2022**, 47, 1899–1902. [Google Scholar] [CrossRef] - Hamh, S.Y.; Park, S.-H.; Jerng, S.-K.; Jeon, J.H.; Chun, S.-H.; Lee, J.S. Helicity-dependent photocurrent in a Bi
_{2}Se_{3}thin film probed by terahertz emission spectroscopy. Phys. Rev. B**2016**, 94, 161405. [Google Scholar] [CrossRef] - Fang, Z.; Wang, H.; Wu, X.; Shan, S.; Wang, C.; Zhao, H.; Xia, C.; Nie, T.; Miao, J.; Zhang, C.; et al. Nonlinear terahertz emission in the three-dimensional topological insulator Bi
_{2}Te_{3}by terahertz emission spectroscopy. Appl. Phys. Lett.**2019**, 115, 191102. [Google Scholar] [CrossRef] - Zhu, L.-G.; Kubera, B.; Mak, K.F.; Shan, J. Effect of Surface States on Terahertz Emission from the Bi
_{2}Se_{3}Surface. Sci. Rep.**2015**, 5, 10308. [Google Scholar] [CrossRef] - Tu, C.-M.; Chen, Y.-C.; Huang, P.; Chuang, P.-Y.; Lin, M.-Y.; Cheng, C.-M.; Lin, J.-Y.; Juang, J.-Y.; Wu, K.-H.; Huang, J.-C.A.; et al. Helicity-dependent terahertz emission spectroscopy of topological insulator Sb
_{2}Te_{3}thin films. Phys. Rev. B**2017**, 96, 195407. [Google Scholar] [CrossRef][Green Version] - Onishi, Y.; Ren, Z.; Novak, M.; Segawa, K.; Ando, Y.; Tanaka, K. Instantaneous Photon Drag Currents in Topological Insulators. arXiv
**2014**, arXiv:1403.2492. Available online: https://arxiv.org/abs/1403.2492 (accessed on 1 September 2022). - Luo, C.W.; Chen, H.J.; Tu, C.M.; Lee, C.C.; Ku, S.A.; Tzeng, W.Y.; Yeh, T.T.; Chiang, M.C.; Wang, H.J.; Chu, W.C.; et al. THz Generation and Detection on Dirac Fermions in Topological Insulators. Adv. Opt. Mater.
**2013**, 1, 804–808. [Google Scholar] [CrossRef][Green Version] - Kuznetsov, K.A.; Safronenkov, D.A.; Kuznetsov, P.I.; Kitaeva, G.K. Terahertz Photoconductive Antenna Based on a Topological Insulator Nanofilm. Appl. Sci.
**2021**, 11, 5580. [Google Scholar] [CrossRef] - Mikhailov, S.A. Non-linear electromagnetic response of graphene. EPL
**2007**, 79, 27002. [Google Scholar] [CrossRef][Green Version] - Mikhailov, S.A.; Ziegler, K. Nonlinear electromagnetic response of graphene: Frequency multiplication and the self-consistent-field effects. J. Phys. Condens. Matter
**2008**, 20, 384204. [Google Scholar] [CrossRef] - Karch, J.; Drexler, C.; Olbrich, P.; Fehrenbacher, M.; Hirmer, M.; Glazov, M.M.; Tarasenko, S.A.; Ivchenko, E.L.; Birkner, B.; Eroms, J.; et al. Terahertz Radiation Driven Chiral Edge Currents in Graphene. Phys. Rev. Lett.
**2011**, 107, 276601. [Google Scholar] [CrossRef][Green Version] - Glazov, M.M.; Ganichev, S.D. High frequency electric field induced nonlinear effects in graphene. Phys. Rep.
**2014**, 535, 101–138. [Google Scholar] [CrossRef][Green Version] - Durnev, M.V.; Tarasenko, S.A. Second harmonic generation at the edge of a two-dimensional electron gas. Condens. Matter arXiv
**2022**, arXiv:2204.04069. [Google Scholar] [CrossRef] - Costache, M.V.; Neumann, I.; Sierra, J.F.; Marinova, V.; Gospodinov, M.M.; Roche, S.; Valenzuela, S.O. Fingerprints of Inelastic Transport at the Surface of the Topological Insulator Bi
_{2}Se_{3}: Role of Electron-Phonon Coupling. Phys. Rev. Lett.**2014**, 112, 086601. [Google Scholar] [CrossRef][Green Version] - Weng, M.Q.; Wu, M.W. High-field charge transport on the surface of Bi
_{2}Se_{3}. Phys. Rev.**2014**, 90, 125306. [Google Scholar] [CrossRef] - Heid, R.; Sklyadneva, I.Y.; Chulkov, E.V. Electron-phonon coupling in topological surface states: The role of polar optical modes. Sci. Rep.
**2017**, 7, 1095. [Google Scholar] [CrossRef] [PubMed] - Principi, A.; Tielrooij, K.-J. Ultrafast electronic heat dissipation through surface-to-bulk Coulomb coupling in quantum materials. Condens. Matter arXiv
**2022**, arXiv:2206.09119. [Google Scholar] [CrossRef] - Jepsen, P.U.; Jacobsen, R.H.; Keiding, S.R. Generation and detection of terahertz pulses from biased semiconductor antennas. J. Opt. Soc. Am.
**1996**, 13, 2424–2436. [Google Scholar] [CrossRef] - Lavrukhin, D.V.; Yachmenev, A.E.; Pavlov, A.Y.; Khabibullin, R.A.; Goncharov, Y.G.; Spektor, I.E.; Komandin, G.A.; Yurchenko, S.O.; Chernomyrdin, N.V.; Zaytsev, K.I.; et al. Shaping the spectrum of terahertz photoconductive antenna by frequency-dependent impedance modulation. Semicond. Sci. Technol.
**2019**, 34, 34005. [Google Scholar] [CrossRef][Green Version] - Lepeshov, S.; Gorodetsky, A.; Krasnok, A.; Rafailov, E.; Belov, P. Enhancement of terahertz photoconductive antenna operation by optical nanoantennas. Laser Photonics Rev.
**2017**, 11, 1770001. [Google Scholar] [CrossRef][Green Version] - Tani, M.; Matsuura, S.; Sakai, K.; Nakashima, S.-I. Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs. App. Opt.
**1997**, 36, 7853–7859. [Google Scholar] [CrossRef][Green Version] - Kuznetsov, P.I.; Luzanov, V.A.; Yakusheva, G.G.; Temiryazev, A.G.; Shchamkhalova, B.S.; Zhitov, V.A.; Zakharov, L.Y. Deposition of heteroepitaxial layers of topological insulator Bi
_{2}Se_{3}in the trimethylbismuth–isopropylselenide–hydrogen system on the (0001) Al_{2}O_{3}and (100) GaAs substrates. J. Commun. Technol. Electron.**2016**, 61, 183–189. [Google Scholar] [CrossRef] - Kuznetsov, P.I.; Yapaskurt, V.O.; Shchamkhalova, B.S.; Shcherbakov, V.D.; Yakushcheva, G.G.; Luzanova, V.A.; Jitov, V.A. Growth of Bi
