Study of dielectric polarization and electrical transport in Bi_1·2Sb_0·8Te_0·4Se_2.6 nanofilms

Abstract

Studying the dielectric response of topological insulators (TIs) can unveil their unique physical mechanisms such as charge transport and spin-orbit coupling effects. However, due to the manifestation of material's topological nature and band structure primarily in nanofilm, such thickness poses challenges for dielectric testing. To date, research on TI dielectric aspects remains relatively unexplored. Therefore, this paper successfully synthesizes nanofilm of quaternary topological insulator Bi_1·2Sb_0·8Te_0·4Se_2.6 (BSTS) using laser molecular beam epitaxy (LMBE) technique. Utilizing a wide-frequency dielectric spectrometer and a comprehensive physical properties measurement system (PPMS), we measured and thoroughly analyzed the dielectric polarization and charge transport characteristics of BSTS. We observed various polarization responses in the frequency range of 10¹–10³ Hz, with the dipole orientation gradually failing to keep pace with the frequency increase in the range of 10³–10⁵ Hz, and the relaxation polarization unable to establish itself in the range of 10⁵–10⁷ Hz, with polarization primarily contributed by displacement polarization. Subsequently, we further analyzed the dependence of BSTS dielectric polarization response on temperature and film thickness, which will help reveal the influence of external factors on TI dielectric response, providing crucial insights for controlling TI materials' dielectric response. This not only deepens our understanding of the fundamental physical properties of this novel material but also offers important scientific basis and technological support for its applications in quantum computing, photonics, spintronics, and other fields.

Highlights

• •Advanced LMBE System: Demonstrates the effectiveness of the Laser Molecular Beam Epitaxy system in creating high-quality BSTS nanofilms.
• •Novelty of BSTS Material: Introduces Bi_1·2Sb_0·8Te_0·4Se_2.6 as a new and promising material in the field of topological insulators.
• •Dielectric Polarization in Topological Materials: Presents the study of dielectric polarization in BSTS, providing valuable data for the operational environment of quantum chips.
• •QuintupleLayers as Polarization Dipoles: Investigates the role of quintuple layers in BSTS as dipoles in its dielectric polarization, offering new insights into its electrical properties.

1. Introduction

As a special type of quantum material [1], topological insulators exhibit insulating properties with a band gap internally, and gapless metallic states on the surface [2]. This intriguing electronic structure results from the combined effects of strong spin-orbit coupling and time-reversal symmetry [3]. The electron spin momentum is locked on the surface states, forming a Dirac cone-like band structure that is symmetrical at the intersection of the electron and hole bands in the electronic structure [4,5]. The topological protection on the surface states could remain stable in the environment of non-magnetic defects and impurities, which is helpful for them to be resistant to being backscattered.

The second-generation strong topological insulators [6], such as Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃, are prone to “topological breakdown” due to their intrinsic selenium vacancy defects and tellurium antisite defects, which causes the coupling between the bulk and surface [7]. The elementally doped quaternary topological insulator BSTS is proposed as a solution to this challenge by improving both the bulk insulating properties and the manifestation of topological surface states. BSTS is considered an ideal material for future spintronic devices or quantum computing chips because of its unique surface states and electron transport mechanisms [8]. Notably, the dielectric constant of BSTS plays a key role in regulating the coupling, interference, and isolation between spin quantum bits, while its dielectric loss significantly affects the efficiency and distance of quantum information transmission [9]. Given this, exhaustive testing and analysis of the dielectric polarization behavior of topological insulators are crucial for their practical application. However, current research on the dielectric polarization behavior of topological insulators remains relatively limited, so this paper aims to fill this research gap.

Dielectric properties, as a critical indicator of a material's response to an electric field, profoundly reflect the dynamics and interaction modes of electrons within the material [10,11]. Specifically, for topological insulators, the study of their polarization behavior and dielectric response is of decisive significance for revealing their intrinsic properties and exploring their potential applications. The surface states of these materials exhibit unique polarization characteristics that is closely linked to their topological properties, in terms of the electronic structure, which differs from conventional insulators or conductors. In-depth investigation of the dielectric response facilitates the understanding of the electron polarization behavior of topological insulators at various frequencies as well as the electron transitions between energy levels and electron transport properties.

