Topological surface states in epitaxial (SnBi 2 Te 4 ) n (Bi 2 Te 3 ) m natural van der Waals superlattices

Topological insulators are good candidates for charge to spin conversion with high efficiency due to their spin-polarized topological surface states (TSS). In this work, we provide experimental evidence for 2D TSS in (SnBi 2 Te 4 ) n (Bi 2 Te 3 ) m natural van der Waals superlattices grown by molecular beam epitaxy using angle resolved photoelectron spectroscopy (ARPES) and magnetotransport. While the TSS overlap with bulk conduction band (BCB) states at the Fermi energy, it is shown that by increasing the Sn composition, the influence of BCB states is reduced and becomes minimum for SnBi 2 Te 4 . The latter compound, found to be in the form of septuplet layers, shows weak antilocalization effect with a prefactor α ~ -0.41, indicating

Topological insulators are good candidates for charge to spin conversion with high efficiency due to their spin-polarized topological surface states (TSS). In this work, we provide experimental evidence for 2D TSS in (SnBi2Te4)n (Bi2Te3)m natural van der Waals superlattices grown by molecular beam epitaxy using angle resolved photoelectron spectroscopy (ARPES) and magnetotransport. While the TSS overlap with bulk conduction band (BCB) states at the Fermi energy, it is shown that by increasing the Sn composition, the influence of BCB states is reduced and becomes minimum for SnBi2Te4. The latter compound, found to be in the form of septuplet layers, shows weak antilocalization effect with a prefactor α ~ -0.41, indicating that the TSS and the bulk behave as one 2D channel in which magnetotransport properties are influenced by large spin-orbit coupling.

I. INTRODUCTION
Three dimensional (3D) topological insulators (TI) have topological surface states (TSS) with their spin locked to the orbital momentum due to large spin-orbit coupling (SOC), offering high charge to spin conversion efficiency [1,2] via the Edelstein effect [3]. Therefore, among other applications, they could be ideal candidates to replace heavy metals (Pt, Ta, etc.) in spin orbit torque (SOT) magnetic devices [2]. Archetypical 3D TIs like the layered Bi2Se3 and Bi2Te3 show promises [2] but their use for practical applications is hampered by the parasitic contribution from the bulk conduction band (BCB). Mixing with other compounds is a means to tailor the surface topological properties in favor of the TSS contribution in the electronic transport. It has been shown for example [4] that doping Bi2Te3 with 0.9% Sn brings the Fermi level inside the bulk energy gap, therefore crossing only the TSS and thus avoiding BCB contribution. The TSS and bulk electronic band structure in compounds containing more Sn at stoichiometric compositions such as the Bi-rich SnBi2Te4, SnBi4Te7, etc., or in alloys with Snrich compositions [5] have not been experimentally investigated in detail. Notably, the parent SnTe is also a topological crystalline insulator (TCI) [6], which creates the prospect that TSS can be obtained over the entire range of Sn composition x (0-1). From previous works on similar compounds PbBi2Te4, PbBi4Te7, GeBi4Te7 and MnBi2Te4 [7][8][9][10][11], it is expected that the Sn-Bi-Te mixed compound will take the form of a natural van der Waals heterostructure of the general form (SnBi2Te4)n(Bi2Te3)m where n layers of SnBi2Te4 alternate with m layers of Bi2Te3. The first member of the series, SnBi2Te4 (n = 1, m = 0) forms a septuplet Te-Bi-Te-Sn-Te-Bi-Te where SnTe takes the middle position at the septuplet layer when it mixes with Bi2Te3, while the second member of the series, SnBi4Te7 (n = 1, m = 1) forms a natural van der Waals superlattice where one SnBi2Te4 septuplet alternates with one Bi2Te3 quintuple. Higher order members of the series, (e.g. SnBi6Te10, (n = 1, m = 2)) form natural van der Waals superlattices where one SnBi4Te7 septuplet alternates with two or more Bi2Te3 quintuples [5].
Theoretical investigations of the different members of the series have been presented showing that they are all TIs with the Fermi level lying in the gap [5,12]. The first member of the series, SnBi2Te4, has already been grown in bulk form (nanoplates) [13] and a weak antilocalization (WAL) effect has been observed in magnetotransport measurements, attributed to TSS possibly intermixed with bulk contributions. In addition, it has been shown [13] that the bulk SnBi2Te4 deviates from ideal since a cation exchange occurs and the middle row of the septuplet is occupied by both Sn and Bi with Sn presence being dominant. No experimental data are available regarding the electronic band structure and the presence of TSS in any member of the series. A direct observation of the TSS by ARPES and their correlation with magnetotransport are required in order to confirm a substantial contribution of TSS to electronic conduction, necessary for SOT devices and spintronics. Moreover, all work so far has been performed on bulk materials grown in equilibrium [13][14][15][16]. Epitaxial thin films grown by out-of-equilibrium techniques such as molecular beam epitaxy (MBE), could add flexibility in tailoring the natural van der Waals superlattice structure and their topological properties and open the route for scalable large area growth of composite TI/magnetic layer devices.
In the present work, we report on the structure and the electronic properties, especially those related to the TSS, of four different TI compounds and alloys, namely Bi2Te3, SnBi4Te7, SnBi2Te4 and Sn1-xBixTe grown by molecular beam epitaxy on InAs(111)/Si(111) substrates.
The layered structure is studied by high-resolution scanning transmission electron microscopy (STEM) revealing a layer stacking in the form of natural van der Waals superlattice. Combining first-principles calculations with in-situ and synchrotron ARPES, we confirm the presence of TSS and correlate them with magnetotransport measurements. By varying the Bi/Sn ratio and monitored by ARPES, we are able to tune the position of the Fermi level with respect to the TSS and the BCB allowing the identification of Sn composition at which the TSS contribution maximizes relative to BCB.

