Topological states and phase transitions in Sb2Te3-GeTe multilayers

Abstract

Topological insulators (TIs) are bulk insulators with exotic 'topologically protected' surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb₂ Te₃ and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb₂ Te₃ -GeTe-Sb₂ Te₃ structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb₂ Te₃ -GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases.

Topological states and phase transitions in SbTe-GeTe multilayers

R A

P

Thuy-Anh Nguyen, Dirk Backes, Angadjit Singh, Rhodri Mansell, Crispin Barnes, David A. Ritchie, Gregor Mussler, Martin Lanius, Detlev Grtzmacher & Vijay Narayan

Topological insulators (TIs) are bulk insulators with exotic topologically protected surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI SbTe and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single SbTe-GeTe-SbTe structure.

Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a demonstrate that the SbTe

states as well as towards controlledly inducing various topological phases.

Topological surface modes

Topological insulators (TIs) are a recently emerged class of materials which are insulating in the bulk, but whose surface harbours topologically protected conducting modes1. The existence of the topological surface modes (TSMs) stems ultimately from the high spin-orbit coupling in TIs which inverts the conduction and valence bands. In other words, the band structure of the TI is topologically distinct from the ordinary band insulator (BI) and the TSMs arise because the band gap must close at a TI-BI interface, or even an interface between a TI and the vacuum2. Importantly, local perturbations (e.g., disorder) which do not alter the topological properties of the system cannot localise the TSMs, and this gives rise to their topological protection. The TSMs have various exotic properties such as a linear Dirac-like dispersion, and a well-dened helicity, i.e., spin and momentum vectors at xed angles to each other. These properties render them useful in a variety of settings such as low-power electronics and spin-based communication and computation. In addition, when TSMs couple to each other they are predicted to produce a very diverse phase diagram of novel topological phases35. In particular, in ref. 3 it was rst proposed that superlattices of alternating TI and BI layers can overall either be TIs or BIs depending on the specics of how the TSMs couple, and under certain conditions be Weyl semimetals6. Experimentally, there have been reports of TIs in superlattice structures including PbSe-Bi2Se3 structures7,8, Bi14Rh3I99, and Sb-Te binary systems10,11, although the crucial aspect of how the TSMs couple across the intervening layers remains unexplored. In this manuscript we investigate the low-temperature (low-T) electrical properties of molecular beam epitaxy (MBE)-grown bi-layer and tri-layer structures of Sb2Te3, a well-known TI12, and GeTe, a narrow band gap semiconductor that goes superconducting at very low T13,14. Intriguingly, our results indicate two-dimensional (2D) transport, indicating that the structures are dominated by the Sb2Te3-GeTe interface. Remarkably, we realise specic situations in which the tri-layer system has either a quadratically dispersive mode or three linearly dispersive Dirac-like modes. Based on very simple assumptions we argue that the two states are topologically distinct, thus suggesting Sb2Te3-GeTe heterostructures to be promising platforms to induce topological phase transitions and also realise multi-TSM systems3,4,15.

TSMs in TIs have been most clearly identied using angle-resolved-photoemission-spectroscopy16,17, although this technique is unable to probe the interior of materials, and thus has limited applicability in studying buried

SCIENTIFIC REPORTS

1

www.nature.com/scientificreports/

Figure 1. The multilayer structures that are investigated are schematically depicted in (a). In (b) we show the T-dependence of where, intriguingly, it is seen that the heterostructures have a lower than both of the parent materials. (c) The carrier concentrations in the multilayers are more than an order of magnitude greater than that of pure Sb2Te3 and this is a direct outcome of the proximity to the larger bandgap material GeTe. (measurements from multiple samples are shown for D1 and T1). In (d) the data shown in (b) is plotted as a 2D resistivity xx.

The right axis shows the measured resistance R. (e) Shows the ratio of xx in T1 and T2 to be 2.9, and that of D1 and T2 to be 2.5 at low T.