The study of topological insulators remains an unknown challenge in terms of dielectric properties and electronic transport. Further research is still required to figure out the influence of dielectric characteristics, temperature dependence, and film thickness at various frequencies. This paper aims to explore the dielectric properties and electronic transport properties of the quaternary topological insulator BSTS, providing theoretical support for its potential applications in electronics, optoelectronics, and quantum chips in magnetic fields.

2. Characterization

BSTS thin films were prepared using an LMBE system, as shown in Fig. 1, where a pulsed laser from an excimer laser irradiated the surface of the target material, combined with a mixed target splicing technique to sputter a high-energy plasma cluster onto the opposing substrate, achieving film growth [12]. The specific experimental steps will be detailed in the subsequent experiment.

Fig. 1.

Principles of thin film preparation in the LMBE system and the XRD characterization and molecular structure model of BSTS. (a) Main components of the LMBE system: an excimer laser and a vacuum epitaxy chamber. The laser is powered by four inert gases: He, Ne, F, and Kr. The pulsed lasers changed the direction of the optical circuit through the first reflector mirror and converged the laser energy through the second transmission mirror. Ion and molecular pumps provide a high vacuum of 10⁻⁷ Pa for the epitaxy chamber. (b) Internal structure of the LMBE system and the principle of thin film preparation: Driven by a pulsed laser, target materials could produce four atoms, including Bi, Se, Sb, and Te. These atoms reach the opposite substrate in the form of a plasma cluster and are deposited as the BSTS film. (c) XRD diffraction spectrum of BSTS. (d) Layered structure and top view of the BSTS structure. BSTS layers are arranged in a Se/Te–Bi/Sb–Se–Bi/Sb–Se/Te pattern and interconnected by van der Waals forces, with each layer of atoms connected by covalent bonds.

To ensure the reliability of the sample quality, various measuring and testing techniques of characterization have been applied in the study. The diffraction peak positions and intensities of the BSTS crystal structure have been identified using X-Ray Diffraction (XRD) research, as shown in Fig. 1c. Compared with the peaks of other topological insulators, it was found that the diffraction peaks of BSTS are highly in line with other c-axis-oriented topological insulator films. The BSTS samples exhibited a typical orthorhombic layered crystal structure, belonging to the space group $R3\bar{m}$ with sixfold symmetry. All BSTS diffraction peaks were part of the (0 0 3n) family. Notably, the (0 0 9) peak was restrained due to the strong substrate peak, indicating a film growth orientation towards the c-axis. The prominent peak shape and narrow half-peak width further demonstrated the excellent crystalline quality of the samples.

Fig. 1d illustrates the hexagonal structure of BSTS, showcasing a layered growth pattern. The film is stacked along the Z-axis, with every five monolayers forming a quintuple layer (QL) [13]. These QLs are arranged in an A (1) - B - A (2) - B – A (1) sequence, where A (1) and A (2) represent two different crystal lattice positions [14]. A (1) can be occupied by either Se or Te elements, while the central layer position in A (2) is occupied mainly by Se for its higher electronegativity compared to Te. Position B is occupied by either Bi or Sb elements. Each monolayer is strongly coupled internally via covalent bonds, while adjacent quintuple layers are weakly coupled through van der Waals forces. The crystal lattice constants were determined to be a = 29.43 Å, b = c = 4.23 Å, according to the computation.