A. Epitaxial growth and natural van der Waals superlattice
Eight samples were grown (see Sec. IV) on InAs(111) substrates with different Bi/Sn ratios and four of them were studied in detail (Table I). Their Bi/Sn ratio is determined by X-ray photoelectron spectroscopy (XPS) using sensitivity factors from literature confirming the nominal ratio estimated from the evaporation rates ( Fig. S1 in Supplemental Material (SM) [17]). Sn composition is controlled by the deposition rates of Sn relative to Bi. Te is supplied under conditions of overpressure such that the growth rate ratio Te/M~ 15 (M=Bi, Sn). Under these conditions, Te is incorporated in the material to obtain the targeted stoichiometric compounds while the excess Te with low sticking coefficient is desorbed  where Sn ideally occupies the middle row. It should be noted that the substrate surface roughness influences the film microstructure as can be seen in Fig. S3. Therefore, the quintuplets are slightly distorted appearing as being non-parallel to each other.

B. First-principles calculations
Ab-initio calculations are focused on SnBi4Te7 and SnBi2Te4, since the parent Bi2Te3 and SnTe TIs are well-studied materials [20][21][22][23]. The topological nature of SnBi4Te7 and SnBi2Te4 is determined by calculating the ℤ2 topological invariants (see Sec. IV) in the kz = 0 and kz = π planes. For the kz = 0 plane, ℤ2 = 1, while for the kz = π plane, ℤ2 = 0. Therefore, a band order inversion occurs, resulting in a non-trivial band gap and the appearance of surface states. The band inversion between Γ " 9 and Γ " 8 is further confirmed by using related software available from the Bilbao Crystallographic server [24,25]    By further increasing Sn in Sn0.64Bi0.36Te alloy, the TSS with the hexagonal symmetry disappears and the ARPES spectral weight is dominated by the trigonally shaped valence band states as expected, since the sample adopts a cubic 3D SnTe-like structure where a valence band maximum appears at Γ " [23]. In short, SnBi2Te4 presents a pronounced TSS with the least interference from BCB states at the Fermi energy. Therefore, SnBi2Te4 compound shows the strongest influence from TSS and it is worth investigating its magnetotransport properties with the aim to correlate the observed TSS with transport properties (see next section). This claim is further supported by imaging the energy and momentum distribution curves at the Fermi level and around Γ point, respectively, for samples S1, S2, S4 and S6 (Fig. S8 in SM [17]).
The evolution of crystal and band structure with composition (Bi/Sn ratio) is demonstrated in Fig. 8. This summarizes our study that by varying the Bi/Sn ratio, we are able to move from one end compound to another, by growing in between a natural van der Waals superlattice where one SnBi2Te4 septuplet alternates with one Bi2Te3 quintuple, and also tune the position of the Fermi level with respect to the TSS and the BCB.