TSMs in structures of the type we report. Electrically, TSMs can be identied by observing quantum corrections to the conductivity at low T. The strong spin-orbit interaction in TIs engenders positive quantum corrections to in the form of weak antilocalization (WAL) at low T18 which manifests as a characteristic cusp in the magnetoresistance described by the Hikami-Larkin-Nagaoka (HLN) equation18:

2 2 2

Here xx indicates the longitudinal component of conductivity and the superscript 2D indicates that the equation is valid for a two-dimensional conducting sheet, B is the magnetic eld perpendicular to the 2D plane, is a parameter= 0.5 for each 2D WAL channel, e is the electronic charge, is Plancks constant divided by 2,

A is the

phase coherence length, and is the digamma function. In TI thin lms it is expected that =1 due to the top and bottom surfaces, although oen transport measurements in TI thin lms are consistent with 0.5, i.e., the existence of a single TSM19. There is a growing consensus that this is due to the interfacial disorder between the TI and substrate which destroys the bottom TSM. Importantly, this hinders progress towards understanding the interaction between TSMs. As an alternative, exfoliated TI structures have been used20 which are signicantly less prone to interfacial disorder, but oer considerably less control over the lm thickness. In this context, therefore, our approach of utilising MBE-grown multilayers is particularly promising in that it potentially overcomes both these limitations.

Results and Discussion

The wafer structures that we report here are schematically represented in Fig.1a. The rst is a double-layer structure with 11 nm of GeTe capped by 25 nm of Sb2Te3, henceforth referred to as D1. The second and third are three-layer Sb2Te3-GeTe-Sb2Te3 sandwich structures which we refer to as T1 and T2, respectively. In T1 each of the three layers is 15nm thick, and T2 consists of a relatively thick 69 nm GeTe layer between 11nm Sb2Te3 layers. The lattice mismatch of 2.5% between Sb2Te3 and GeTe is small enough to allow for coherent growth (see Methods). In addition, to benchmark our results, we have studied pure Sb2Te3 and GeTe lms of thickness 48nm and 34 nm, respectively. Figure1b shows the resistivity P vs T of Hall bar devices fabricated from the dierent wafers. The rst important fact to note is that, surprisingly, the multilayer structures are consistently less resistive than the pure samples, and closer in resistivity to Sb2Te3. Especially noteworthy in this context is that T2, which has the largest relative proportion of GeTe (76%), has the lowest and shows the strongest deviation from pure GeTe. These observations clearly indicate that the individual layers do not behave simply as independent resistors connected in parallel, but rather interact with each other. One possibility is that the band bending at the interface between GeTe (band gap 0.65 eV21) and Sb2Te3 (band gap 0.2 eV22) serves to draw and conne additional charge carriers into Sb2Te3, and thus enhance its conductivity. This notion is corroborated by the measured areal carrier densities in D1, T1 and T2 being over an order of magnitude greater than in Sb2Te3 (Fig.1c). Here we consider the areal rather than bulk carrier density since at low T the conduction in Sb2Te3 is largely through the

2 2 2 2

D

D

D

=

xx

xx

A A

xx ( B e eB eB

) (0) 2 ln 4

1

2 4 (1)

+

SCIENTIFIC REPORTS

2

www.nature.com/scientificreports/

Figure 2. (ac) Show the WAL characteristics for D1, T1 and T2, respectively. Also shown are ts to the HLN formula (Equation1). The traces are oset vertically for clarity. In (d) we observe that the rate of decoherencein T2 and Sb2Te3 is consistent with that expected due to inter-particle interactions, whereas in D1 and T1the rate of decoherence is higher. (e) The parameter which is a measure of the number of WAL channels contribute to the transport is seen to be 0.5 (corresponding to 1 WAL channel) for all the wafers except T2 in which is approximately 1.5, suggesting the presence of three 2D WAL channels. (f) At low-T all the wafers show a logarithmic increase in xx as is expected in 2D systems. It is conceivable that in T1 and T2 GeTe is showing hints of superconductivity at 0.35K, but this is unlikely to inuence the transport unless T is reduced signicantly.

