The aim of the research was the studying of the topological insulators Bi2-xSbxTe3-ySey thin films with the different thickness and chemical composition. The obtained time dependences of terahertz radiation have indicated that the generation of THz waves was more efficient in the island film having a total thickness of about tens nanometers with the composition close to the Ren’s curve, where the volume contribution to the conductivity was suppressed. We have demonstrated an amplification of the THz radiation power by applying an external electric field to a topological insulator. This effect can be useful for fabricating photoconductive THz antennas based on topological insulators.

Topological insulators (TIs) attract the interest of specialists from various fields of modern physics: condensed matter, quantum information, laser physics, spintronics, which is due to very unusual physical properties of these materials associated with the topology of electronic states.1–3 Because of the energy bands inversion that takes place on the surface of a topological insulator (TI), a new type of linear-spectrum electronic state arises.4 Currently angle-resolved photoemission spectroscopy (ARPES) indicates the presence of Dirac electrons in many TIs.1,2,5 Techniques for fabrication and characterization of various topological insulators (like thin films, nanocrystals, heterostructures, and so on) are intensively developed.6–9 At present, much interest to topological materials is also stimulated by studies of their terahertz range (THz) response to optical laser radiation.10–14 Among the studies of terahertz response for thin films of topological insulators, the Kerr effect should be mentioned. The colossal Kerr rotation was explained by the cyclotron resonance of the surface states of the topological insulator Bi2Se3.15 It was also shown that skyrmions formed at the interface between thin-film multiferroics and a topological insulator can give rise to high figure-of-merit magneto-optical Kerr effects.16 In addition to fundamental aspects of this response, TIs are very promising objects for practical applications, as the materials for engineering THz radiation sources and detectors.10,17–20

The main point in the THz generation mechanism in optically pumped TIs is the excitation of a nonlinear photocurrent due to the photovoltaic and photon drag effects. These two effects are described by the quadratic and cubic susceptibility of a TI, respectively. Because of the structural symmetry features of TI films, the intensity of the THz radiation depends strongly on the orientation and, specifically, on the azimuthal angle of rotation of the sample. Previously, the generation of terahertz radiation was investigated in topological insulators of binary compositions such as Bi2Te3, Bi2Se3, Sb2Te3.21–23 In addition to TIs with binary chemical composition, materials of ternary compositions (Bi1-xSbx)2Te3 are intensively studied.24,25 The THz generation in samples with variable chemical composition and the type of electronic conductivity (n- or p-types) was studied in detail.26 It was found that the photon drag effect is the predominant mechanism for the generation of THz radiation in these materials.

Usually a TI is a sequence of quintuple layers (QL), the thickness of each quintuple layer being about 1 nm. With the increasing of the total number of QLs, starting from a certain number the material becomes a topological insulator, and the band gap in the electron energy spectrum disappears. Transmission of Bi2Se3 samples with different thicknesses was studied in the terahertz range 0.1-2.5 THz.27 At a thickness equal to 8 QL, Bi2Se3 samples showed the topological properties and herewith a topological phase transition occurred.

In addition to TIs of binary and ternary compositions, TIs of quaternary Bi2−xSbxTe3-ySey compounds (BSTS) are actively investigated.28–31 It was shown, that there is some optimal curve in the composite diagram y(x) (the Ren curve) near which the topological properties of BSTS are most clearly manifested.32 This occurs due to the substantial suppression of the volume contribution to the conductivity. Along this curve, the effects of acceptors and donors mutually cancel each other, leading to an increase in the resistance of the main part of the sample and the predominance of the surface electronic transport. Previously the generation of radiation in BSTS was studied in details, the dominant role of the photon drag mechanism was shown, and the third-order rotational symmetry of the THz signal was found.28 The THz power depended on the azimuthal angle of rotation of the sample, which correlated with the presence of three planes of mirror symmetry of the crystal structure of this material. While studying the THz generation, it is important to take into account the mechanisms of fast relaxation of carriers excited by the laser radiation. An ultrafast carrier relaxation was observed in quaternary BSTS compounds.31 It was shown that in addition to other mechanisms (thermalization, phonon radiation, interzone scattering), the main contribution to relaxation at times of the order of several picoseconds is provided by Auger recombination processes involving the second electron knocked out of the upper part of the conduction band.