D. Topological surface states contribution in magnetotransport
After the ARPES study, the sample was protected with 3 nm Al deposited by MBE in-situ. The Al was then naturally oxidized in air. The sample was then patterned in Hall bar for the magnetoresistance study. Magnetoresistance measurements at low temperature (6 K) for SnBi2Te4 are presented in Fig. 9. The raw data in Fig. S9 of SM [17] indicate that the main contribution in Hall resistance comes from the antisymmetric part which is further analyzed here. The antisymmetric part of Hall resistance in Fig. 9(a) is non-linear, indicating that at least two types of carriers contribute. The fitting reveals that the two types of carriers are both electrons, one with a large density attributed to the BCB nBCB = -4.69 (±0.1)×10 14 cm -2 and low mobility μBCB = 43.2 (±2) cm 2 V -1 •s -1 , and the other with a lower density nTSS = -6.9 (±0.03)×10 12 cm -2 and higher mobility μTSS = 1260 (±2) cm 2 •V -1 •s -1 . The latter density nTSS agrees within a factor of 2 with the TSS density n2D = 1.37×10 13 cm -2 estimated from ARPES (see previous section). Because the surface changed from ARPES to transport measurement (Al capping), this discrepancy can be ascribed to band bending [30]. In order to calculate the carrier density from Hall resistance, we assumed TSS with in-plane helical spin-orbit coupling, ignoring possible out-of-plane spin components. Therefore, the contribution to the Hall resistance of the low electron density is attributed to the 2D TSS. The higher electron density is considered to be a contribution from BCB, which is also present in the ARPES measurements at the Fermi level. The appearance of only two distinct carrier contributions in the Hall data attributed to TSS and BCB imply that possible unoxidized Al cap may not have an effect on magnetotransport otherwise an additional (third) type of carriers would have been observed, which is not the case here.  effect [31] as a result of the large SOC in topological insulators [ Fig. 9(b)]. While the appearance of a dip in B⊥I is associated with a 2D TSS, the emergence of a similar magnetoresistance dip in parallel magnetic fields is an indication that a WAL effect originating from the bulk SnBi2Te4 contributes to the conductance in addition to TSS [31][32][33]. Fig. 9(c) shows the magnetoconductance ΔG as a function of the magnetic field, which, in a rough approximation, is derived from the measured magnetoresistance using [34]: The experimental curves are fitted using the Εq. (2) and (3) for out-of-plane and in-plane B field, respectively: (3) where BΦ = ħ/(4e # " ), lΦ is the phase coherence length and ψ is the digamma function. We find α⊥ and lΦ by fitting the magnetoconductance to the Hikami-Larkin-Nagaoka (HLN) formula (Eq. (2)) [35,36] for the perpendicular magnetic field and then α|| and β (0<β<1) by fitting the magnetoconductance for the parallel magnetic field to Eq. (3) [36][37][38] with lΦ ~ 52 nm being determined from Eq. (2). This is only an approximation, since in general, lΦ for in-plane longitudinal transport is expected to be different compared to the one for transverse transport across the film thickness due to film anisotropy. From the Eq. 2 and 3 the values of prefactors α⊥ and α||, -0.42 and -0.39 are obtained, respectively. Our results agree well with the data reported for bulk grown SnBi2Te4 nanoplates [13].
More specifically, in Ref. [12] the MR dip is also present in both orientations of the B field and the fitting yields α = -0.4, and lΦ = 108.4 nm. In the present work, the perpendicular and inplane field measurements yield similar values of α which are very close to -0.5, indicating that the system behaves as a single transport channel system [39] where the two surfaces are connected through the bulk. A value of β = 0.24 is determined from Eq. (3), a parameter which is related to the surface state penetration depth revealing thus the correlation strength between the upper and the lower TSS. The higher this correlation, the closer the parameter β approaches the value 1 [39].
Zeeman and electron-electron interaction effects were ignored in the analysis of perpendicular magnetoresistance data since they are suppressed in perpendicular magnetic fields [34]. On the other hand, these effects are considered to introduce parabolic dependence of parallel magnetoconductance for low magnetic field strength [34,40,41], which however is not observed in our films. This led to the conclusion that the influence of these effects is rather small. Moreover, electron-electron interactions are expected [41] in films <6 nm, considerably thinner than the ones used in this work (~22 nm).

A. Film growth and surface preparation
The InAs(111)/Si(111) substrates were chemically cleaned in a 5N HF solution in isopropyl alcohol for 5 min to etch the surface oxide and subsequently rinsed in isopropyl alcohol for 30 s in order to avoid reoxidation of the substrate. An annealing step at 400° C in UHV follows to get a clean and flat InAs(111) (In-terminated) surface as evidenced by RHEED. Where appropriate, mild Ar+ sputtering was used (E ≈ 1.5 keV, p ≈ 2×10 −5 mbar, t ≈ 30 s) prior the annealing step to obtain a clean surface as evidenced by a 2 × 2 reconstruction in RHEED pattern attributed to In surface vacancies [42].

C. X-Ray Diffraction (XRD)
X-ray diffraction was performed with a laboratory diffractometer (Bruker D8) with a Cu Kα source.