TSMs and thus expected to be two-dimensional (2D)12. As a reference, the bulk carrier concentration in GeTe was measured to be 5.51026m3 which, when scaled by the thickness of GeTe is ~1019m2, is comparable with D1, T1 and T2. In Fig.1d we plot the 2D resistivity

t

xx , where t is the thickness of the lm, as a function of T: in order of increasing xx we nd T2, followed by T1 and Sb2Te3 which are very similar below 100K, followed by D1 and then GeTe. The strong dissimilarity between the characteristics of T1 and T2 suggests that there is more physics underlying the heterostructures than just band bending. We return to this fact aer having inspected the low T electrical characteristics.

In Fig.2ac we show the low-eld magnetoconductivity

+

/( )

xx xx xx xy

1/2 23, but instead is very well-described by the HLN formula (Equation1) with

A decays as a power law ~T where the exponent is plotted in Fig.2d. Apart from Sb2Te3 and T2, all the structures are observed to undergo decoherence signicantly faster than the = 0.5 expected in 2D Nyquist scattering due to inter-particle interactions24. Figure2e shows that is 0.5 for Sb2Te3, T1 and D1, but is 1.5 for T2 (see Supplementary Figure S2 for error estimates on ). Recalling that

gets a contribution of 0.5 for each 2D WAL state, we conclude that Sb2Te3, T1 and D1 have one 2D mode each while T2 has three. While this is consistent with T2 being the least resistive sample under investigation (Fig.1), there are two important points to consider: First, as discussed earlier in the manuscript, it is expected that 0.5 for Sb2Te3 since the TSM at the substrate interface is destroyed. However, unexpectedly we nd that even in D1, in which the Sb2Te3 film is grown on a well-lattice-matched MBE-grown GeTe film, a second TSM is not observed. Second, the occurrence of three 2D modes in T2 agrees with the three TI-BI interfaces (apart from the TI-substrate interface), but this is in apparent contradiction with the observation of only one 2D mode in T1. In a previous study it was found that bare GeTe thin lms with t=34nm have 114, i.e., one WAL mode on each side of the lm, but GeTe has been intentionally omitted from this plot since it shows superconducting correlations below T 1.5K which strongly inuence the HLN ts14.

In the following we investigate the precise role played by GeTe in these heterostructures. First, in order to check whether the tendency of GeTe to become superconducting at very low T has any inuence on the transport properties of the multilayer structures we inspect the T-dependence of xx for T < 10 K in Fig.2f. We nd clearly that dxx/dT is negative below 3K, qualitatively similar to bare Sb2Te3 and in strong agreement with our hypothesis that transport in the multilayers is largely conned to Sb2Te3. There may be a maximum in T1 and T2 around 0.35K, but even if this does signal the onset of superconductivity, it is unlikely that this perceptibly aects the transport. Indeed, within the picture that the band gaps of Sb2Te3 and GeTe conspire to inject charges from the latter to the former, it is evident why superconductivity is not observed in these samples: the superconducting temperature Tc of GeTe is a monotonically increasing function of its carrier concentration13 and thus reducing the chemical potential in GeTe, as is achieved when placing it in close proximity to Sb2Te3, will only further suppress

and

A as t parameters. We nd that

2 2 of D1, T1 and T2, respectively, and observe a pronounced cusp-like minimum around B = 0 T. Here xy is the Hall resistivity. The signal, expectedly, is not consistent with bulk WAL (see Supplementar y Figure S1) where

^

B B

( ) (0)

xx xx xx

SCIENTIFIC REPORTS

3

www.nature.com/scientificreports/

Figure 3. The high-eld magnetoresistance of Sb2Te3 (a) and T2 (c) is qualitatively dierent from D1 and T1 (b), with the latter being quadratic in B over the entire eld range explored. Moreover, it is observed in (b) that the magnetoresistance characteristics of D1 and T1 are almost identical, thus suggesting similar underlying physics. The insets in (b,c) show the magnetoresistance as a function of

B2, clearly bringing out the contrasting behaviours of T1/D1 when compared to T2. The observed linear magnetoresistance in Sb2Te3 and T2 is a commonly observed feature in materials with a linear dispersion relation.