In this article, we report a study of the THz emission properties of Bi2-xSbxTe3-eSey films with different thicknesses. In recent studies of the growth of the Bi2Se3 and Bi2Te3-xSex films on sapphire substrates, it was found that the 3D Stransky-Cranstanov growth mechanism dominates at the initial growth stage. The two-dimensional mechanism dominates only after reaching a thickness of 80-100 nm.33,34 The thinnest of our samples was an island film with a total thickness of about 40 nm, grown by the MOCVD method on a sapphire substrate. The THz generation capabilities of all the samples were studied not only for as-grown films, but also for THz antennas arranged at the sample surfaces under application of an external bias field.

Rhombohedral Bi2−xSbxTe3-ySey films, labeled as TI-1, TI-2 and TI-3, were grown on (0001) Al2O3 substrates with a thin (10 nm) ZnTe buffer layer of orientation (111) at atmospheric pressure of hydrogen in a horizontal quartz reactor. Trimethylbismuth, trimethyantimony, diethylzinc, diethyltellurium and diethylselenium were used, respectively, as bismuth, antimony, zinc, tellurium and selenium organometallic sources. The buffer ZnTe layer was grown in a single process cycle with a BSTS film at a temperature of 463 °C. The VI/V ratio in the vapor phase was close to 6 and the total partial pressure of V-group precursors was 6 x10-5 bar. To determine the elemental composition of the film under investigation, we used an energy dispersive X-ray spectrometer X-MaxN with the active area 50 mm2, which was docked with the electron microscope. To standardize and optimize the profiles of emission lines of characteristic radiation the following standards were used: crystals Bi2Se3 (Bi-Mα and Se-Lα) Sb (Sb-Lα), ZnS (Zn-Lα), PbTe (Te-Lα) and Al2O3 (Al-Kα and O-Kα). Measurement of the standards and the analysis of the samples were performed under identical conditions at an accelerating voltage of 10 kV and an electron probe current of 1.4 nA. The sample TI-1 was a film of bismuth telluride Bi2Te3 (x,y=0). For the sample TI-2 the values x = 0.18 and y = 0.57 were determined, and for the sample TI-3 these values were x = 0.08 and y = 0.96 (see Table I). The thicknesses of samples TI-1 and TI-2 were quite sizable and equal to 400 nm and 800 nm, correspondingly. All the films had the (0001) orientation. The surfaces of as-grown films and the thicknesses of the islands were studied using the atomic force microscope (AFM) Smart SPM, AIST-NT7. Examples of AFM scans are shown in Fig. 1. One can see in Figs. 1a, 1b, 1d, 1e that the surfaces of the samples TI-1 and TI-2 are rather smooth. The very small inhomogeneities have typical depths of 1-5 nm. But the sample TI-3 consists of a “network” of channels with separated islands on the buffer layer. In Fig. 1c one can see dark areas which correspond to the dips up to the ZnTe buffer layer. Depths of these dips are of 40 nm (Fig. 1f). Separate islands (light hexagons) reach a height of 90 nm. The mean transverse sizes of the islands are within 150–300 nm.

TABLE I.

Characteristics of Bi2-xSbxTe3-eSey samples.

Bi2-xSbxTe3-ySey
SamplecompositionThicknessRoughness,
r12.5pt)2-3 codexyd, nmnm
TI-1 400 0.81 
TI-2 0.18 0.57 800 0.49 
TI-3 0.08 0.96 40 13.9 
Bi2-xSbxTe3-ySey
SamplecompositionThicknessRoughness,
r12.5pt)2-3 codexyd, nmnm
TI-1 400 0.81 
TI-2 0.18 0.57 800 0.49 
TI-3 0.08 0.96 40 13.9 
FIG. 1.