In the Scanning Electron Microscope (SEM) measurement, the surface morphology of BSTS thin films is shown in Fig. 2a and b. It could be observed that the samples exhibited their characteristics of being dense and uniform, and the surface grains primarily showcase the truncated triangles and hexagonal structures, which is consistent with the crystal lattice structure of topological insulators. To ensure the reliability of BSTS sample quality and the accuracy of lattice constants, we conducted Transmission Electron Microscopy (TEM) testing on it. The lattice fringes are shown in Fig. S1a, and the RHEED images are shown in Fig. S1b. The TEM testing process will be presented in the Method section. A smooth and even surface could be observed through Atomic Force Microscopy (AFM), which showed that the film thickness reached 25 nm and the film roughness was relatively low (Fig. 2c and d). The prepared BSTS exhibited a highly stable stoichiometric proportion, according to Energy Dispersive Spectroscopy (EDS) testing (Table 1), with a ratio of 2:3 between the total number of Bi and Sb atoms and the Te and Se atoms. This constant chemical proportion provides a more stable topological surface state for BSTS. Based on these results, the chemical formula for BSTS thin films is confirmed as Bi_1·2Sb_0·8Te_0·4Se_2.6. The doping of BSTS refers to the atomic-level substitution doping based on binary strong topological materials such as Bi₂Se₃ (or Bi₂Te₃). This doping preserves the crystal structure of traditional binary topological materials, only replacing atoms at the same positions, resulting in a target structure similar to Bi_xSb_2-xTe_ySe_3-y. It does not alter the crystal structure of the material itself. This is why BSTS exhibits morphology and topological properties similar to binary topological materials. Moreover, this atomic-level doping enables complementary intrinsic defect types of the two opposite phases in binary topological materials.

Fig. 2.

Morphological Characterization of BSTS Films in SEM and AFM Tests. (a) Surface morphology at a magnification of 100KX. (b) Surface morphology at a magnification of 40KX. (c) Cross-sectional height map of the sample, with the film surface shown on the left and the substrate on the right. (d) A planar graph of the sample's surface roughness.

Table 1.

Atomic weight and percentage composition of the four elements in BSTS.

Element	Weight percentage	Atomic percentage
Bi	37.76	21.05
Te	9.86	9.00
Sb	14.13	13.52
Se	38.25	56.43
Total	100.00	100.00

In the study, the Angle-Resolved Photoemission Spectroscopy (ARPES) is applied to observe and analyze the electronic band structure of BSTS [15,16]. This technique is conducive to detecting the electronic states, energy, and momentum distribution on the film surface directly, which provides crucial information for the understanding of the topological properties of BSTS films. As shown in Fig. S2, special attention was paid to the electronic states near the Fermi level (E_F), and a distinct Dirac cone structure has been observed in the study, indicating well-defined topological surface states in BSTS. Further analysis revealed that, the bulk conduction band (BCB) was located about 140 meV above the Dirac point (DP), showing the presence of a gap, which is a characteristic of topological insulators [17]. The ARPES spectra revealed the existence of BSTS Dirac cone-type surface states, and demonstrated its extraordinary topological characteristics. Besides, the interaction of surface and bulk electronic states near the Fermi level shaped the unique electronic properties of BSTS. These findings are crucial for the understanding of the unique properties of BSTS as a topological insulator, as well as provide key theoretical support for subsequent dielectric response and electrical transport property testing.

