## Introduction

The Bi2Te3 family (Bi2Te3, Bi2Se3, Sb2Te3, and Sb2Se3) of topological insulators (TI) was first predicted by Zhang et al.1 to have both topologically protected surface states2 (TPSS) and an insulating bulk phase3, which were later confirmed experimentally. In contrast to the three-dimensional TI Bi1−xSbx, which possesses remarkably complex surface states4, the surface states of Bi2Te3 are much simpler, consisting of only a single Dirac cone5. This simplicity makes Bi2Te3 an ideal system for studying the physics of TIs. Moreover, with a band gap of 0.17 eV – well above the room temperature energy – Bi2Te3 is in principle well-suited for use in electronic devices.

The Bi2Te3 family also exhibits tunability of thermoelectric properties6, phonon dynamics7, and charge carrier dynamics by adjusting their thickness8,9. Importantly, reducing the thickness in a TI increases the surface-to-volume ratio, which significantly enhances the relative contribution of topological surface states to the measured conductance5,10. The crystal structure of the Bi2Te3 family is characterized by a quintuple layer (QL) structure (Fig. 1a), which is comprised of five atomic, covalently bonded planes, while the QLs are weakly held together van der Waals (vdW) forces. Consequently, Bi2Te3 can be mechanically exfoliated similarly to graphene, and thicknesses down to a single QL can be achieved11. Upon decreasing the thickness to below 80 nm, the loss of infinite crystal periodicity results in the symmetry breaking along the z-axis and consequently in the appearance of the Raman-forbidden $${A}_{1u}^{2}$$ mode in Raman spectra of exfoliated Bi2Te312,13.

Bi2Te3 thin films with broken symmetry have been shown to have topologically non-trivial surface states down to ~3 QLs14.

To date, studies have primarily focused on probing topological surface states at the TI/vacuum interface, which requires careful consideration of surface quality and ultra-high vacuum (UHV) conditions3. Studies of the TI/substrate interface, however, may relax the technical requirements as the effect of ambient conditions on the interface quality is negligible15,16. Still, atomically smooth TI layers grown via molecular beam epitaxy (MBE) are required for investigations of phenomena taking place at the TI/substrate interface. The quality of the interface and charge carrier properties can then be studied using light scattering spectroscopy17. Similarly, surface acoustic phonons have been recently employed as a “sonar” probe of electron-phonon coupling at the interface of Bi2Te3 and GaAs18.

Bi2Te3 has a rhombohedral crystal structure with space group $${D}_{3d}^{5}$$ ($$R\bar{3}m$$) and five atoms in the unit cell. From group theory, Bi2Te3 has twelve optical branches with the allowed symmetries $${A}_{1g}$$, $${A}_{2g}$$ $${E}_{g}$$, $${A}_{1u}$$, $${A}_{2u}$$, and $${E}_{u}$$. Since Bi2Te3 is centrosymmetric, the rule of mutual exclusion applies: normal modes cannot be both IR and Raman active13. However, IR-active modes in the range of ~50–160 cm−1 have been observed in Raman19,20 and inelastic He scattering21 measurements of Bi2Te3. These Raman-forbidden and bulk IR modes arise either from breaking of the crystal symmetry in the z-direction (due to the limited thickness of a few QLs) or from surface phonons coupling to topological surface states13. At present, the symmetry loss in TI thin films is attributed to a large density of domain boundaries formed during coalescence of crystal islands with different lattice orientations, and the Froehlich electron–phonon interaction has been suggested to play a significant role in the Raman scattering processes21. However, Li et al. showed that symmetry breaking may also result from the fabrication technique. For example, when using the so-called “scotch tape” exfoliation method, the fragmentation of QLs into sub-quintuple layers leads to the emergence of the Raman-forbidden mode A1u in thick slabs of Bi2Te314.

In this paper, we present a surface-phonon-based micro-Raman and tip-enhanced Raman spectroscopic (TERS) (Fig. 1b) study of interactions between Bi2Te3 and various substrates on which the TI was grown using MBE. Modifications of the interactions are facilitated by the generation of surface plasmons on various substrates, charge transfer from a semiconducting substrate, and a periodic potential applied to the sample via a corrugated sapphire substrate. These interactions induce symmetry breaking in the z-direction of Bi2Te3, effectively separating the surface properties from the bulk. Symmetry breaking is manifested in the emergence of Raman-forbidden modes, which imply both modified interactions between Bi2Te3 and substrate and modified long-range interactions between Bi2Te3 QLs. Our results hint at the possibility of observing topologically protected states at the Bi2Te3/substrate interface – even for thick Bi2Te3 samples – which would be a breakthrough for fabrication of nanoelectronics devices for lossless electron transport.