_{2}Te_{3}films and other phases of Bi-Te system by MOVPE. J. Cryst. Growth**2016**, 455, 122–128. [Google Scholar] [CrossRef] - Kuznetsova, P.I.; Shchamkhalova, B.S.; Yapaskurt, V.O.; Shcherbakov, V.D.; Luzanova, V.A.; Yakushcheva, G.G.; Jitov, V.A.; Sizov, V.E. MOVPE deposition of Sb
_{2}Te_{3}and other phases of Sb-Te system on sapphire substrate. J. Cryst. Growth**2017**, 471, 1–7. [Google Scholar] [CrossRef] - Park, C.B.; Kim, T.-H.; Sim, K.I.; Kang, B.; Kim, J.W.; Cho, B.; Jeong, K.-H.; Cho, M.-H.; Kim, J.H. Terahertz single conductance quantum and topological phase transitions in topological insulator Bi2Se3 ultrathin films. Nat. Commun.
**2015**, 6, 6552. [Google Scholar] [CrossRef] - Tinkham, M. Energy Gap Interpretation of Experiments on Infrared Transmission through Superconducting Films. Phys. Rev.
**1956**, 104, 845. [Google Scholar] [CrossRef] - Bilbro, L.S.; Valdés Aguilar, R.; Logvenov, G.; Pelleg, O.; Bozovic, I.; Armitage, N.P. Temporal correlations of superconductivity above the transition temperature in La
_{2−x}Sr_{x}CuO_{4}probed by terahertz spectroscopy. Nat. Phys.**2011**, 7, 298–302. [Google Scholar] [CrossRef][Green Version] - Kuznetsov, K.; Kuznetsov, P.; Frolov, A.; Kovalev, S.; Ilyakov, I.; Ezhov, A.; Kitaeva, G. Bulk and surface terahertz conductivity of Bi
_{2−x}Sb_{x}Te_{3−y}Se_{y}topological insulators. Opt. Eng.**2021**, 60, 82012. [Google Scholar] [CrossRef] - Ren, Z.; Taskin, A.A.; Sasali, S.; Segawa, K.; Ando, Y. Optimizing Bi
_{2−x}Sb_{x}Te_{3−y}Se_{y}solid solutions to approach the intrinsic topological insulator regime. Phys. Rev.**2011**, 84, 165311. [Google Scholar] [CrossRef][Green Version] - Deinert, J.-C.; Iranzo, D.A.; Pérez, R.; Jia, X.; Hafez, H.A.; Ilyakov, I.; Awari, N.; Chen, M.; Bawatna, M.; Ponomaryov, .N.; et al. Grating-Graphene Metamaterial as a Platform for Terahertz Nonlinear Photonics. ACS Nano
**2021**, 15, 1145–1154. [Google Scholar] [CrossRef] - Hafez, H.A.; Kovalev, S.; Deinert, J.-C.; Mics, Z.; Green, B.; Awari, N.; Chen, M.; Germanskiy, S.; Lehnert, U.; Teichert, J.; et al. Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions. Nature
**2018**, 561, 507–511. [Google Scholar] [CrossRef] - Theodosi, A.; Tsilipakos, O.; Soukoulis, C.M.; Economou, E.N.; Kafesaki, M. 2D-patterned graphene metasurfaces for efficient third harmonic generation at THz frequencies. Opt. Express
**2022**, 30, 460–472. [Google Scholar] [CrossRef] - Song, J.C.W.; Reizer, M.Y.; Levitov, L.S. Disorder-Assisted Electron-Phonon Scattering and Cooling Pathways in Graphene. Phys. Rev. Lett.
**2012**, 109, 106602. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pogna, E.A.A.; Jia, X.; Principi, A.; Block, A.; Banszerus, L.; Zhang, J.; Liu, X.; Sohier, T.; Forti, S.; Soundarapandian, K.; et al. Hot-Carrier Cooling in High-Quality Graphene Is Intrinsically Limited by Optical Phonons. ACS Nano
**2021**, 15, 11285–11295. [Google Scholar] [CrossRef] [PubMed] - Tielrooij, K.J.; Principi, A.; Saleta Reig, D.; Block, A.; Varghese, S.; Kiessling, T.; Ilyakov, I.; Ponomaryov, A.; Oliveira, T.; Chen, M.; et al. Light: Science & Applications, 2022; accepted for publication.
- Sobota, J.A.; Yang, S.; Analytis, J.G.; Chen, Y.L.; Fisher, I.R.; Kirchmann, P.S.; Shen, Z.-X. Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi
_{2}Se_{2}. Phys. Rev. Lett.**2012**, 108, 117403. [Google Scholar] [CrossRef] [PubMed] - Gao, Y.-B.; He, B.; Parker, D.; Androulakis, I.; Heremans, J.P. Experimental study of the valence band of Bi
_{2}Se_{3}. Phys. Rev. B.**2014**, 90, 125204. [Google Scholar] [CrossRef][Green Version] - Bieńkowski, Z.; Lipiński, E. Amatorskieanteny KF i UKF; Komunikacji i Łączności: Warsaw, Poland, 1978. [Google Scholar]
- Onishi, Y.; Ren, Z.; Segawa, K.; Kaszub, W.; Lorenc, M.; Ando, Y.; Tanaka, K. Ultrafast carrier relaxation through Auger recombination in the topological insulator Bi
_{1.5}Sb_{0.5}Te_{1.7}Se_{1.3}. Phys. Rev.**2015**, 91, 85306. [Google Scholar] [CrossRef]