3. Discussion

Compared to traditional binary topological insulators, BSTS showcases significant advantages. The inherent defects and bulk-surface coupling issues in binary topological insulators lead to impaired bulk insulation performance, increased conductivity dissipation in the bulk band, and a less prominent effect of dissipation-free surface states. BSTS, with its precise control of the chemical composition of four elements and the complementarity between antisite and vacancy defects, significantly enhances its bulk insulating properties, making its topological surface states more prominent. However, the exfoliation of BSTS materials could be a huge challenge since the growth of these materials requires them to be on substrates, which is difficult for the measurement of their dielectric response, leading to disturbance of the substrates in the measurement of dielectric information. To address this problem, we chose N-type doped silicon with a resistivity lower than 0.005 Ω cm as the substrate material. Compared to BSTS, the doped Si substrate can be regarded as an electrode in broadband dielectric spectroscopy, effectively reducing the influence of the substrate on the results. The material's dielectric loss exhibits distinct frequency-dependent characteristics because various polarization mechanisms, such as electronic polarization, ionic polarization, and dipole reorientation exerted on the frequency, are highly sensitive to the change of frequency. This dependency results in the non-immediate response of materials in the polarization process to the change in the applied electric field, which could be regarded as a relaxation process. Thus, the dielectric constant in complex form is applied to illustrate the material's reaction to an alternating electric field during the analysis: ${\epsilon }^{*}={\epsilon }^{\prime }-i{\epsilon }^{″}$, where ${\epsilon }^{\prime }$ is the real part of the dielectric constant indicating the material's polarization capability, and ${\epsilon }^{″}$ is the imaginary part related to energy loss in the dielectric material. In practical applications, the dielectric loss of materials is commonly represented by the loss tangent value $\tan \delta$, given by $\tan \delta =\frac{{\epsilon }^{″}}{{\epsilon }^{\prime }}$. Additionally, the study shows that parasitic capacitance in the spectrometer could affect the results, so dielectric tests were conducted by using a non-capacitive pure resistor to obtain the exact parasitic capacitance: $C_0$. Given the potential contact issues between the sample and copper electrodes, conductive tape was used in the experiment to ensure tight contact between them (Fig. 3a). In the measurement of BSTS's dielectric information, the thickness $d$ and area $S$ of the samples were also taken into account. Based on the sample's capacitance $C_1$, thickness $d_1$, and area $S$, the formula for BSTS's dielectric constant was derived: ${{\epsilon }_1}^{\prime }=\frac{C_1{d}_1}{{\epsilon }_{0}S}$ [18]. As shown in Fig. 3b, the capacitance $C$ yielded in the dielectric test of the BSTS film is the result of parallel coupling of $C_1$ and $C_0$, thus $C_1$ could be obtained from the following formula: $C_1=C-C_0$. The dielectric loss formula for BSTS is: ${{\epsilon }_1}^{″}=\frac{d_1}{\omega {\epsilon }_0{R}_{1}S}$, where $R_1$ is the resistance of BSTS.

Fig. 3.

Schematic diagram of dielectric testing for BSTS films. (a) Installation diagram for the dielectric test of BSTS films. (b) Polarization model diagram for the dielectric test of BSTS films.

Fig. 4a and b exhibit the frequency spectra of the dielectric constant and dielectric loss of BSTS at room temperature. From Fig. 4a, it is evident that in the low-frequency region (10¹–10³Hz), various polarization responses of BSTS, including electronic polarization, dipole reorientation polarization, and relaxation polarization, are capable of varying with frequency, leading to complex dielectric response behavior. In the mid-frequency range (10³–10⁵Hz), dipole reorientation polarization inside the BSTS begins to lag behind the changes in the external electric field frequency. This lag effect causes the dielectric constant to decrease as the frequency increases. This phenomenon reflects that the lag effect of relaxation polarization is intensified with the change of frequency. The reason is that two QLs in BSTS can form a pair of dipoles (Fig. S3), which will adjust the direction of the electric dipole moment in response to the polarization change induced by the external electric field. Besides, the distribution of positive and negative charges in the dipoles is conducive to reducing the impact of the internal electric field. Entering the high-frequency region (10⁵–10⁷Hz), the relaxation polarization cannot be established in time. The polarization of BSTS is mainly contributed by displacement polarization, and the dielectric constant is kept at a stable value. In Fig. 4b, it is observed that in the low-frequency range (10¹–10³Hz), $\tan \delta$ shows a downward trend with the increasing of the frequency for the conductive loss dominates in this frequency range and the relaxation polarization loss reaches almost zero. As the frequency increases, conductive loss gradually decreases. In the mid-frequency range (10³–10⁵Hz), $\tan \delta$ increases with the raising of the frequency for the relaxation polarization loss increases with the raising of the frequency, leading to an increase in the dielectric loss of the material, and the BSTS's dielectric loss peaks in the relaxation zone. In this frequency range, a decrease in the dielectric constant and an increase in dielectric loss were observed. This may be attributed to the involvement of the unique topological surface states of the topological insulator, which could lead to such a scenario. Alternatively, it could be due to resonance of the electronic structure of the topological insulator within the frequency range of 10³–10⁵ Hz, resulting in a decrease in the dielectric constant and causing energy dissipation, thereby increasing dielectric loss. In the high-frequency range (10⁵–10⁷Hz), dielectric loss gradually decreases. The reason is that the dipole reorientation polarization cannot keep up with the changes in the external electric field direction at high frequency, and relaxation polarization loss decreases, leading to a gradual decrease of $\tan \delta$ in the high-frequency area.