Tc. At the typical carrier concentrations obtained in the bare GeTe samples Tc0.1K14, and this essentially precludes the possibility of observing superconductivity at the temperatures our experiments are performed at (0.3K). Yet, the strong variation of xx between the dierent multilayer structures clearly indicates that GeTe is not playing a passive role in the transport. This is especially seen in the contrast between the tri-layer structures T1 and T2: it is seen that xx(T1) 3xx(T2), corresponding almost exactly with the ratio of the number of 2D modes as given by the HLN formula (Fig.1d). Since the data are clearly indicative of missing WAL modes in T1, we conjecture that certain TSMs in the measured heterostructures hybridise25,26 and become gapped. Importantly, this mechanism would undermine their topological nature and modify the 2D band dispersion from being linear, Dirac-like, to being parabolic near the band minimum.

To investigate the proposed scenario further we study the high-field magnetoresistance characteristics. Figure3a exemplies a commonly observed feature in TIs (or Dirac materials, to be more precise), namely a large and linear magnetoresistance19,2729. There are various circumstances which can eect such behaviour including very large carrier concentrations19, transport in heavily disordered conductors30, and the exclusive occupancy of the lowest Landau level31,32. The rst two of these are not applicable to our experimental system since the carrier concentration, which is similar between the multilayers, clearly does not inuence the nature of magnetoresistance (Fig.3), and the level of disorder in MBE-grown lms is expected to be small. On the other hand, the third criterion is known to be experimentally more accessible in Dirac materials than those with a parabolic dispersion19. That is, in our experimental system we can directly correlate the presence or absence of large, linear magnetoresistance to the presence or not of Dirac-like states. Thus, a critical conclusion we arrive at from Fig.3(a,b) is that D1 is not, as one would naively expect, simply a TI layer on a lattice-matched, insulating substrate, but has at least one gapped state which dominates the magnetoresistance at high elds. Since the Sb2Te3 layer is signicantly thicker than 6 nm, the approximate thickness below which the top and bottom TSMs are known to hybridise in Sb/Bi-based TIs25,33,34 it is unlikely that the top TSM has developed a gap. Which then implicates the lower TSM, but raises the question as to what it hybridises with. Recalling that 34 nm thick GeTe harbours two surface states14, our data strongly points in favour of the 2D modes on either side of the 11nm thick GeTe layer hybridising with each other. This is also consistent with the fact that T1 has only one 2D WAL mode where, as per the previous arguments, the two embedded TSMs hybridise across the 15 nm thick GeTe layer. This idea is rmly reinforced by the data in Fig.3b where we nd that the magnetoresistance of D1 and T1 agree quantitatively, thus indicating similar underlying physics. Of particular interest in this regard is the fact that in T1, both hybridising states are topological in nature, but in D1, the bottom state is necessarily not topological (but Dirac-like35). The hybridisation picture also provides an estimate of the wavefunction extent outward from the interface. Since hybridisation is possible across a 15nm thick GeTe layer, we can conclude that the wavefunctions on either side have signicant overlap and therefore must have a spatial extent of 7.5nm. Clearly, however, the wavefunction is not symmetric about the GeTe-Sb2Te3 interface since its extent in Sb2Te3 is 5.5nm. Such asymmetry is not unexpected being dependent on factors such as the band osets between the dierent materials and precise form of the interface conning potential.