**Figure 2.**Frequency dependence of the real and imaginary parts of conductivity of Bi

_{2}Se

_{3}and BSTS films.

**Figure 3.**Sketches of experimental setups for studying the generation of the third terahertz harmonic (

**a**) and the generation of terahertz radiation in the antenna (

**b**).

**Figure 4.**Third harmonic generation. Dependence of the peak amplitude of the outgoing third harmonic field on the pump field amplitude for graphene (black circles), BSTS (blue circles), and Bi

_{2}Se

_{3}(red circles). Colored dashed lines: corresponding fittings. The points of intersection of the extrapolation curves are marked with arrows.

**Figure 5.**Waveform (

**a**) and spectrum (

**b**) of THz pulse from PCA. Inset: results of the pump-probe experiment.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kuznetsov, K.A.; Tarasenko, S.A.; Kovaleva, P.M.; Kuznetsov, P.I.; Lavrukhin, D.V.; Goncharov, Y.G.; Ezhov, A.A.; Ponomarev, D.S.; Kitaeva, G.K.
Topological Insulator Films for Terahertz Photonics. *Nanomaterials* **2022**, *12*, 3779.
https://doi.org/10.3390/nano12213779

**AMA Style**

Kuznetsov KA, Tarasenko SA, Kovaleva PM, Kuznetsov PI, Lavrukhin DV, Goncharov YG, Ezhov AA, Ponomarev DS, Kitaeva GK.
Topological Insulator Films for Terahertz Photonics. *Nanomaterials*. 2022; 12(21):3779.
https://doi.org/10.3390/nano12213779

**Chicago/Turabian Style**

Kuznetsov, Kirill A., Sergey A. Tarasenko, Polina M. Kovaleva, Petr I. Kuznetsov, Denis V. Lavrukhin, Yury G. Goncharov, Alexander A. Ezhov, Dmitry S. Ponomarev, and Galiya Kh. Kitaeva.
2022. "Topological Insulator Films for Terahertz Photonics" *Nanomaterials* 12, no. 21: 3779.
https://doi.org/10.3390/nano12213779