## Results

Micro-Raman measurements of 50-nm-thick Bi2Te3 grown on a flat, insulating sapphire substrate (Fig. 1c) reveal Raman-active $${A}_{1g}^{1}$$, $${A}_{1g}^{2}$$, and $${E}_{g}^{2}$$ modes in agreement with those previously reported for bulk samples12 in the range of ~50–160 cm−1. The $${A}_{1g}^{1}$$ and $${A}_{1g}^{2}$$ modes are out-of-plane vibrations with respect to the plane of van der Waals-bonded layers, while the $${E}_{g}^{2}$$ mode represents an in-plane vibration. The $${A}_{1g}$$ and $${E}_{g}\,\,$$modes can be used to probe the interactions both between and within QLs. It has been shown that with decreasing Bi2Te3 thickness – and consequent decrease in interlayer interactions – the intensity of the $${A}_{1g}^{2}$$ mode increases, reflecting less restrained out-of-plane $${A}_{1g}^{2}$$ vibrations22,23. This decrease in interlayer interaction for thin films also results in the appearance of a surface phonon mode (SPM)11, which is visible in our micro-Raman spectra at 90 cm−1.

TERS measurements on the same sample (and substrate) show additional excitations that are absent in micro-Raman spectra (Fig. 1d). Two peaks at ~55 and ~76 cm−1 (reported in refs11,24), labeled P1 and P2, are observed only in TERS spectra. The most striking difference in the TERS spectra is the emergence of the $${A}_{1u}^{2}$$ mode at 119.2 cm−1, an IR-active and Raman-forbidden mode that exhibits predominantly out-of-plane atomic motion25. Its appearance in Bi2Te3 Raman spectra has previously been attributed to symmetry breaking in the z-direction in sufficiently thin films11. The observation of this mode in TERS spectra suggests that LSP generation from the TERS technique can also induce symmetry breaking in Bi2Te3. LSP generation is evidenced by the more than 10-fold intensity enhancement of TERS spectra compared with micro-Raman spectra26,27,28 (see Fig. 1). Further detail on the Raman peaks observed in micro-Raman and TERS measurements of Bi2Te3 on sapphire are provided in Table S1.

To confirm that the appearance of the $${A}_{1u}^{2}$$ mode is the result of LSP generation and not unique to the sapphire substrate, additional micro-Raman and TERS measurements were performed on 75-nm and 50-nm-thick Bi2Te3 grown on semiconducting Si and GaAs substrates, respectively. Figure 2a shows micro-Raman spectra for Bi2Te3 on Si, which features the characteristic $${A}_{1g}^{1}$$, $${A}_{1g}^{2}$$, and $${E}_{g}^{2}$$ modes, as well as a surface phonon mode at ~93 cm−1. The unassigned P2 mode is also present in this sample, along with an additional mode at ~108 cm−1 (labeled P3). TERS spectra of the same sample (Fig. 2c) show the emergence of the Raman-forbidden $${A}_{1u}^{2}$$ mode, providing further evidence that LSP generation from TERS induces symmetry breaking.

A large signal from the characteristic mode of the Si substrate at ~520 cm−1 is observed via TERS measurements, but not in micro-Raman spectra (Fig. S1). Observation of the Si mode suggests that the measurement is quite sensitive to the Bi2Te3/Si substrate interface – a result of the difference in the penetration depth for Raman and TERS measurements. The light penetration depth is given by $$l=\sqrt{\pi fn{\mu }_{e}{\mu }_{m}}\,$$, where f is light frequency, $${\mu }_{e}$$is the electron mobility, $${\mu }_{m}$$is the magnetic permeability, and n is the electron concentration. We suggest that TERS-induced localized surface plasmons increase the local electron concentration n, leading to an increase of the light penetration depth and consequent appearance of the Si peak.