AFM topographic images and height profiles of Bi2-xSbxTe3-ySey topological insulator samples: (a), (d) TI-1; (b),(e) TI-2; (c), (f) TI-3. Inset on (c) shows orientations of electric field vector for pump and THz-signal.

FIG. 1.

AFM topographic images and height profiles of Bi2-xSbxTe3-ySey topological insulator samples: (a), (d) TI-1; (b),(e) TI-2; (c), (f) TI-3. Inset on (c) shows orientations of electric field vector for pump and THz-signal.

Close modal

We use experimental setup for time-domain spectroscopy of the THz emission in the backward geometry (Fig. 2).37 The pump was an Er+ fiber laser in the Q-switched mode locking near a threshold regime at 1.56 μm wavelength. This laser operated in a picosecond mode, generating optical pulses of 2.5 ps duration with a repetition rate of 70 MHz. The pump beam was divided into two unequal parts with a mean power of 100 and 20 mW, respectively. The low-power beam was focused on a photoconductive dipole antenna. The high-power beam, after propagation through the delay line and an optical chopper, was focused through a hole in the parabolic mirror onto the TI sample. The angle of incidence was 15°. The sample was in contact with copper electrodes (the distance between them was 0.5 mm) so that external voltage could be applied. The THz radiation generated in the sample in the backward direction was collected by four parabolic mirrors and focused on the commercial THz antenna. The antenna was oriented to register vertical components of the THz field collinear with the polarization of the pump. Thus, the electric field of THz waves generated in the direction opposite to pumping was measured at different time intervals after the arrival of the pump pulse.

FIG. 2.

Experimental setup for THz-wave generation in the backward geometry.

FIG. 2.

Experimental setup for THz-wave generation in the backward geometry.

Close modal

In our experiments, the distance l=500 μm between the electrodes of THz antennas fabricated on the surfaces of TI samples was comparable with the THz wavelengths. This is the case of Hertz dipole time-varying radiation; the expression for the generated THz electric field takes the following form:35 

E(r,t,θ)=14πn2c2rp̈(t)+ncr2ṗ(t)+1r3p(t)sinθ.
(1)

Here, p is the time-varying dipole moment, n is the refractive index of the medium between the electrodes, θ is the generation angle with respect to the axis of the dipole. The two last terms in the parentheses describe the near-field and quasi-static effects. Usually they are not essential in our approximations. Finally, taking into account the connection between p and the current density, one can obtain an expression for a i-th component of an electric field:

Ei(r,t)=14πnlc2drji(t)tsin(θ).
(2)

Here, d defines the thickness of an active layer, and ji(t) is the corresponding current density component. Apart from the current induced by an external electric field Ebias, there can be other contributions to ji(t). With appropriate accuracy, relations between the corresponding current density and its contribution to the generated field can be depicted by Eq. (2) with some special values of d and l and the angle of effective dipole orientation θ. Onishi et al. have proved that the photon drag effect (PDE) is the predominating THz-generation mechanism for Bi2-xSbxTe3-eSey compounds studied without any applied voltage.28 However, in the general case one has to take into account also the terms both from an external (Ebias) and some internal build-in (Ein) electric fields,

ji(t)=χijsl(3)(t)kjEs(t)El(t)+σif(t)Efbias+σik(t)Ekin.
(3)

Here, χijsl(3) is the PDE tensor, kj and Es are the corresponding components of the pump wave-vector and electric field, σif is the linear conductivity tensor. Thus, one can expect the interference between different contributions to the oscillating current in the generated THz field.