The conclusion that the buried TSMs in T1 hybridise across the GeTe layer can also be arrived at by contrasting the behaviours of T1 and T2: Fig.2e suggests that none of the TSMs in T2 hybridise and this is buttressed by the observation in Fig.3c that xx vs B is linear above 5 T. Therefore, since the TSMs anking the Sb2Te3 layer in T2 do not hybridise, they must not in T1 either where the Sb2Te3 layers are thicker. Thus the only possibility is that we are observing the hybridisation of TSMs across the GeTe layer, i.e., between TSMs associated with dierent TI layers. To the best of our knowledge this is the rst experimental demonstration of hybridisation between TSMs not related by symmetry. More importantly, our data evidences a critical thickness of GeTe at which the Sb2Te3-GeTe-Sb2Te3 heterostructure undergoes a topological phase transition, thus indicating it to be a promising system in which to study topological phase transitions15,3638.

SCIENTIFIC REPORTS

4

www.nature.com/scientificreports/

But then what of the remaining TSM on the top surface of D1 and T1? Being gapless, this mode will dominate the low T transport characteristics, but the high-eld transport will be dominated by the non-Dirac-like modes which have a dramatically lower magnetoresistance. Notably, it was shown in ref. 39. that the size of the WAL eect should reduce as the gap in the surface states widens relative to the Fermi energy, i.e, we do not expect the gapped states to contribute signicantly to the measured WAL. In this context, Fig.1e where we nd the ratios xx(T1)/xx(T2) and xx(D1)/xx(T2) to be constant below T 30 K, sheds light on the relevant energy scales.

Both the ratios are ~3, consistent with the ratio of the number of 2D modes. This temperature scale corresponds to 2.6 meV, which is two orders of magnitude smaller than the band gap of Sb2Te3, and thus the decrease in xx(T1)/xx(T2) and xx(D1)/xx(T2) with increasing T most likely corresponds to the activation of the hybridised TSMs. We, therefore, have obtained a crude measure of the hybridisation gap to be about 2.6meV. Not only does this provide an experimentally measured parameter useful for simulations of TI-BI superlattices, it also shows the experimental system to be a versatile platform to realise and manipulate multiple TSMs. In conclusion, we have demonstrated a phase transition in the topological properties of Sb2Te3-GeTe-Sb2Te3 structures as the thickness of the GeTe layer is varied. We have demonstrated this system to be a close realisation of the model proposed by Burkov and Balents3 to induce novel topological phases. We have provided the rst experimental demonstration of hybridisation between TSMs associated with dierent TIs and shown the experimental system to be potentially exploitable in applications requiring multiple TSMs in parallel.

The GeTe and Sb2Te3 lms were grown on Si(111) wafers using MBE. Before the deposition, the Si substrates were cleaned by the HF-last RCA procedure to remove the native oxide and passivate the surface with hydrogen. Subsequently, the substrates were heated in-situ at 750C for 20min to desorb hydrogen atoms from the surface. The Ge, Sb, and Te material uxes were generated by eusion cells with temperatures of 1250C, 440C, and 330C, respectively. For all samples the Te shutter was opened 2seconds before the Ge or Sb shutter in order to saturate the Si substrate surface with Te. During the entire growth process the substrate was set at 280C. The lattice parameters of Sb2Te3 and GeTe are, respectively, aSb2Te3= 4.26 and aGeTe= 8.32, and thus the lattice mismatch at 2:1 correspondence is (2aSb2Te3aGeTe)/aGeTe=2.5%.

Device fabrication and electrical measurements. We used photolithography and argon ion milling to fabricate Hall bar devices of dimensions 100 m 1050 m, aer which Ti/Au ohmic contacts were deposited using a li-o process. The devices were packaged and measured in a He 3 cryostat with a base T=280mK, and equipped with a 10 T superconducting magnet. Resistance and Hall measurements were made in a standard four-terminal setup with an excitation current Iex=0.11A at frequency f=17Hz.

