# Fileset

[s41467-022-33643-9.pdf](https://mdr.nims.go.jp/filesets/d26f57bb-62fd-4070-9e4f-424ee545dd5a/download)

## Creator

Su Kong Chong, Lizhe Liu, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Taylor D. Sparks, Feng Liu, Vikram V. Deshpande

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Emergent helical edge states in a hybridized three-dimensional topological insulator](https://mdr.nims.go.jp/datasets/aa1448b1-4055-4a81-9b17-87f2520a82d1)

## Fulltext

Emergent helical edge states in a hybridized three-dimensional topological insulatorArticle https://doi.org/10.1038/s41467-022-33643-9Emergent helical edge states in a hybridizedthree-dimensional topological insulatorSu Kong Chong 1 , Lizhe Liu 2, Kenji Watanabe 3, Takashi Taniguchi 3,Taylor D. Sparks 2, Feng Liu 2 & Vikram V. Deshpande 1As the thickness of a three-dimensional (3D) topological insulator (TI)becomes comparable to the penetration depth of surface states, quantumtunnelingbetween surfaces turns their gaplessDirac electronic structure into agapped spectrum.Whether the surface hybridization gap can host topologicaledge states is still an open question. Herein, we provide transport evidence of2D topological states in the quantum tunneling regime of a bulk insulating 3DTI BiSbTeSe2. Different from its trivial insulating phase, this 2D topologicalstate exhibits a finite longitudinal conductance at ~2e2/h when the Fermi levelis aligned within the surface gap, indicating an emergent quantum spin Hall(QSH) state. The transition from the QSH to quantum Hall (QH) state in atransverse magnetic field further supports the existence of this distinguished2D topological phase. In addition, we demonstrate a second route to realizethe 2D topological state via surface gap-closing and topological phase transi-tion mechanism mediated by a transverse electric field. The experimentalrealization of the 2D topological phase in a 3D TI enriches its phasediagram and marks an important step toward functionalized topologicalquantum devices.Despite the well-studied topological surface states in 3D TIs1, theirpeculiar gapped surface states in the presence of broken symmetryhave still been a subject of intense studies for exotic topologicalquantum states. Even in the absence of symmetry breaking, the strongcoupling between the topological surface states in a 3D TI can be amedium to realize interesting states, e.g. the quantum spin Hall (QSH)effect2–4. Such 2D TIs host a surface gap with inverted bands initiatedvia hybridization of the surface states of the parent 3D TIs. From thetheoretical perspective, the gapped surface spectrum exhibits anoscillatory behavior alternating between topologically trivial and non-trivial 2D states as a function of layer thickness2–4. Although thehybridization gap has been systematically probed in prototypical 3DTIs Bi2Se3 by angle-resolved photoemission spectroscopy (ARPES)5,6,and Sb2Te3 by scanning tunneling microscopy7, the anticipated 2D TIphases and theirQSH states await to beconfirmed electrically indevicemeasurements. Previous transport measurements in the hybridizationregime were restricted by disorder and inhomogeneity in TI thin filmspreventing the observation of the surface hybridization gap8,9. Also,the crystal quality of the TI films limited the mobility which con-strained the mean free path to microscopic length scales10. From thetechnical point of view, electrical measurements can resolve the pre-vailing small energy gap scales beyond the resolution limit of ARPES5,6.Band inversion through a gap-closing and reopening mechanismis a hallmark of a topological phase transition (TPT)1. In addition to thelayer-dependent topological phases varying with the thickness of 3DTIs, a TPT can be controllably induced through band distortions by in-plane or out-of-plane magnetic field11,12, strain, or pressure13,14, andelectric field7,15–18. The external in-plane magnetic field can induce gap-closing by oppositely shifting the two surface bands11. However, astrongmagnetic field is required to fully close the surface gap which isimpractical for most applications. Another mechanism with which totransform the band topology is by distorting the crystal lattices, suchas strain or pressure-induced TPTs in ZrTe513 and BiTeI14, respectively.Finally, the most preferred route is a TPT driven by perpendicularReceived: 12 May 2021Accepted: 22 September 2022Check for updates1Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA. 2Department of Materials Science and Engineering, University ofUtah, Salt Lake City, UT 84112, USA. 3National Institute for Material Science, Tsukuba, Japan. e-mail: sukong.chong@utah.edu; vdesh@physics.utah.eduNature Communications |         (2022) 13:6386 