Fig. 4.

Frequency-dependent Dielectric Constant and Loss of BSTS. (a) Dielectric constant of BSTS as a function of frequency. (b) Dielectric loss of BSTS as a function of frequency. (c) Frequency-dependent dielectric constant of BSTS at −80 °C, −50 °C, −20 °C, and 20 °C. (d) Frequency-dependent dielectric loss of BSTS at −80 °C, −50 °C, −20 °C, and 20 °C. (e) Frequency-dependent dielectric constant of BSTS films with thicknesses of 25 nm, 50 nm, 100 nm, and 500 nm at room temperature. (f) Frequency-dependent dielectric loss of BSTS films with thicknesses of 25 nm, 50 nm, 100 nm, and 500 nm at room temperature.

We found significant differences between the experimental results and those of traditional insulators (Crosslinked polyethylene), which was within our expectations. While TIs are referred to as "insulators," their transport mechanisms and band structures differ greatly from traditional insulators. Due to strong spin-orbit coupling effects and topological protection, the surface of TIs exhibits conductive states, which resemble metallic properties; meanwhile, the interior presents an insulating state. However, this insulating state is not entirely insulating in the traditional sense but rather resembles a semiconductor state. Moreover, the coupling between the surface and bulk of TI materials, exacerbated by intrinsic defects and measurement errors, further weakens this "insulating state" within the bulk, thereby amplifying the differences from traditional insulators.

During the dielectric testing process, it is noted that all samples showed similar dielectric trends after the observation of the dielectric response of BSTS thin films at different temperatures. To further explore the effect of temperature on BSTS's dielectric properties, we selected BSTS films with a thickness of 25 nm, which exhibited the most prominent topological properties, and performed the experiments at temperatures of −80 °C, −50 °C, −20 °C, and 20 °C (Fig. 4c). We observed that the dielectric constant of BSTS generally decreased with the increase in temperature. It can be explained that the dielectric constant was impacted by the weakening of dipole reorientation polarization resulting from the intensified molecular thermal motion as the temperature rises. The topological surface states of BSTS also played a key role in this process. With the raising of the temperature, the characteristics of the topological surface states and the contributions made by electronic polarization may change as a result of increased thermal excitation of electrons within BSTS. As shown in Fig. 4d, the rising of the temperature led to the upper-right movement of $\tan \delta$ with the change of the frequency. This indicates that at lower temperatures, relaxation polarization could not be established in time, leading to a lag of dipole reorientation in response to the changing frequency in the external electric field. The thermal motion energy of the dipoles increased with the raising of the temperature, leading to the acceleration of their rotation. It shortens the time of relaxation and increases the relaxation polarization loss, causing a rightward movement of $\tan \delta$. Additionally, the conductive loss increased with the rise in temperature, leading to an upward trend of $\tan \delta$.

Furthermore, we observed that the dielectric response of BSTS is also significantly influenced by the thickness of the film. By analyzing the dielectric constant frequency spectra of films of different thicknesses at a temperature of −80 °C (Fig. 4e), we determined the dependency between the BSTS dielectric constant and film thickness. It was found that the dielectric constant of BSTS increases with the film thickness, which indicates that the dielectric response of BSTS suffered more suppression in thinner films. The reason would be that the thinner films have a larger specific surface area, which enhances the influence of topological surface states within the film and significantly affects the overall polarization process. Fig. 4f shows that the dielectric loss moves to the upper-left in response to frequency changes as film thickness increases. This shift could be explained by an increase in dipole moments, as dipoles formed by 2QL may transform into larger dipoles composed of 4QL in the case of a film thickness increase (Fig. S3). During the frequency-changing process, the lag in following the rapid frequency changes is caused by the dipoles' delayed response to changes in electric field, which extends the relaxation time and causes $\tan \delta$ to shift to the left. Additionally, as the film thickness increases, the reduction of the specific surface area of BSTS may lead to a weakening of the topological insulator's surface states and a decrease in spin-orbit coupling effects. By doing so, bulk conductivity would be the dominant conduction mechanism, causing an increase in bulk conductivity and conductive losses. As a result, $\tan \delta$ exhibits an upward movement as film thickness increases.