Data availability. Supporting data for this paper is available at the DSpace@Cambridge data repository (http://dx.doi.org/10.17863/CAM.16)

References

1. Hasan, M. & Kane, C. Topological insulators. Rev. Mod. phys. 82, 3045 (2010).2. Moore, J. The birth of topological insulators. Nature 464, 194 (2010).3. Burkov, A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).4. Li, X., Zhang, F., Niu, Q. & Feng, J. Superlattice valley engineering for designer topological insulators. Sci. Rep. 4, 6397 (2014).5. Owerre, S. Weyl semimetal in ultra-thin lm of topological insulator multilayer. http://arxiv.org/abs/1601.03707 (2016).6. Hasan, M., Xu, S.-Y. & Bian, G. Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks. Phys. Scripta T164, 014001 (2015).

7. Nakayama, K. et al. Manipulation of topological states and the bulk band gap using natural heterostructures of a topological insulator. Phys. Rev. Lett. 109, 236804 (2012).

8. Sasaki, S., Segawa, K. & Ando, Y. Superconductor derived from a topological insulator heterostructure. Phys. Rev. B (R) 90, 220504 (2014).

9. Rasche, B. et al. Stacked topological insulator built from bismuth-based graphene sheet analogues. Nat. Mater. 12, 422 (2013).10. Takgaki, Y., Giussani, A., Tominaga, J., Jahn, U. & Calarco, R. Transport properties in a Sb-Te binary topological-insulator system. J. Phys.: Condens. Matter. 25, 345801 (2013).11. Takagaki, Y., Jahn, U., Giussani, A. & Calarco, R. Multiple state transport deduced by weak antilocalization and electron-electron interaction eects in SbxTe1x layers. J. Phys.: Condens. Matter 26, 095802 (2014).

12. Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single dirac cone on the surface. Nat. Phys. 5, 438 (2009).13. Hein, R. A., Gibson, J. W., Mazelsky, R., Miller, R. C. & Hulm, J. K. Superconductivity in germanium telluride. Phys. Rev. Lett. 12, 320 (1964).

14. Narayan, V., Nguyen, T.-A., Mansell, R., Ritchie, D. & Mussler, G. Interplay of spin-orbit coupling and superconducting correlations in germanium telluride thin lms. Phys. Status Solidi RRL 10, 253 (2016).

15. Tominaga, J., Kolobov, A. V., Fons, P., Nakano, T. & Murakami, S. Ferroelectric order control of the dirac-semimetal phase in GeTe-Sb2Te3 superlattices. Adv. Mater. Interfaces 1, 1300027 (2014).

16. Hsieh, D. et al. A topological Dirac insulator in a quantum spin hall phase. Nature 452, 970 (2008).17. Hsieh, D. et al. Observation of unconventional quantum spin textures in topological insulators. Science 323, 919 (2009).18. Hikami, S., Larkin, A. I. & Nagaoka, Y. Spin-orbit interaction and magnetoresistance in the two-dimensional random system. Prog. Theor. Phys. 63, 707 (1980).

19. Veldhorst, M. et al. Magnetotransport and induced superconductivity in Bi based three-dimensional topological insulators. Phys. Status Solidi RRL 7, 26 (2013).

20. Checkelsky, J., Hor, Y., Cava, R. & Ong, N. Bulk band gap and surface state conduction observed in voltage-tuned crystals of the topological insulator Bi2Se3. Phys. Rev. Lett. 106, 196801 (2011).

21. Di Sante, D., Barone, P., Bertacco, R. & Picozzi, S. Electric control of the giant Rashba eect in bulk GeTe. Adv. Mater. 25, 509 (2013).22. Madelung, O., Rssler, U. & Schulz, M. O. Antimony telluride (Sb2Te3) band structure, energy gap in Non-Tetrahedrally Bonded Elements and Binary Compounds I (Springer-Verlag, Berlin Heidelberg 1998).

23. Kawabata, A. Theory of negative magnetoresistance i. application to heavily doped semiconductors. Journ. Phys. Soc. Japan 49, 628 (1980).

SCIENTIFIC REPORTS

5

www.nature.com/scientificreports/

24. Altshuler, B., Tagliacozzo, A. & Tognetti, V. Quantum phenomena in mesoscopic systems (IOS Press, Amsterdam 2003).25. Zhang, Y. et al. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat. Phys. 6, 584 (2010).