11234567890():,;1234567890():,;http://orcid.org/0000-0002-2016-9802http://orcid.org/0000-0002-2016-9802http://orcid.org/0000-0002-2016-9802http://orcid.org/0000-0002-2016-9802http://orcid.org/0000-0002-2016-9802http://orcid.org/0000-0001-5111-0750http://orcid.org/0000-0001-5111-0750http://orcid.org/0000-0001-5111-0750http://orcid.org/0000-0001-5111-0750http://orcid.org/0000-0001-5111-0750http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0001-8020-7711http://orcid.org/0000-0001-8020-7711http://orcid.org/0000-0001-8020-7711http://orcid.org/0000-0001-8020-7711http://orcid.org/0000-0001-8020-7711http://orcid.org/0000-0002-3701-8058http://orcid.org/0000-0002-3701-8058http://orcid.org/0000-0002-3701-8058http://orcid.org/0000-0002-3701-8058http://orcid.org/0000-0002-3701-8058http://orcid.org/0000-0001-7681-0833http://orcid.org/0000-0001-7681-0833http://orcid.org/0000-0001-7681-0833http://orcid.org/0000-0001-7681-0833http://orcid.org/0000-0001-7681-0833http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33643-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33643-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33643-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33643-9&domain=pdfmailto:sukong.chong@utah.edumailto:vdesh@physics.utah.eduelectric fields, which can realize a functional all-electrical topologicalswitch between normal and inverted gap states by controlling theelectric potential between top and bottom surfaces16,17.In this work, we study themagneto-electrical transport propertiesof the ultrathin BiSbTeSe2 3D TIs in the intersurface hybridizationregime. We identify the normal insulator and 2D topological insulatorphases as indicated by their distinct responses to temperature andmagnetic field. We further demonstrate that these trivial and topolo-gical insulating phases can be reversibly tuned by a perpendicularelectric field through a gap-closing mechanism. The highly tunabletopological phases enrich the phase diagram of 3D TIs in the 2Dthin limit.ResultsTopological phase diagramWe first perform the first-principles calculations for the intersurfacehybridized Bi0.7Sb1.3Te1.05Se1.95 (hBSTS) 3D TI. The hybridizationbetween the top and bottom surface states of the BSTS creates atunneling gap. The gap sizes extracted from the calculated bandstructures for BSTS thickness ≤10 quintuple layers (QL), where 1QL≈1 nm19, are shown in Supplementary Figs. 1, 2. The parity of the hybri-dizationgap is evaluated in SupplementaryTable 1. A negative parity ofthe gap occurs when the hole sub-band is at a higher energy level thanthe electron sub-band, and thus the total parity reads negative, ana-logous to the description of the negative gap due to the bulk bandinversion in 3D TIs. Similar to the binary Bi2Se3 and Bi2Te3 3D TIcompounds2–4, the parity of BSTS hybridization gap exhibits an oscil-latory pattern, indicating switching between the band and QSH insu-lators via thickness modulation as shown at the zero-field limitin Fig. 1a.The hBSTS exhibits unique electromagnetic responses. In a per-pendicular magnetic field, the surface states’ hybridization essentiallylifts the degeneracy of the N =0 surface Landau level (LL) and causes asplitting into an electron and hole-like N =0 sublevels20. The hybridi-zation gap can thus be defined as the energy difference between thetwo sublevels, denoted by E0. The analytical formula of E0 reveals alinear relationwithmagneticfield, expressed as E0 = eC0 +eB_eC2 � μBgB221,where μB and g are the Bohr magneton and effective g-factor; eC0 andeC2 are the parameters related to the constant and quadratic terms ofthe topological surface states’ Hamiltonian, and the third termdescribes the Zeeman energy splitting of surface bands (Fig. 1b).Meanwhile, in the presence of an external perpendicular electric field,the surface states’Hamiltonian is againmodified by the electric field asHU = eEz � z15. The external electric field can induce a Rashba-typesplitting in the surface band15,16 due to the structure inversion asym-metry in the gapped surface states, resulting in a shrinkage of thehybridization gap (Fig. 1b).Combining the responses of the hybridization gap to magneticand electric fields, we construct phase diagrams for hBSTS with trivialandnon-trivial topological phases, basedonanalytical formulations, asillustrated in Fig. 1a. The figures investigate and compare the switchingof topological phases in thickness range with distinct topology. ForhBSTS with an inverted surface gap, both perpendicular magnetic andelectric fields are accountable for the termination of the QSH gap bybreaking the time-reversal and inversion symmetries, respectively. Thecritical switching fields, denoted as Bc and Ec, draw the maximummagnetic and electric fields for the QSH state at which boundaries thesurface gap vanishes. In contrast, the normal surface hybridization gapreveals noteworthy phase switching only in electric field, while the out-of-plane magnetic field results in monotonic widening of the surfacegap21. The closure of trivial gap and reopening of inverted gap ascontrolled by electric field is another route to realize a QSH state.Hybridization gapExperimentally we have employed three differentmethods to evaluateenergy gaps in the hBSTS. The first method is thermal activation(QL)ac+1-109bGrhBNh-BSTS Von/offbsstss-0 LL+0 LLFig. 1 | Topological phase transitions. a Topological phase diagrams for parity ofthe surface hybridization gap modulated by external magnetic and electric fieldsacting perpendicular to the c-axis plane of the variable thickness hBSTS. The redandblue color codes represent theopposite signofparity as a representation of thenormal and inverted surface hybridization gaps, respectively. The zero-field gapparity is determined by DFT. The diagrams are drawn based on the Hamiltonian oftopological surface states HSOC under distortions of magnetic HZ and electric HUfields. b Surface band structure of the hBSTS and its evolution under the externalmagnetic and electric fields. The zeroth LLs bands reside on the surface band edgesare labeled, while the higher order LLs are omitted for simplicity. The transverseelectric field shifts the top and bottom surface bands and results in the Rashba-likesplitting as the illustration. c Schematic of an electric field controlled topologicaltransistor device based on an hBSTS in a vdW dual-gating configuration.Article https://doi.org/10.1038/s41467-022-33643-9Nature Communications |         (2022) 13:6386 2energy by fitting the temperature dependent conductance. Figure 2ashows the four-terminal resistance (Rxx) as a function of back gatevoltage (Vbg) measured at different temperatures for a 9 nm hBSTS.The amplification of Rxxpeak with the decrease in temperature impliesan insulating state developed at charge neutrality point (CNP) due tothe intersurface hybridization. The inset of Fig. 2a displays the Gxx (=1/ρxx) data taken at the CNP on an Arrhenius plot, where two thermallyactivated conductance slopes corresponding to the bulk (>100K) andsurface activation (<100K) gaps are observed. Fitting of the secondslope to the activation relation Gxx =G0xx expð�EA=2kBTÞ22 yields asurface activation energy (EA) of ~3meV. The second method is toprobe the non-linear current–voltage characteristics bymeasuring thedifferential conductance (dI/dV). Figure 2b (inset) displays a dI/dVmapas functions of bias voltage (Vb) and Vbg for the 9 nm hBSTS. As the Vbgsweeps across the CNP, the dI/dV reaches an overall minimum, whichelucidates the nature of the surface gap. The diamond-shaped featurearises from charge transport across the surface states when the che-mical potential is aligned to or detuned from the hybridization gap atthe CNP23. A tunneling gap of ~16meV is determined from the dI/dVversusVb plot (Fig. 2b) across the centerminimum. The third approachis to determine the chemical potential relation, μ(n), by integrating thereciprocal quantum capacitance, 1/CQ, with respect to charge density(n)24. The capacitance dip at the CNP (n ≈0/cm2) (Fig. 2c) indicates aminimum density of state (DoS) corresponding to the insulating state.The μ(n) plotted in Fig. 2c reveals a step feature, where the step heightof ~21meV gives the hybridization gap for the 9 nm hBSTS.The hybridization gap sizes as a function of hBSTS flake thicknessextracted from the three methods are summarized in Fig. 2d. Thedetails of the layer-dependent hybridization gap analyses are pre-sented in Supplementary Fig. 3–6. We note that the thermal activationis often smeared by disorder potential fluctuation, resulting in a muchsmaller activation energy gap than the actual surface gap especiallywhen gap size is comparable to the disorder25. Despite varying values,these threemethods reveal the same trendof nearly exponential decaywith the increase of hBSTS thickness. The hybridization gap can thusbe approximated by the relation as 4h / e�λd26, where the character-istic length (λ) is fitted to ~0.44±0.02 – 0.66±0.01 nm−1 for the threeapproaches. This exponential dependence confirms the single-particlegap nature by excluding the predicted many body effects, such astopological excitonic states in the overlapped thickness range, as theyare less sensitive to the change in film thickness27. Furthermore, ourDFT calculations (Supplementary Fig. 1) based on the molecularstructure of BSTS, as depicted in Fig. 2d, are in good agreement withour experimental trend, further verifying its single-particle origin. Wenote that ourmeasured single-particle tunneling gap of hBSTS crossesover to the 3D limit at a larger thickness than the previouslymeasuredcrossover thickness in Bi2Se35. Such discrepancy can be explained bythe resolution limit of ARPES in resolving gap size of the order of meVenergy scale. A more detailed triggering of the hybridization gap inBi2Se3 using a tight-binding model28 resolves the exponentially decayof the hybridization gap at thickness beyond 6QL. Sub-meV hybridi-zation gaps were also detected in 12–17 nm Bi2Se3 using phase-coherent transport9.Normal and inverted gapsWehave noted two inverted surface gap regimes at hBSTS thickness of9 QL (<10meV) and 5–6 QL (30–40meV), based on our DFT calcula-tions of the surface gap topology (Supplementary Table 1). Thetransport properties in the first inverted regime are studied. Differentfrom the monotonically increasing Rxx for the 9 nm hBSTS, the 10 nmFig. 2 | Probinghybridizationgap. aRxx versusVbgplots atdifferent temperatures.Inset in (a) is an Arrhenius plot of Gxx versus T −1 for Vbg fixed at the CNP. b dI/dVversus Vb curve at insulating region (Vbg~ −1.5 V). Inset in (b) is a color map of dI/dVas functions of bias voltage (Vb) and Vbg. c C and μ(n) as a function of n induced byVbg with Vtg fixed at the overall CNP. The data in (a–c) were collected on the same9nm hBSTS device. Inset in (c) is an optical image of an 8 nm hBSTS vdWheterostructure device. Scale bar in (c) inset is 10 μm. d Hybridization gap (Δh)obtained from the three different approaches plotted in log scale as a function ofBSTS flake thickness. Error bars in (d) are the standard deviation from the fittings.The dashed line in (d) is the Δh extracted from our DFT calculations. Inset in (d) is aschematic of a hybridized surface band.Article https://doi.org/10.1038/s41467-022-33643-9Nature Communications |         (2022) 13:6386 3sample shows Rxx maximum saturating at ~12 kΩ (~h/2e2) at tempera-ture below 50K. This weak temperature response in the 10 nm hBSTSat low temperature suggests a finite conductance state existing/developing in the hybridization gap29. The full data set of Rxx at alltemperatures for the 9 nm and 10 nm hBSTS as presented in colormaps of Fig. 3a(i) and (ii), respectively, further elaborate their distincttemperature dependence behaviors. Figure 3b compares the gate-dependence of Rxx at temperature of 1.5 K for the 9 nm and 10 nmhBSTS. The Rxx reaches amaximum value of ~500 kΩ (~h/0.05e2) as thechemical potential is tuned into the surface gap, indicating a normalinsulating state for the 9 nm hBSTS. Contrary to the strong resistivesignal, the 10 nm hBSTS exhibits a finite resistance of ~h/2e2 within thehybridization gap regime as indicated by its dI/dV color map insertedin the figure. This again supports the inverted natureof the surface gapfor the 10 nm hBSTS. We further show that the two-terminal and non-local resistances measured in different configurations agree with theexpected values for helical edge states derived from theLandauer–Buttiker formalism30 (Supplementary Fig. 7 and Supple-mentary Table 3). Similar observations are reproduced in an additional10 nm hBSTS device (Supplementary Fig. 8). However, we note thatsimilar transport features were not observed in the second invertedsurface gap regime (5–6QL) as identified by our DFT calculations. Onepossible reason is the significant reduction of themobility below 7 nm,thus shortening the mean free path and obscuring the transport sig-nature for the 2D topological phase. A more complex device config-uration as implemented in monolayer WTe210 will be needed to clarifythe QSH phase in the second inverted regime.To quantitatively evaluate the bulk surface and edge transport, weconstruct a simple conductance model by considering the total con-ductance as a parallel sum of the surface and edge conductance,Gxx =Gsurf +Gedge =1ρsurf+ 1ρedge. The surface resistivity (ρsurf) exhibits athermally activated behavior with temperature as ~exp(αT), whereasthe edge resistivity (ρedge) will saturate in the quantum limit of ~h/2e2 atsufficiently low temperature. Since the edge channel is absent in thenormal gap, the total resistivity for 9 nm hBSTS can be simplified toρxx 9nmð Þ=ρsurf . Thus, the total resistivity for 10 nm hBSTS can beapproximated to the relation as 1ρxx 10nmð Þ≈1ρxx 9nmð Þ +1ρedge. To verify thisrelation, we plot the ρedge as a function of temperature as inserted inFig. 3a. Figure 3a shows excellent quantization of the edge con-ductance at a value of h/2e2 in accordance with the quantum spin Hallstate. This analysis also shows that the quantization of ρedge persists upto 20K, indicating a QSH gap of ~2meV for the 10 nm hBSTS. We notethat this QSH gap is smaller than the surface hybridization gapFig. 3 | Normal and inverted gaps. a Rxx versus temperature for the 10 nm and9 nm hBSTS. Error bars in (a) are the standard deviation of the extracted Rxx values.Inset in (a) is ρedge calculated for the 10 nmhBSTSas a functionof temperature. Thehorizontal dashed line corresponds to h/2e2. Right panels in (a) are color maps ofRxx as functions of T and Vbg for the (i) 9 nm and (ii) 10 nm hBSTS. Unit of the Rxx iskΩ. Dashed lines in the color maps trace the CNPs at different temperatures. b Rxxversus Vbg–VD for the 10 nm and 9 nm hBSTS. Inset in (b) is a color map of dI/dV asfunction of Vb and Vbg for the 10nm hBSTS. (i) Plots σxx and σxy versus Vbg at themagnetic field of 18 T for the (c) 9 nm and (d) 10 nm hBSTS. Inset in (c) is aschematic of the LLs form in the hybridized surface state. Inset in (d) is a schematicof surface band structure evolution undermagnetic field for the 10 nm hBSTS withinverted gap. Black and red arrows in line profiles in (c) and (d) present the twoN =0 LL bands residing at the hole and electron band edges, respectively. (ii) Colormaps of theσxx as functions ofmagnetic field andVbg for the (c) 9 nmand (d) 10 nmhBSTS. Thewhite dashed lines in colormaps in (c) and (d) trace the development ofN = 0 LLs in electron and hole sublevels with magnetic field. (iii) Gxx versus B takenat the CNPs for the (c) 9 nm and (d) 10 nm hBSTS. Red arrows in (d) point to the Bcfor the transition from QSH to QH states.Article https://doi.org/10.1038/s41467-022-33643-9Nature Communications |         (2022) 13:6386 4(~8meV) as estimated from the differential conductance measure-ment. Given that the device size is larger than the inelastic mean freepath, backscattering between the helical edge states31 can occur athigher temperature, which can cause the deviation of ρedge fromquantization.Magnetic-field responseThe normal and inverted surface gaps of hBSTS present distinctbehaviors in perpendicular magnetic field. We first discuss the normalgap feature. Line profiles in Fig. 3c plot the longitudinal conductivity(σxx) and Hall conductivity (σxy) as a function of Vbg measured at amagnetic field of 18 T for the 9 nm hBSTS. The two N = 0 LL bandsdeveloped in the σxx plot are assigned to the electron and hole bandedges of the hybridization gap as illustrated by the schematic of thesurface banddiagram in the inset of Fig. 3c. This splitting of N =0 LLs isa key signature of the Landau quantization of intersurfacehybridization20,21. The established ν = 0 plateau in the σxy plot withinthe N = 0 LL, together with the development of ν = −1 and +1 QHplateaus symmetrically about zeroth plateau, further supports the LLsof the hybridized surface states. Color map of σxx in Fig. 3c illustratesthe development of the N = 0 LLs as a function of magnetic field.Similar behaviors were also observed for the 8 nm hBSTS (Supple-mentary Fig. 9). TheN =0 LL energy spacing (E0) derived from the μ(n)relation shows a linear magnetic field dependence (SupplementaryFig. 10), in agreement with the analytical model21. The fitting of E0 tomagnetic field yields eC0 ~ 0.016 eV and eC2 ~ 80 eV Å2 for the 9 nmhBSTS, which is comparable to the fitting parameters of the surfacestates’ Hamiltonian32.The gate-dependent σxx and σxy plots for the inverted gap hBSTS(10 nm) measured at the magnetic field of 18 T (Fig. 3d) show a similartype of N = 0 LLs splitting. The relatively narrow zeroth LL plateauwidth in charge density compared to the 9 nmhBSTS is consistentwithits smaller size of hybridization gap as previously discussed in the gapanalyses. Interestingly, the development of theN=0LLswithmagneticfield traced by the dashed lines along the σxx minimum in Fig. 3dreveals an intriguing feature. The two N = 0 sublevels develop oppo-sitely as revealed by the σxx color map at lowmagnetic field, signifyingthe inversion of electron and hole sublevels at zero field. As the mag-netic field increases, these two sublevels eventually cross and developinto normal QH states with the two sublevels interchanged. This isequivalent to an inverted-to-normal surface gap evolution with mag-netic field to transform from its topologically non-trivial into a trivialgap state as illustrated in surface band diagram in Fig. 3d. This mag-netic field mediated TPT is similar to the band crossing for the QSHeffect observed in HgTe/CdTe quantum well 2D TIs33. The sublevels’crossing feature forming symmetrically about the opposite magneticfield further confirms thismagnetic field-driven topological transition.Figure 3c, d(i) compare Gxx curves as a function of magnetic fieldfor the 9 and 10nm hBSTS, respectively, with their chemical potentialstuned into surface gaps. The levels crossing point at Bc of ~9(−9) T isclearly resolved in the Gxx curves of the 10nm hBSTS (Fig. 3d). This Bcappears to be consistent with its surface gap size (~8meV) obtainedfrom gap analyses and the opening rate of ~1meV/T revealed in 9 and8nm hBSTS (Supplementary Fig. 10). A similar feature is captured in aparallel magnetic field (Supplementary Figs. 11, 12) except no QH stateevolves. Comparing with quantum wells, the QSH state in hBSTS per-sists strongly in magnetic field. The Gxx falls off more slowly with themagnetic field as inferred by the width of Gxx peak centered at zeromagneticfield of ~2 T (~28mT forHgTe/CdTequantumwells31). Also, theslope of dGxx/dB in linear region (B = 0–2 T) of ~0.2–0.3 e2/h/T is nearlytwo orders of magnitude smaller than the quantum wells31,34. The dGxx/dB slope reflects directly the disorder strength (W) of the QSH state35. Inour case, the estimated W of a few meV indicates a moderate to weakdisorder (W≤Δh) regime with insignificant bulk scattering, thus pro-viding a cleaner platform to study the one-dimensional edge channel.Electric-field responseAn external electric field can also modulate the surface bands toinduce TPTs. The effect of a transverse electric field can be triggeredby controlling voltages on top and bottom gates through the hBSTS asillustrated in Fig. 1c. The diagonal resistance maximum along thetransverse electric field observed in the dual-gate mapping (Supple-mentary Fig. 15) presents a key feature resulting from the strongcoupling between surface states. To better elucidate the electric fieldresponse, we converted the dual-gate voltages into the displacementfield (D) versus total charge density (n) relation36, as presented indescending order of thickness in Fig. 4a–d. Magnitudes of the corre-sponding hybridization gaps at zeroD are revealed by their dI/dVmapsinserted in the figures. Line profile of ρxx versus D (Fig. 4a) for theinverted gap hBSTS (10 nm) shows a gradual decrease from its quan-tized h/2e2 value at large D, inferred as a transition into a semi-metallicphase. Whereas for the normal gap hBSTS (9 nm), the ρxx at the CNP issuppressed by more than one order of magnitude at D ~100mV/nmand tends to saturate to a value of order h/e2 at large D, suggesting asignificant gap reduction by D (Fig. 4b). This ρxx change is highlysymmetric with respect to opposite polarities ofD. The suppression ofρxx inD becomes less pronounced in thinner hBSTS (Fig. 4c, d), furthersignifyingmodulation of hybridization gapwithD. For comparison, weplot the change in resistivity Δρxx/ρxx(0) for the variable thicknesshBSTS in the normal gap regime in Fig. 4e. Consistently, the Δρxx/ρxx(0)–D response scales down monotonically with decreasing thick-ness of hBSTS.To further investigate the Δh–D relation, we again deploy ourthree gap estimation methods to probe the gap size for the 9 nmhBSTS versus D, as summarized in Fig. 4f. The gap analyses areexamined in detail in Supplementary Fig. 16–19. Consistent with theρxx–D trend, a significant reduction in hybridization gap with D isindicated by all threemethods. The same trend is observed inoppositepolarity of D, suggesting that the gap reduction is due to brokenstructure inversion symmetry between top and bottom surface statesby transverse electricfield15,16. The appreciable reduction of the surfacegap is attributed to the electric field that is effectively applied throughthe vdW layers. The gap size reaches a minimum saturation value of<1meV, indicating a critical displacement field, DC at ~250mV/nm.Similar analyses are implemented for the 8 and 6 nm hBSTS, while forsimplicity only gap calculated from CQ are included in Fig. 4f. Their DCcanbe extrapolated from the curves as ~400 and ~750mV/nm for the 8and 6 nm hBSTS, respectively. Meanwhile, an effective gap-closingstrength of ~1.2 eÅ can be estimated from the Δh/D ratio for the 9 nmhBSTS, which is comparable to DFT calculated value Δh/E of ~2–3 eÅ(Supplementary Figs. 13, 14).A direct consequence of the surface gap termination is theemergence of topological edge state due to the change in surfacebandtopology. To analyze this effect, we again apply the parallel con-ductance addition model and evaluate ρedge for the 9 nm hBSTS atappliedD values. Assuming an edge channel evolves with D, ρxx(D) willfollow the relation: 1ρxx Dð Þ =1ρxx 0ð Þ +1ρedge. From this relation, ρedge(D) isobtained at different temperatures and plotted in Fig. 4g showingsuppression of thermal activation with the increase in D. This analysisshows that, at large D (250mV/nm), ρedge behavior resembles thetemperature curve of the inverted gap hBSTS (inset of Fig. 3a) andapproaches the h/2e2 value at low temperature (<40K), indicating anemerging helical edge state. This gap-closing mechanismmediated bytransverse electric field is illustrated by the evolution of surfacespectra (insets of Fig. 4g), which offers an alternative route towardhigh-temperature topological edge channels.In summary, we realized distinct topological phases by mappingthe evolution of the surface gap of BSTS 3D TI with thickness, tem-perature, and transverse magnetic and electric fields in the quantumtunneling regime. The trivial and topological phases in hBSTS wereidentified by their diverging and finite (~h/2e2) resistances,Article https://doi.org/10.1038/s41467-022-33643-9Nature Communications |         (2022) 13:6386 5respectively, in response to temperature and gate voltages. The helicaledge state reveals more than one order ofmagnitude smaller disorderstrength compared to HgTe/CdTe quantum wells. By studying thedevelopment of zeroth LL sub-bands in the perpendicular magneticfield, we observed an inverted-to-normal surface gap crossingaccompanied by a transition from QSH to QH edge states. We furtherrealized surface gap closing with electric field, together with anemerging edge conductance for the normal insulating gap hBSTS,implying a transition between trivial and topological phases mediatedby the electric field. These compelling signatures of TPTs and thereversible switching mechanisms hold promise for TI-based topologi-cal field-effect transistors (Supplementary Table 4).MethodsDFT calculationsOur calculations were performed within the framework of densityfunctional theory as implemented in the Vienna ab initio simulation(VASP)37. The projector augmentedwave potentials were adoptedwiththe generalized gradient approximations of Perdew–Burke–Ernzerhofexchange-correlation functional, and the cutoff energy was set to520 eV. The relaxation is performed until all forces on the free ionsconverge to 0.01 eV/Å and theMonkhorst-Pack k-point meshes of 10 ×10 × 1 were used, which have been tested to be well convergence. Thevacuum space is at least 20Å, which is large enough to avoid theinteraction between periodical images. The different BSTS systemswere treated with virtual crystal approximation. The van der Waalsinteraction is described by DFT-D3method. In addition, the spin-orbit-coupling was included in the calculations of the electronic structure.Device fabricationVariable thicknesses of hBSTS crystal flakes were exfoliated from thebulk crystal38 and then transferred using a micromanipulator transferstage into the heterostructures of Gr/hBN sandwiched layers. Wefabricated thehBSTSdevices into theHall bar configurationwithCr/Au(2 nm/60 nm) as the contact electrodes. The top and bottom Gr/hBNlayers serve as the gate-electrode/dielectric layers for applying ofperpendicular electric field to the hBSTS (Fig. 1c). The thickness of theBSTS flakes was measured by a Bruker Dimension Icon atomic forcemicroscopy. The device dimensions were obtained from the imagestaken by a high-resolution optical microscope. hBSTS devices withthickness ranging from 10 nm down to 1 nm were fabricated and stu-died. The device specifications are presented in SupplementaryTable 2.MeasurementsLow-temperature electrical transport measurements were performedin a helium-4 variable temperature insert with a base temperature of1.6 K and magnetic field up to 9 T. Four probe resistances of thedevices were measured using a Stanford Research SR830 lock-inamplifiers operated at a frequency of 17.777Hz. The devices wereFig. 4 | Surface gap inversion by external electric field. (i) Color maps of Rxx asfunctions of displacement field (D) and total charge density (n) for the differentthickness hBSTS in the order of (a) 10 nm, (b) 9 nm, (c) 8 nm, and (d) 7 nm. TheD and n are calculated from dual-gate voltages as: D= 1εoεb4Vbgdb� εt4V tgdt� �, andn=Cbg4Vbg +Ctg4V tg. (ii) Line profiles of Rxx versus D for the respective thicknesstaken at n ≈0 cm−2. Inset in (a–d) is the dI/dV color maps as functions of Vb and Vbgfor the respective samples. eΔρxx/ρxx(0) as a function ofD for different thicknesseshBSTS. fHybridization gaps as a function ofD for the variable thickness hBSTS. Thegap size determined from the three different methods is labeled with differentsymbols as CQ (rhombus), dI/dV (square), and EA (circle). Error bars in (f) are thestandard deviation from the fittings. g ρedge= 1/[ρxx(D)−1 – ρxx(0)−1] as a function oftemperature for the 9 nm hBSTS at different D. Inset in (g) is a schematic of surfaceband structure evolution under electric fields for the 9 nm hBSTS.Article https://doi.org/10.1038/s41467-022-33643-9Nature Communications |         (2022) 13:6386 6typically sourced with a constant AC excitation current of 10–20 nA.Two Keithley 2400 source meters were utilized to source DC gatevoltages separately to the top and bottomGr gate electrodes. Variabletemperature transport measurements were controlled by a Lakeshoretemperature controller. The differential conductance was measuredusing a Stanford Research SR830 lock-in amplifier coupled to a model1211 current preamplifier. The devices were sourced with an AC exci-tation voltage of 100 μV. The DC bias voltage in a range from40–1200mV was swept across the source-drain electrodes. Magneto-transport measurements at high magnetic field were carried out in ahelium-3 variable temperature insert at a base temperature of 0.3Kelvin and magnetic field up to 18 tesla based at the National HighMagnetic Field laboratory. Two synchronized Stanford ResearchSR830 lock-in amplifiers were used to measure the longitudinal andHall resistances concurrently on the BSTS devices. Capacitance wasmeasured in a capacitance bridge configuration24 connected betweenthe BSTS device and the parallel gold strip as a reference capacitor.Two synchronized (at a frequency of ~50–70 kHz) and nearly equal-amplitude AC excitation voltages (range of 15–40mV) were appliedseparately to the top and bottom Gr gates, whose relative magnitudewas chosen to match the ratio of geometric capacitances of top andbottom surfaces. A third AC excitation voltage was applied to thereference capacitorwith the amplitude set to null themeasured signal.The reference capacitors were calibrated to be ~300–400 fF using astandard capacitor (Johanson Technology R14S, 1 pF). The capacitancedata were acquired by monitoring the off-balance current at the bal-ance point as the DC gate voltages were changed.Data availabilityThe data that support the findings of this study are available within thearticle and its supplementary information files. Source data are pro-vided with this paper.References1. Xu, S.-Y. et al. Topological phase transition and texture inversion ina tunable topological insulator. Science 332, 560–564 (2011).2. Liu, C.-X. et al. Oscillatory crossover from two-dimensional to three-dimensional topological insulators. Phys. Rev. B 81, 041307 (2010).3. Lu, H.-Z., Shan, W.-Y., Yao, W., Niu, Q. & Shen, S.-Q. Massive Diracfermions and spin physics in an ultrathin film of topological insu-lator. Phys. Rev. B 81, 115407 (2010).4. Linder, J., Yokoyama, T. &Sudbø, A. Anomalousfinite size effects onsurface states in the topological insulator Bi2Se3. Phys. Rev. B 80,205401 (2009).5. Zhang, Y. et al. Crossover of the three-dimensional topologicalinsulator Bi2Se3 to the two-dimensional limit. Nat. Phys. 6,584–588 (2010).6. Sakamoto, Y., Hirahara, T., Miyazaki, H., Kimura, S.-I. & Hasegawa, S.Spectroscopic evidence of a topological quantum phase transitionin ultrathin Bi2Se3 films. Phys. Rev. B 81, 165432 (2010).7. Zhang, T., Ha, J., Levy, N., Kuk, Y. & Stroscio, J. Electric-field tuningof the surface band structure of topological insulator Sb2Te3 thinfilms. Phys. Rev. Lett. 111, 056803 (2013).8. Nandi, D. et al. Signatures of long-range-correlated disorder in themagnetotransport of ultrathin topological insulators. Phys. Rev. B98, 214203 (2018).9. Kim, D., Syers, P., Butch, N. P., Paglione, J. & Fuhrer, M. S. Coherenttopological transport on the surface of Bi2Se3. Nat. Commun. 4,2040 (2013).10. Wu, S. et al. Observation of the quantum spin Hall effect up to 100kelvin in a monolayer crystal. Science 359, 76–79 (2018).11. Xu, Y., Jiang, G., Miotkowski, I., Biswas, R. R. & Chen, Y. P. Tuninginsulator-semimetal transitions in 3D topological insulator thinfilmsby intersurface hybridization and in-plane magnetic fields. Phys.Rev. Lett. 123, 207701 (2019).12. Zhang, S.-B., Lu, H.-Z. & Shen, S.-Q. Edge states and integer quan-tum Hall effect in topological insulator thin films. Sci. Rep. 5,13277 (2015).13. Mutch, J. et al. Evidence for a strain-tuned topological phase tran-sition in ZrTe5. Sci. Adv. 5, eaav9771.14. Xi, X. et al. Signatures of a pressure-induced topological quantumphase transition in BiTeI. Phys. Rev. Lett. 111, 155701 (2013).15. Liu, G., Zhou, G. & Chen, Y.-H. Modulation of external electric fieldon surface states of topological insulator Bi2Se3 thin films. Appl.Phys. Lett. 101, 223109 (2012).16. Kim, M., Kim Choong, H., Kim, H.-S. & Ihm, J. Topological quantumphase transitions driven by external electric fields in Sb2Te3 thinfilms. Proc. Natl Acad. Sci. 109, 671–674 (2012).17. Collins, J. L. et al. Electric-field-tuned topological phase transition inultrathin Na3Bi. Nature 564, 390–394 (2018).18. Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346,1344–1347 (2014).19. Ko, W. et al. Atomic and electronic structure of an alloyed topolo-gical insulator, Bi1.5Sb0.5Te1.7Se1.3. Sci. Rep. 3, 2656 (2013).20. Zyuzin, A. A. & Burkov, A. A. Thin topological insulator film in aperpendicular magnetic field. Phys. Rev. B 83, 195413 (2011).21. Pertsova, A., Canali, C. M. & MacDonald, A. H. Thin films of a three-dimensional topological insulator in a strong magnetic field:microscopic study. Phys. Rev. B 91, 075430 (2015).22. Cho, S., Butch, N. P., Paglione, J. & Fuhrer, M. S. Insulating behaviorin ultrathin bismuth selenide field effect transistors. Nano Lett. 11,1925–1927 (2011).23. Han, M. Y., Özyilmaz, B., Zhang, Y. & Kim, P. Energy band-gapengineering of graphene nanoribbons. Phys. Rev. Lett. 98,206805 (2007).24. Chong, S. K., Tsuchikawa, R., Harmer, J., Sparks, T. D. & Deshpande,V. V. Landau levels of topologically-protected surface states pro-bed by dual-gated quantum capacitance. ACS Nano 14,1158–1165 (2020).25. Rosen, I. T. et al. Absence of strong localization at low conductivityin the topological surface state of low-disorder Sb2Te3. Phys. Rev. B99, 201101 (2019).26. Shan, W.-Y., Lu, H.-Z. & Shen, S.-Q. Effective continuous model forsurface states and thin films of three-dimensional topologicalinsulators. N. J. Phys. 12, 043048 (2010).27. Tilahun, D., Lee, B., Hankiewicz, E. M. & MacDonald, A. H. QuantumHall superfluids in topological insulator thin films. Phys. Rev. Lett.107, 246401 (2011).28. Pertsova, A. & Canali, C. M. Probing thewavefunction of the surfacestates in Bi2Se3 topological insulator: a realistic tight-bindingapproach. N. J. Phys. 16, 063022 (2014).29. Du, L., Knez, I., Sullivan, G. & Du, R.-R. Robust helical edge transportin gated InAs/GaSb bilayers. Phys. Rev. Lett. 114, 096802 (2015).30. Roth, A. et al. Nonlocal transport in the quantum spin Hall state.Science 325, 294–297 (2009).31. König, M. et al. Quantum spin Hall insulator state in HgTe quantumwells. Science 318, 766–770 (2007).32. Liu, C.-X. et al. Model Hamiltonian for topological insulators. Phys.Rev. B. 82, 045122 (2010).33. Bernevig, B. A., Hughes Taylor, L. & Zhang, S.-C. Quantum spin Halleffect and topological phase transition in HgTe quantum wells.Science 314, 1757–1761 (2006).34. Gusev, G. M., Olshanetsky, E. B., Kvon, Z. D., Mikhailov, N. N. &Dvoretsky, S. A. Linear magnetoresistance in HgTe quantum wells.Phys. Rev. B 87, 081311 (2013).35. Maciejko, J., Qi, X.-L. & Zhang, S.-C. Magnetoconductance of thequantum spin Hall state. Phys. Rev. B. 82, 155310 (2010).36. Chong, S. K., Han, K. B., Sparks, T. D. & Deshpande, V. V. Tunablecouplingbetween surface states of a three-dimensional topologicalArticle https://doi.org/10.1038/s41467-022-33643-9Nature Communications |         (2022) 13:6386 7insulator in the quantum Hall regime. Phys. Rev. Lett. 123,036804 (2019).37. Kresse, G. & Hafner, J. Ab initio molecular dynamics for open-shelltransition metals. Phys. Rev. B 48, 13115–13118 (1993).38. Han, K.-B. et al. Enhancement in surface mobility and quantumtransport of Bi2−xSbxTe3−ySey topological insulator by controllingthe crystal growth conditions. Sci. Rep. 8, 17290 (2018).AcknowledgementsThis material is based upon work supported by the National ScienceFoundation, the Quantum Leap Big Idea under Grant No. 1936383. Aportion of this work was performed at the National High Magnetic FieldLaboratory, which is supported by National Science Foundation Coop-erative Agreement No. DMR-1644779 and the State of Florida. Theauthors acknowledge Brian Skinner for helpful comments.Author contributionsS.K.C. and V.V.D. designed, conducted the experiments, and preparedthe manuscript. K.W. and T.T. provided single crystal hexagonal boronnitride. T.D.S. provided a single crystal BiSbTeSe2 three-dimensionaltopological insulator. L.L. and F.L. performed theoretical calculations tosupport the experimental data. All authors contributed to the discussionof the results and approved the final version of the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-022-33643-9.Correspondence and requests for materials should be addressed toSu Kong Chong or Vikram V. Deshpande.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of thiswork. Peer reviewer reports are available.Reprints and permission information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons license and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022Article https://doi.org/10.1038/s41467-022-33643-9Nature Communications |         (2022) 13:6386 8https://doi.org/10.1038/s41467-022-33643-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Emergent helical edge states in a hybridized three-dimensional topological insulator Results Topological phase diagram Hybridization gap Normal and inverted gaps Magnetic-field response Electric-field response Methods DFT calculations Device fabrication Measurements Data availability References Acknowledgements Author contributions Competing interests Additional information