Topological insulators have garnered significant attention for the unique bandgap structure and surface conductive states derived from the topological properties of band structure. Thus, in-depth exploration of the electrical transport properties of BSTS's topological surface states is of considerable scientific value. To figure out the electrical transport properties of BSTS, the Physical Property Measurement System (PPMS) was applied to identify the electrical transport properties of the samples [19]. Resistance measurements were performed using the co-linear four-probe method, while Hall resistance was assessed using the van der Pauw method. The topological surface states were more prominent in thinner films, so we chose a BSTS sample of 25 nm for zero magnetic field surface resistivity testing at different temperatures (Fig. 5a). A notable correlation between the resistivity of BSTS and temperature could be observed. The reason is that the conductivity of BSTS has two aspects: bulk and surface conduction. At low temperatures, the bulk conduction is suppressed, so the surface conduction becomes the dominant transport mechanism. Then, the surface resistivity decreases with the reduction of carrier scattering off phonons, and electron conduction is primarily dominated by topological surface states. This phenomenon is formed since the charged carrier density of the samples decreases with the fall in temperature. At high temperatures, bulk conduction becomes the dominant transport mechanism for the effect of thermally excited carriers. This unique characteristic indicates that BSTS displays ideal conductive surface states and topological protection at low temperatures, which is in favor of information transfer via electron spin, and offers potential applications in areas such as quantum computing chips, spintronics, etc [20].

Fig. 5.

Electrical Transport Characterization of BSTS Film Samples with a Thickness of 25 nm in PPMS. (a) Resistivity versus temperature curve for the film sample under zero field, within a temperature range of 2K–300K. (b) Hall resistance versus magnetic field curve for the film sample at room temperature, within a magnetic field range of -9T to +9T.

The curve of Hall resistance variation with magnetic field shown in Fig. 5b showcases the electronic transport characteristics of BSTS at room temperature. We calculated the Hall coefficient $RH=1/ne$ and drove the formula for bulk carrier concentration: $nb=1/\left|RH\right|e$. Given the direct relationship between conductivity $\sigma$, bulk carrier concentration $nb$, and mobility $\mu$, represented as $\sigma =ne\mu$, we can further derive the formula for bulk carrier mobility: $\mu =1/ne\rho$, according to the resistivity generated in the measurements at room temperature. Additionally, the surface carrier concentration $ns=nbd$ and key parameters such as Hall coefficient, carrier concentration, and mobility based on the computing of the experimental data have been shown in Table 2 [21]. Compared to the resistivity (1.14 × 10⁻⁴ Ω cm) and mobility (653.5 cm²/Vs) of typical binary topological insulators, BSTS displays higher bulk resistivity due to the reduction of mobility, which is conducive to enhancing bulk insulation and increasing the contribution of topological surface states in electronic transport to make them more obvious [22]. The remarkable presence of topological surface states showcases the enhancement of spin-orbit coupling effects in BSTS. Such findings and improvements not only provide a new perspective for the exploration of the theory of spin Hall effects but also offer essential criteria for selecting suitable materials in the research and development of spintronic devices, quantum computing, and quantum superconducting material.

Table 2.

BSTS electrical test date.