Temporal waveforms of THz pulses were detected by scanning the delay time between laser pulses excited by a topological isolator (as THz generator) and a THz detector. Since there was a strong angular dependence of the THz signal on the pump polarization, we rotated the sample around an axis normal to the sample surface to achieve the maximum THz signal (changing the angle φ), while an observation angle θ was fixed. The threefold rotational symmetry for THz radiation was obtained: Ei(r, t, φ) ∝ sin(3φ).28 Therefore, we turned the crystal around the normal to the surface at such an azimuthal angle that the pump polarization vector was in the mirror symmetry plane (Fig. 1c). The experimental waveforms of THz pulses emitted by the investigated TI samples at zero applied voltage are shown in Fig. 3. In the case of samples TI-1 and TI-2, we observe a single THz pulse, obviously, generated in the backward direction with respect to the pump propagation. But for TI-3, THz radiation the signal consists of three repeating parts of approximately the same shape and amplitude. While the first pulse again corresponds to the backward generation, the second part follows the first one after 9 ps. It can be explained as another THz pulse, initially generated in the forward direction in the TI sample and then reflected from the backward surface of the Al2O3 substrate, because the Al2O3 absorption coefficient in the considered terahertz frequency range is rather small. And the third part, delayed from the first pulse by 18 ps, arises from the second series of reflections in the sapphire substrate of this forward-generated THz pulse. As it was shown by a direct TDS measurement, there was no THz generation from the pure substrate. We assume that the last two pulses are not seen in the waveforms of the TI-1,2 samples because of the low THz transmission of these “thick” TI films. The spectral width is limited to 0.4 THz, and this is well correlated with the laser pulse duration. The generation maximum is achieved at about 100 GHz.

FIG. 3.

Time-domain waveforms of THz pulses generated from the TI-samples compared to InGaAs/InP.

FIG. 3.

Time-domain waveforms of THz pulses generated from the TI-samples compared to InGaAs/InP.

Close modal

A promising result is that the amplitude of the THz signal from the “thin” sample TI-3 is almost 5 times greater than that in the “thick” samples. This can not be explained only by an increased THz transmission of the TI-3 sample, since we observe the same behavior for the first THz pulse generated in a backward geometry, i.e., directly by the surface layer of the topological insulator. A possible origin of for this THz field amplification can be connected with excitation of surface plasmons in a thin film of TI-3. Apparently a similar amplification for PDE was observed in a single-layered graphene, which was placed on a percolated 10 nm layer of aurum.36 The electric field of the plasmons was localized and amplified on the Au surface. The surface of TI-3 sample is very heterogeneous and looks like the Bruggeman structure; therefore plasmons can be excited due to quasi-synchronous processes. The chemical composition of the TI-3 sample is very close to the Ren’s curve, where the surface contribution to conductivity is more pronounced than the same volume contribution.31 This feature can also affect the efficiency of THz generation. Another promising result is that the signal amplitude from a thin topological insulator is comparable to a signal from the widely known InGaAs semiconductor material, which is used for the production of THz photoconducting antennas operating under pumping at frequencies from the infrared communication range. Fig. 3 shows the THz waveform for TI-3 sample obtained in the same set-up for an InGaAs sample grown under low-temperature conditions (T=200° C) by the molecular-beam epitaxy on an (411) oriented InP substrate.37 The fact that comparable THz signals are generated in free samples of InGaAs and TI-3 indicates high THz generation capabilities of the considered thin TI films.