D. Magnetotransport
Samples are lithographed in 50 width by 150 length µm 2 Hall bars, allowing precise control of the current uniformity and direction. We used a dc current source and nanovoltmeters to measure simultaneously the transverse and longitudinal resistance. The magnetic field is provided by a superconducting coil and the sample is mounted on a goniometer in order to vary the field direction relative to the current one. To insure proper electrical contacts, contacts were prepared using lift-off of Ti(20nm)/Au(150nm) Au deposited using evaporation.

E. ARPES measurements
Specially prepared samples with 20-nm-thick Te capping were measured at the SOLEIL-

F. First-principles calculations
The first-principles calculations were performed using the Vienna Ab initio Simulation Package [44,45] and projector-augmented waves [46]. The generalized-gradient approximation with Perdew-Burke-Ernzerhof [47] parameterization was used as exchange correlation functional. The kinetic energy cut-off was set at 500 eV, using the Monkhorst-Pack scheme [48] employing a 9 × 9 × 9 k-point mesh. The atomic positions were fully optimized by conjugate gradient, using a force threshold of 10 −3 eV Å −1 . The Maximally-Localized Wannier functions are fitted based on s and p orbitals of Sn, Bi and Te atoms using the Wannier90 code [49] and the ℤ2 and the projected Brillouin zone calculations were carried out by the WannierTools software [50]. Spin-orbit coupling was included in band structure calculations.

IV. DISCUSSION AND CONCLUSIONS
In this work, it is confirmed by TEM and XRD that MBE grown SnBi2Te4 thin films form septuplet layers separated between each other by a van der Waals gap. Further analysis of the TEM images reveals that Sn occupies predominately the middle row although significant exchange with Bi occurs similar to those also observed in bulk grown SnBi2Te4 nanoplates [13]. On the other hand, the Bi-rich SnBi4Te7 compound is ordered in the form of natural van Further evidence of the TSS in the SnBi2Te4 compound has been obtained from magnetotransport measurements. A non-linear Hall resistance [ Fig. 9(a)] indicates the presence of two types of carriers (electron-like). One of them with the highest mobility of 1260 cm 2 •V -1 •s -1 has a concentration of 6.9×10 12 cm -2 which is only a factor of ~2 smaller than the value of 1.37×10 13 cm -2 estimated from ARPES for the 2D TSS, attributed to the different band bending [30] caused by the Al capping which is added after ARPES for the transport measurements.
Based on the aforementioned, it is concluded that the 2D TSS probed by ARPES correlates well with the high mobility carriers revealed from Hall measurements.
Additional information is obtained from longitudinal magnetoresistance. A resistance dip near zero magnetic field B (< 0.25 T) appearing in both BꓕI and B||I configurations is attributed to a weak antilocalization (WAL) effect originating from the strong spin orbit coupling in this material. In general, the appearance of a dip in the B||I measurement is considered to be an indication [29,31,32] of a bulk contribution in addition to the contribution from the TSS.
Conclusions about the different contributions can be extracted from the values of the measured α and β prefactors. Α value of α ~ -0.5 indicates contribution from one 2D channel only, while α = -1 signifies the additive contribution of two independent 2D channels [29,40]. Although typically in the literature analysis is mainly based on the parameter α, the value of β gives important information too. The latter parameter measures the extent of TSS penetration inside the film [39]. Then, a large value of β ~ 1 indicates that there is a strong coupling between the top and bottom TSS leading to a single 2D TSS channel transport. In our films though, the measured β = 0.24 is rather small indicating that the two TSS contribute independently to magnetotransport, in which case, we would expect α ~ -1. However, the measured value of a is ~ -0.42, close to -0.5 typically valid for a one 2D channel contribution. It is therefore concluded that the whole film with d < lΦ consisting of two interfaces and one bulk contribution behaves as one 2D channel with α = -0.42 as also argued previously for Bi2Se3 [39].
The behaviour in our SnBi2Te4 films is similar to that obtained in thick (~50 nm) Bi2Te3 films [31,32]. Notably, for thinner Bi2Te3 films (~5 nm) a sole contribution from 2D TSS, acting as one channel, has been reported [31,51], suggesting that thinning SnBi2Te4 down to a few nm could be a viable route to isolate a pure 2D TSS transport.
It should be mentioned that in several materials, a transition from a WAL to a WL regime occurs leading to negative magnetoresistance at higher magnetic fields, due to enhanced disorder and lack of topological protection [52,53]. With rare exceptions [31,32,51], in TIs, including our SnBi2Te4 in the present work, such transition is absent, and the behavior is characterized by a zero-field dip followed by a parabolic behavior to higher fields. This is considered as evidence that there is sufficient topological protection of TSS in our films that prevents the crossover from WAL to WL regimes.