26. Murakami, S. Hybridization of Topological Surface States and Emergent States, in Topological Insulators: Fundamentals and Perspectives (Wiley-VCH Verlag GmBH & Co. KGaA, Weinheim, Germany 2015).

27. Qu, D.-X., S, H. Y., Xiong, J., Cava, R. & Ong, N. Quantum oscillations and hall anomaly of surface states in the topological insulator Bi2Te3. Science 329, 821 (2010).

28. Tang, H., Liang, D., Qiu, R. L. J. & Gao, X. P. A. Two-dimensional transport-induced linear magneto-resistance in topological insulator Bi2Se3 nanoribbons. ACS Nano 5, 7510 (2011).

29. Wang, X., Du, Y., Dou, S. & Zhang, C. Room temperature giant and linear magnetoresistance in topological insulator Bi2Te3 nanosheets. Phys. Rev. Lett. 108, 266806 (2012).

30. Parish, M. & Littlewood, P. Non-saturating magnetoresistance in heavily disordered semiconductors. Nature 426, 162 (2003).31. Abrikosov, A. Galvanometric phenomena in metals in the quantum limit. Sov. Phys. JETP 29, 746 (1969).32. Abrikosov, A. Quantum magnetoresistance. Phys. Rev. B 58, 2788 (1998).33. Li, Y.-Y. et al. Intrinsic topological insulator Bi2Se3 thin lms on si and their thicknes limit. Adv. Mater. 22, 4002 (2010).34. Jiang, Y. et al. Landau quantization and the thickness limit of topological insulator thin lms of Sb2Te3. Phys. Rev. Lett. 108, 016401 (2012).

35. Krempask, J. et al. Surface versus bulk contributions to the giant Rashba splitting in the ferroelectric -GeTe(111) semiconductor. http://arxiv.org/abs/1503.05004 (2016).

36. Kim, J., Kim, J. & Jhi, S.-H. Prediction of topological insulating behavior in crystalline Ge-Sb-Te. Phys. Rev. B (R) 82, 201312 (2010).37. Sa, B., Zhou, J., Sun, Z., Tominaga, J. & Ahuja, R. Topological insulating in GeTe/Sb2Te3 phase-change superlattice. Phys. Rev. Lett. 109, 096802 (2012).

38. Kim, J., Kim, J., Kim, K.-S. & Jhi, S.-H. Topological phase transition in the interaction of surface dirac fermions in heterostructures. Phys. Rev. Lett. 109, 146601 (2012).

39. Lu, H.-Z., Shi, J. & Shen, S.-Q. Competition between weak localization and antilocalization in topological surface states. Phys. Rev. Lett. 179, 076801 (2011).

Acknowledgements

T.-A.N., D.B., D.A.R. and V.N. acknowledge funding from the Leverhulme Trust, UK, T.-A.N., D.B., A.S., R.M., C.B., D.A.R. and V.N. acknowledge funding from EPSRC (UK). G.M., M.L. and D.G. acknowledge nancial support from the DFG-funded priority programme SPP1666. V.N. acknowledges useful discussions with Michael Pepper.

Author Contributions

T.-A.N., D.B. and V.N. performed the experiments, T.-A.N., D.B., R.M. and A.S. fabricated the devices, G.M., M.L. and D.G. grew the samples, V.N. wrote the paper with inputs from R.M., G.M., D.B. and T.-A.N. All the authors reviewed the manuscript.

Additional Information

Supplementary information accompanies this paper at http://www.nature.com/srep

Competing nancial interests: The authors declare no competing nancial interests.

How to cite this article: Nguyen, T.-A. et al. Topological states and phase transitions in Sb2Te3-GeTe multilayers. Sci. Rep. 6, 27716; doi: 10.1038/srep27716 (2016).

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

SCIENTIFIC REPORTS

6