Micro-Raman spectra of 50-nm-thick Bi2Te3 grown on GaAs also exhibit the characteristic Raman-active modes, SPM, and unassigned P2 mode (Fig. 2b). Unlike samples grown on sapphire and Si substrates, however, the Raman-forbidden $${A}_{1u}^{2}$$ mode is visible without TERS-induced plasmon generation. Consequently, another mechanism must be responsible for symmetry breaking in this sample. As will be further discussed below, a plausible mechanism is charge transfer from the GaAs substrate. TERS spectra on the same sample are nearly identical, but with larger Raman intensities due to the characteristic signal enhancement of the technique (Fig. 2d). Further details of the fittings of Raman spectra for Bi2Te3 on Si and GaAs are given in Tables S2 and S3, respectively.

Finally, we examine the effect of a periodic strain potential on 30-nm-thick Bi2Te3 films grown on a corrugated sapphire substrate. Due to the instability of sapphire’s m-plane surface when annealed at high temperatures, it undergoes spontaneous faceting that results in the formation of V-shaped nanogrooves. Our annealing procedure resulted in substrates with corrugation height and period of h = 20 nm and w = 250 nm, respectively (Fig. 3a). Bi2Te3 was then grown directly onto the corrugated substrate to induce a periodic strain potential. Further details of the procedure are provided in Supporting Information.

Micro-Raman measurements of Bi2Te3 grown on corrugated sapphire were carried out with the laser at an incident angle of θ = 10° with respect to the plane of the substrate (see Fig. 3c). This was done to maintain the same scattering geometry as micro-Raman measurements on flat substrates, compensating for the corrugation angle. For TERS measurements, it is more important that the laser beam is properly focused on the apex of the metallic tip shown in Fig. 1b, rather than on the sample surface, and so the standard angle of θ = 0° was used. Both micro-Raman and TERS spectra reveal $${A}_{1u}^{2}$$ mode emergence (Fig. 3d,e), suggesting that symmetry breaking is induced by the applied periodic strain potential. Additional details of the modes fitted in Fig. 3d,e are listed in Table S4.

## Discussion

Broken symmetry of a TI can lead to separation of bulk and surface conduction, and exploiting this phenomenon provides a crucial step forward for experimental studies of TIs and realization of TI-based devices. However, the design process of nanoelectronics devices based on TIs should take into consideration thermodynamic conditions for which the devices are designed. It is a well-known fact that at elevated temperatures, quantum effects are washed out, and, consequently the special properties of the electrically conducting surfaces disappear. Therefore, to suppress the thermal excitation of charge carriers from the bulk into TIs surface states, the energy gap of the system must be increased.

An excellent candidate for nanoelectronic devices is Bi2Se3 with a band gap of 0.3 eV, which is twice the value of Bi2Te3 of 0.15 eV1, which makes the observation of TI behavior at room temperature more robust. On the other hand, by decreasing the thickness of Bi2Te3 down to 1 QL, its energy gap can reach 0.45 eV14,29. This implies suppression of contribution of the bulk electrons into surface states of thin TI layers. Moreover, thermal excitations are related to scattering by acoustic phonons (AP) and decreasing the TI thickness leads to a reduction of bulk AP. Finally, for sufficiently thin TI layers (between 3 QL’s and 9 QL’s), topologically protected surface states appear30 and only surface phonons remain. The electron-surface AP coupling18 can lead to spin-like oscillations of electrons, which can be exploited in device applications. Here, we demonstrated that not only thickness reduction leads to the symmetry breaking, but also LSP generation and interactions of the TI with different substrates. Therefore, we expect that Bi2Te3– based devices, grown on selected substrates, will preserve the unique transport properties at the TI/substrate interface even at room temperature. Such conducting edge states at room temperature were recently reported in the two-dimensional TI bismuthene grown on SiC31.

Previous work has demonstrated that reducing the thickness of Bi2Te3 results in symmetry breaking along he z-axis of the material, and consequently the emergence of the Raman-forbidden $${A}_{1u}^{2}$$ mode and SPM11,12,13,24,32. Due to the broken symmetry, various surface phenomena have been observed in ultrathin (1-2 nm) Bi2Te39,12. Symmetry-breaking in Bi2Te3 can also be induced by interactions with the substrate: the effect of a magnetic substrate on symmetry breaking was presented in ref.33, in which the emergence of ferromagnetism in the bottom surface of Bi2Se3 was demonstrated by observation of an additional Shubnikov–de Haas frequency.

In our experiments, we demonstrate three additional mechanisms for symmetry breaking: surface plasmon generation, charge transfer, and the presence of a periodic potential. By employing micro-Raman and TERS spectroscopy, we link the emergence of Raman-forbidden optical phonon modes to underlying broken symmetry of Bi2Te3.

It is well established that the TERS technique uses the local plasmon mode of a sharp metallic nanotip to confine and enhance the electric field near the tip apex. LSP generation in the sample occurs via tip-sample coupling and tip-induced sample heating, which can elevate the sample’s temperature34,35,36. The excellent thermoelectric properties of Bi2Te3 result in localization of thermally activated electric charges. This, paired with the photoelectric effect from the incident laser light37,38,39,40, results in an increase in local charge density and increases the light penetration depth. We attribute the appearance of the characteristic Raman mode of the Si substrate to this effect, and it is clear evidence of electron-phonon coupling at the Bi2Te3/Si interface. A similar effect has been observed with Bi2Te3 on a ZnO substrate, for which surface plasmons enhance the photoluminescence from ZnO41.

Surface plasmons in Bi2Te3 can also be generated due to various inter- and intra-band transitions, including bulk interband transitions in the visible range, intraband transitions within topologically protected surface bands in the mid-infrared, and interband transitions between bulk states and topologically protected surface states spanning the UV to near-infrared35. The existence of such surface plasmons in Bi2Te3 has been confirmed by High Resolution Transmission Microscopy (HRTEM) measurements28. In our experiments, LSP generation is evidenced by roughly three- and ten-fold intensity enhancements in TERS measurements compared with micro-Raman for Bi2Te3/Si and Bi2Te3/flat sapphire samples, respectively. Additionally, LSP generation results in a symmetry breaking of the material evidenced by the appearance of the Raman-forbidden $${A}_{1u}^{2}\,\,$$mode in TERS spectra.

We also show that electron transfer from the substrate can break the symmetry of Bi2Te3, as we observe of the $${A}_{1u}^{2}$$ mode in both micro-Raman and TERS measurements on a GaAs substrate (Fig. 2). The work functions for GaAs and Bi2Te3 are 4.69 eV and 5.3 eV, respectively. Thus, once the materials are in contact, electrons transfer from GaAs to Bi2Te3, leading to a large increase in electron density18,42,43. The charge transfer from a substrate to a TIis also responsible for tuning vertical location of helical surface states23. Wu et al. assert that the substantial electronic hybridization at the interface decreases coupling between the first and second QL of the TI, shifting the topologically protected states upward from the first to the second QL.

The $${A}_{1u}^{2}\,\,$$mode was also observed in both micro-Raman and TERS spectra collected from Bi2Te3 on a corrugated sapphire substrate (Fig. 3e). We suggest that the substrate corrugation induces sufficient strain in Bi2Te3 to result in symmetry breaking44. This agrees with ref.45, which reports that tensile and compressive deformations of Bi2Te3 QLs can cause a shift in the atomic layers of Bi and Te and, as a result, a reduction in symmetry. More detailed theoretical investigations have shown that the lattice constant of Bi2Te3 increases at a rate of 0.012 Å per 1% of in-plane uniaxial strain ranging between −6% to 6% (compressive to tensile)46 and the band gap increased from 0.07 to 0.16 eV between −3 to 3% strain43. Strain also induces flexoelectricity and subsequent electric polarization in Bi2Te3 – a signature of symmetry breaking in the z-direction47. Therefore, uniaxial strain induced by the corrugated substrate can alter the properties of Bi2Te3 through both symmetry breaking and strain-induced modifications to the band structure.

Optical phonons are a common tool for probing intra- and inter-layer interactions between van der Waals-bonded layers such as those in Bi2Te3 QLs. Previous studies have demonstrated that the $${A}_{1g}^{1}$$ and $${A}_{1g}^{2}\,\,$$modes redshift and blueshift, respectively, with decreasing Bi2Te3 thickness11,48 and the intensity ratio $$I=\frac{I({A}_{1g}^{2})}{I({E}_{g}^{2})}$$ increases with decreasing thickness due to less restrained out-of-plane $${A}_{1g}^{2}\,\,$$vibrations13. This indicates that the long-range interaction between QLs is weakened as the thickness decreases. The SPM is also a sensitive indicator of Bi2Te3 thickness, as it has been shown that the mode increases in intensity as thickness is reduced from 40 nm to a single QL. We observed the SPM mode in all collected micro-Raman and TERS spectra, providing further evidence of weak interactions between QLs in investigated samples. Furthermore, since the out-of-plane and surface modes in Bi2Te3 are sensitive to the interaction between QLs, one can use them to derive information about symmetry breaking in the direction perpendicular to the QLs.

Analysis of the intensity ratio I of Bi2Te3 on various substrates revealed that local surface plasmon generation, charge transfer, and a periodic strain potential all act to increase I (Table 1). This implies that these mechanisms decrease interlayer interactions in the material – a phenomenon that was previously only associated with thickness reduction in Bi2Te3. In each case, the ratio increase is primarily due to an increase in $${A}_{1g}^{2}$$ mode intensity rather than a decrease in $${E}_{g}^{2}$$ mode intensity, suggesting that out-of-plane $${A}_{1g}^{2}$$ vibrations become less restrained due to weaker interlayer bonding. This effect is most pronounced for the charge transfer mechanism, as I for Bi2Te3 on GaAs is nearly an order of magnitude larger than for Si or flat sapphire substrates. For LSP generation and strain mechanisms, the effect is more modest: values of I based on TERS measurements were ~30% larger than those for micro-Raman and ~10% larger for measurements on corrugated compared with flat sapphire. Additionally, the $${A}_{1g}^{2}$$ mode was found to blueshift by an average of ~3.5 cm−1 in TERS measurements compared with micro-Raman (Tables S1-S4), as would be expected for Bi2Te3 exhibiting weaker interlayer bonding.

Based on the emergence of the Raman-forbidden $${A}_{1u}^{2}$$ mode and changes in intensities and frequencies of Raman-active optical modes, one can conclude that LSP generation, charge transfer, and application of a periodic potential can each modify the interactions between individual QLs and break the symmetry of bulk Bi2Te3. Such effects – which have previously only been observed in Bi2Te3 thin films – suggest that isolation of surface phenomena is achievable in bulk Bi2Te3 via proper selection of substrate and experimental technique.

## Conclusions

The analysis presented herein has shown that LSP generation, charge transfer, and application of a periodic potential can modify the long-range interactions between QLs in a Bi2Te3 sample near the substrate interface. This leads to the emergence of Raman-forbidden modes and enhanced out-of-plane vibrations characteristic of topologically insulating Bi2Te3 thin films with broken symmetry. Our results highlight the need for further investigations of the quantum Hall effect in Bi2Te3 samples with broken symmetry and raise the possibility of isolating topologically protected surface states from bulk states at the interface between Bi2Te3 and a substrate – a potential breakthrough for engineering lossless devices based on TIs.

The periodic strain introduced by corrugation causes density fluctuations of the TI layer leading to transverse spin fluctuation49,50. For thin TI layers, charge-like and spin-like plasmons can be distinguished, as the first couple to optical and the latter to acoustic phonons, respectively50. Investigations of the acoustic phonon dispersion in TIs with and without magnetic field should be able to validate the spin-charge separation hypothesis.

Next, electron transport measurements addressing the Bi2Te3/substrate interface should be undertaken to determine if surface conduction can be isolated from bulk via the mechanisms discussed in this work.

## Methods

### Sample fabrication

Bi2Te3 thin films were grown via MBE on Si(111), GaAs (001) with a 2° offcut towards [110], and m-plane $$[101\bar{0}]$$ cut sapphire (α-Al2O3) substrates with flat and corrugated surfaces. The growth temperature was kept at 220 °C. The thicknesses of the Bi2Te3 films grown on these substrates were as follows: 75 nm on Si, 50 nm on GaAs, and 30 nm and 50 nm on sapphire substrates. Corrugated sapphire substrates were fabricated using a special heat-treatment procedure that results in surface reconstruction51,52,53. Further details of the sample fabrication are presented in the Supporting Information.

### Tip-Enhanced Raman Spectroscopy (TERS) and micro-Raman Spectroscopy

For TERS measurements, a Renishaw inVia spectrometer and NTMDT TERS system were employed in the top-illumination and top-collection type geometry and equipped with a 3 mW, 633-nm wavelength laser.

Micro-Raman spectra were measured in a backscattering configuration using a commercial Renishaw inVia micro-Raman system and a 3 mW, 633 nm wavelength laser. All spectra were measured under 50x magnification resulting in a beam spot about 0.7 μm in diameter. A spectral resolution of about 1 cm−1 was achieved using a 1200 l/mm grating. Additional micro-Raman spectra were collected using the NTMD system with a Renishaw spectrometer to compare with TERS measurements; spectra were collected in the tip-retracted position to acquire only the far-field Raman component. The Raman spectra collected using these two systems were comparable.

Details on the TERS technique can be found in the Supporting Information.