We applied a voltage between copper electrodes that come into contact with the surface of TI-3 sample to study how the THz generation is amplified by an external electric field. The sample had a resistivity of 2.2·105 Ohm/cm, the applied voltage was +30 V and -30V. Fig. 4a shows the THz emission waveforms from TI-3 obtained for two opposite voltage polarities. It is clearly seen that when the polarity of the bias voltage is changed, most part of the THz signal also changes its phase by 180 degrees. This part of the signal is well described as a result of multiplication of the zero-voltage signal for TI-3 at Fig. 4 by some amplification coefficient (∼2 in case of +30 V and a little less in case of -30 V). This behavior indicates the generation mode character of radiating antenna. Nevertheless, the observed waveforms contain some additional signal, which does not change its polarity with the voltage. To reveal this part we have summarized the signals, observed with +30 V and -30V voltages. Half of this sum is shown in Fig. 4b (see the dotted line). The opposite-sign parts of the signals from Fig. 4a almost canceled each other, so that one could expect to observe the residual constant part of the same shape as the zero-voltage signal. However, this is not true. For comparison, we repeat the zero-voltage signal for TI-3 from Fig. 3 in Fig. 4b together with this residual signal. It is clearly seen that the antenna pulses contain additional parts corresponding to higher modulation frequencies. This fact is also illustrated in Fig. 4c where the spectra of the both waveforms are shown. The spectrum of the residual part of the antenna signal is about two-times broader than the spectra of all the other signals observed for TI-1, i.e. the zero-voltage signal, and the polarity-sensitive parts of +30 V and -30V voltages signals. The peak frequency corresponds to times that are of order or even less than the pump pulse duration. It means that some carrier relaxation effects proceed at considerably shorter relaxation times, than it is usually assumed to describe the THz emission of free TI samples. We believe that this effect arises from the relaxation of fast non-equilibrium charge carriers accelerated by an external field. Probably electrons are captured by the traps that are p-type impurities with energy above the bulk valence band maximum in the energy of 3-6 meV or other defects.38 It should also be noted that there is another hypothetical possibility that the applied voltage breaks the inverse symmetry of the bulk, which leads to an additional non-linear effect.

FIG. 4.

Amplification of THz radiation in an external electric field applied to Bi2-xSbxTe3-ySey island film: (a) Signals observed at a voltage Ub=+30 V (filled circles) and Ub=-30 V (hollow circles). (b) Zero-voltage signal (solid line) and half-sum of signals detected with Ub=+30 V and Ub=-30 V (dotted line). (c) Spectrum of zero-voltage signal (hollow squares) and spectrum of half-sum of signals at Ub=+30 V and Ub=-30 V (filled squares).

FIG. 4.

Amplification of THz radiation in an external electric field applied to Bi2-xSbxTe3-ySey island film: (a) Signals observed at a voltage Ub=+30 V (filled circles) and Ub=-30 V (hollow circles). (b) Zero-voltage signal (solid line) and half-sum of signals detected with Ub=+30 V and Ub=-30 V (dotted line). (c) Spectrum of zero-voltage signal (hollow squares) and spectrum of half-sum of signals at Ub=+30 V and Ub=-30 V (filled squares).

Close modal

In its standard notation, the PDE emission mechanism should be insensitive not only to the polarity of the applied voltage, but also to the existence of any external static field. Since the high-frequency part of the signal is observed only in the case of non-zero external static field, we unable to attribute this effect to PDE as it has been previously proved for free Bi2-xSbxTe3-eSey samples.28 The observed signal can have the nonlinear character with the respect to applied voltage and be dependent on the second degree of the external static field. However, this dependence as well as the effect of the ultra-low relaxation times, corresponding to the observed parts of the antenna signals, needs an additional special study.

In conclusion, we have studied the emission of THz radiation by samples of Bi2-xSbxTe3-eSey topological insulators with various thicknesses and chemical composition, pumped by 2.5 ps laser pulses of 1.56 μm wavelength. Rhombohedral Bi2−xSbx Te3-ySey films were grown on (0001) Al2O3 substrates with thin (10 nm) ZnTe buffer layer with orientation (111) at atmospheric pressure of hydrogen. It was found that the intensity of the THz signal from the island film of TI is 25 times higher than the same of TI samples with a thickness of hundreds of nanometers. The effect of THz radiation amplification in an external electric field in a topological insulator has been demonstrated for the first time.

The authors are grateful to Dr. A.G. Temiryazev for assistance in measuring by AFM and Dr. T.V. Murzina, Dr. M.A. Chernobrovkina, and Dr. M.V. Chekhova for discussions and help. The study of THz emission was performed under the support of the RFBR grants 18-29-20101, 19-02-00598. The growth and characterization of the Bi2-xSbxTe3-eSey samples was supported by grant 17-19-01057 of the Russian Science Foundation.

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