Temperature	Carrier type	Carrier areal density	Carrier bulk density	Bulk resistivity	Hall coefficient	Bulk carrier mobility
300 K	p	5.74 × 1014cm−2	2.87 × 1020cm−3	1.54 × 10−3 Ω cm	0.022 cm3/C	14.14 cm2/Vs

4. Conclusion

In this study, we successfully fabricated high-quality quaternary topological insulator thin films Bi_1·2Sb_0·8Te_0·4Se_2.6 with stable stoichiometry using the LMBE system. The excellent surface morphology and unique band structure of BSTS samples have been confirmed according to the characterization tests. Through broadband dielectric spectroscopy, an in-depth analysis of BSTS's polarization behavior at different frequencies was carried out, and new opinions of its topological surface states in dielectric polarization were delivered. Additionally, by studying the dependencies of BSTS's dielectric response in terms of temperature and thickness, we found that topological surface states play a crucial role in the regulation of the dielectric response. The bulk resistivity (1.54 × 10⁻³ Ω cm) and carrier concentration (2.87 × 10²⁰ cm⁻³) of BSTS have been attained through the PPMS tests, which illustrates that the topological surface states of BSTS are more distinct than those of binary topological insulators. The research is of great significance for the understanding of the electronic properties of topological insulators and provides crucial experimental evidence for their application in high-tech fields such as quantum computing, spintronics, and low-power electronic devices.

5. Method

Film Growth: In the experiment, an LMBE system (LMBE450 type, Japan) was used to prepare BSTS films (Fig. 1). The laser ablation mixing splicing target preparation method improves the preparation efficiency by nearly 70 times compared to the single-element target of the molecular beam epitaxy (MBE) heating beam source furnace. First, a cleaned Si substrate was placed on the substrate holder within the epitaxy chamber. Second, the excimer laser of the LMBE system emitted pulsed lasers, which drive their energy from four inert gases (He, Ne, F, and Kr). Going through the reflectors and transmitters that have been adjusted precisely, the laser focused and bombarded four types of target materials in the epitaxy chamber (Bi₂Se₃, with the target purity of 99.999%; Sb₂Te₃, with the target purity of 99.999%; Te, with the target purity of 99.99%; and Se, with the target purity of 99.99%). As the target rack rotated at a constant speed, the pulsed laser uniformly irradiated each area of the mixed-spliced targets. This process produced atoms of Bi, Se, Sb, and Te, which were sputtered onto the opposite substrate in the form of a plasma cluster, completing the growth of BSTS films.

Dielectric Testing: We utilized a wide-frequency dielectric spectrometer (Novocontrol Concept 80) to examine the dielectric properties of BSTS. Initially, a layer of conductive adhesive tape was affixed onto the surface of the BSTS sample and onto the substrate, sandwiching it between two copper electrodes (diameter: 25 mm, thickness: 3 mm). Upon initializing the wide-frequency dielectric spectrometer, we configured the relevant parameters using the specialized software of Novocontrol Concept 80, including the sample thickness (265 μm), electrode diameter (25 mm), testing frequency (10¹–10⁷ Hz), and testing temperatures (−80 °C, −50 °C, −20 °C, and 20 °C). The prepared sample electrodes were then placed onto the testing apparatus and secured with knobs. Subsequently, the entire testing setup was positioned within a cooling container connected to a liquid nitrogen device for testing under specific temperature conditions. Upon completion of the preparation, the testing program of the wide-frequency dielectric spectrometer was initiated. The sample was cooled or heated according to the predetermined temperature settings. Once the desired temperature was reached, the dielectric response information at the specific temperature was tested. The testing system generated spectra plots of the sample's dielectric constant and dielectric loss on the computer based on the acquired data.

TEM Testing: We employed a Transmission Electron Microscope (FEI Talos-F200S) to examine the crystal structure of BSTS. The TEM was operated at an accelerating voltage of 300 kV. Initially, the TEM was powered on and underwent initialization and adjustments to ensure the stability and accuracy of the electron beam. The focal length and alignment of the electron beam were adjusted accordingly. The thin film sample was placed on the TEM sample stage, and its position and tilt angle were adjusted to achieve optimal observation. The focusing function of the TEM was activated to adjust the electron beam focus, and an appropriate magnification was selected. High-resolution imaging mode was chosen based on the sample's characteristics. Finally, images of the sample were captured using a camera.

CRediT authorship contribution statement

Tao Xu: Writing – original draft, Resources. Yueqian Zheng: Writing – review & editing, Writing – original draft. Xuan Wang: Funding acquisition, Formal analysis. Zhi Sun: Project administration, Data curation. Bai Han: Supervision, Software.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article: