Tuning of Topological Dirac States via Modification of van der Waals

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C: Physical Processes in Nanomaterials and Nanostructures

Tuning of Topological Dirac States via Modification of van der Waals Gap in Strained Ultrathin BiSe Films 2

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Wonjun Yang, Chang Woo Lee, Dasol Kim, Hyunsik Kim, Jonghyeon Kim, Hwan Young Choi, Young Jai Choi, Jae Hoon Kim, Kyungwha Park, and Mann-Ho Cho J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06296 • Publication Date (Web): 28 Sep 2018 Downloaded from http://pubs.acs.org on October 2, 2018

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The Journal of Physical Chemistry

Tuning of Topological Dirac States via Modification of van der Waals Gap in Strained Ultrathin Bi2Se3 Films Won Jun Yang1, Chang Woo Lee1, Da Sol Kim1, Hyun Sik Kim1, Jong Hyeon Kim1, Hwan Young Choi1, Young Jai Choi1, Jae Hoon Kim1, Kyungwha Park2,*, Mann-Ho Cho1,*

1

Department of Physics and Applied Physics, Yonsei University, Seoul 120-749, Korea 2

Department of Physics, Virginia Tech, Blacksburg, Virginia, 24061, USA

ABSTRACT

Robust massless Dirac states with helical spin textures were realized at the boundaries of topological insulators such as van der Waals (vdW) layered Bi2Se3 family compounds. Topological properties of massless Dirac states can be controlled by varying film thickness, external stimuli, or environmental factors. Here we report single-crystal-quality growth of ultrathin Bi2Se3 films on flexible polyimide sheets and manipulation of the Dirac states by varying vdW gap. X-ray diffraction unambiguously demonstrates that under uniaxial bending stress the vdW gap substantially changes with inter-atomic-layer distances unaltered. Terahertz and photoelectron spectroscopy indicate tuning of the number of quantum conducting channels and of work function, by the stress, respectively. Surprisingly, under compressive strain, transport measurements reveal dimensional crossover and suppressed weak antilocalization. First-principles calculations support the observation. Our findings suggest that variation of vdW gap is an effective means of tuning the Fermi level and topological Dirac states for spintronics and quantum computation.

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INTRORUCTION Massless Dirac states have been realized at the boundaries of two-dimensional (2D) or threedimensional (3D) topological insulators (TIs)1-3 where conduction and valence bands are inverted due to spin-orbit coupling (SOC). Robustness of such Dirac states and helical spin textures were shown to be useful for spintronics2-9 and quantum computation2-3,10-12. Van der Waals (vdW) layered Bi2Se3 family TIs are typically electron- or hole-doped due to either inherent vacancies or antisites13-15 or external dopants16-19, which set the Fermi level within the conduction band or valence band. Interface chemistry and chemical instability at the interface of topological heterostructures have been extensively studied20-22, since this information is crucial for device applications using TIs. One of the most important findings from the reported data is that topological properties of the Dirac states can be modified and controlled by varying film thickness, external stimuli, or environmental factors. A quantum phase transition from TI to trivial insulator was predicted for Bi2Se3 family by increasing tensile stress along the crystal c axis23-24. Weak vdW coupling between adjacent quintuple layers (QLs) facilitates expansion of mostly the vdW gap rather than uniform expansion of inter-atomic-layers. This may lead to a decrease in SOC and eventually the absence of band inversion23-24. Pressure was also applied to induce a phase transition between normal insulator and TI in Bi2S3 and BiTeI25-26. Uniaxial stress was experimentally applied to TIs via mechanical means27, grain boundaries28, heterostructure interfaces16-17,20-21,29-31, or chemical doping/intercalations32-34. In the previous studies16-17,20-21,28-34, the stress application was irreversible and unidirectional (compressive or tensile), while in Ref.27, the stress was applied reversibly but only with out-of-plane compressive strain up to 2%. Moreover, the structures under stress16-17,20-21,28-34 were either limited to studies of structural properties16-17,20-21,32-34, or incompatible with direct characterizations of pure effects of strain on topological/quantum 2 ACS Paragon Plus Environment

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properties16-17,20-21,28-31. This is because other environmental factors than strain such as lattice mismatch, unintentional interfacial layers, or charge transfer between the TI and substrate, also affect the topological and quantum properties of the surface-state Dirac cone in the structures under stress. The outcomes in Ref. 27 cannot be applied to our case since Bi2Se3 is typically electron-doped and a clear surface-state Dirac point appears within the bulk band gap, while Sb2Te3 in Ref. 27 is hole-doped and a surface-state Dirac point is buried under the bulk valence band region. Here we present single-crystal-quality growth of ultrathin Bi2Se3 films (~5-6 nm) on polyimide sheets. In contrast to the previous studies16-17,20-21,27-34, this set-up allows both reversible compressive and tensile stress to be applied to the TI films along the out-of-plane direction (crystal c axis), and facilitates structural, optical and transport measurements for microscopic characterizations under the stress. X-ray diffraction (XRD) measurements demonstrate significant modification of the vdW gap under uniaxial compressive or tensile stress. Terahertz time-domain spectroscopy shows that quantum-well states (QWSs) move out of the Fermi level under compressive stress. Surprisingly, transport measurements suggest unambiguous crossover from a 2D to 3D temperature dependence as well as substantial suppression of weak antilocalization (WAL), under 4.03% compressive stress. This unusual transport behavior has not been observed in strained ultrathin TI films. Density-functional theory (DFT) calculations support the observation with insight into the mechanism of the changes and spin-momentum locking. The observed shifts of the Fermi level and Dirac cone in the ultrathin Bi2Se3 film under compressive stress are opposite to those for the ultrathin Sb2Te3 film discussed in Ref. 27. Our findings suggest effective means and set-ups to examine the microscopic origin of changes in the topological Dirac states and to tune their properties by adjusting the vdW gap, which can be applied to other vdW topological materials3,35-37 or to superconducting states in Cu3 ACS Paragon Plus Environment


doped Bi2Se332.

MATERIALS and METHODS Single-crystal preparation, growth, and structural characterization. Single-crystal-quality Bi2Se3 films of 5 QLs, 6 QLs, and 20 QLs were grown on 500 µm thick polyimide sheets by using MBE and a self-ordering process13,38-40 which was shown to be effective in synthesis of high-quality van-der-Waals-type V2VI3 crystal structures without single-crystal substrates27,40. A sequential thermal evaporation process for 5, 6, and 20 cycles of Bi(4.86 Å)/Se(18.46 Å) on polyimide substrates was followed by an in-situ annealing process at 250 °C for 20 min by using a halogen lamp under a vacuum of 2 × 10-8 Torr. Each step of the evaporation process was controlled by an individually operated shutter, which was linked with a quartz crystal monitor and a programmed system. During the annealing process, excess nonstoichiometric Se was diffused out. The synthesized Bi2Se3 films on polyimide sheets were crystallized with an orientation along the [0001] direction in hexagonal unit cell or [111] direction in rhombohedral unit cell. To investigate the structural characteristics, X-ray diffraction (XRD) measurements were carried out by using a conventional high-resolution-XRD system with a Cu K-α beam source (Fig. 1a), and by using the 5A beamline of Pohang Accelerator Laboratory (PAL, Pohang, Korea) with a beam source of wavelength of about 1 Å (Fig. 1b). Terahertz measurements and fitting procedure. Terahertz time-domain spectroscopy was used to probe electromagnetic response from both free carriers and phonons of the Bi2Se3 thin films in a frequency range of 0.5-3 THz. In a chronological order, after being removed from the MBE chamber, the sample was loaded into a terahertz instrument within 3 min by using a portable desiccator of less than 0.01 Torr, and the measurement was completed within 20 min. Additionally, in order to completely eliminate the aging effect and to check on reproducibility, 4 ACS Paragon Plus Environment

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the experiment was carried out dozens of times using fresh 5-QL and 6-QL samples, changing the sequential order of the measurement such as starting with flat samples and then bending, or starting with bent samples and then flattening. Free carriers from both TSSs and QWSs can directly couple to the terahertz radiation. Detected resonance frequencies of the phonon modes provide information on the oscillator strength and the line shape arising from the coupling. Terahertz measurements were conducted with a TeraView TPS 3000 spectrometer. Complex transmittance signals were normalized by using signals from the polyimide substrate and those from the Bi2Se3 film on the substrate. The transmittance signals were then converted into complex conductance spectra based on Tinkham’s formula41, which is valid in the ultrathin-film limit. The formula reads / = 1/[1 + /( + 1)] , where tfs and ts are complex transmission coefficients for the Bi2Se3 film on the substrate and for the bare substrate, respectively. Here Z0, , d, and are vacuum impedance, optical conductivity, film thickness, and refractive index of the bare substrate, respectively. Optical conductance G(ω) was fitted by using a Drude-Lorentz model13: () = () + () + !"#

or () + !"# ()

(4)

+ + ∗ ',-.* ∗ ',)** + 4% + ,)** 4% + ,-.* Ω∗ +',-.* Ω∗ +','3 () = + 2 4% Ω+ ,'3 − + − Γ'3 4% Ω+ ,-.* − + − Γ-.*

() =

Here and are Drude and Lorentz components of the conductance, respectively. The background effect is considered in ≡ (1 − 5 )/4%, where 5

is background dielectric

constant. From the Drude terms, ∗ 6,788 9∗ 6,:;8 < is the plasma frequency of the TSSs (QWSs) multiplied by a square root of the thickness of surface dsurface (the TI film thickness dbulk), and ,)** 9,-.* < is the scattering rate of the TSSs (QWSs). From the Lorentz terms,

Ω∗ 6,:;8 9Ω∗ 6,6ℎ < is the oscillator strength for intersubband transitions among the QWSs (A1u 5 ACS Paragon Plus Environment


phonon) multiplied by a square root of dbulk, and Ω0,:;8 9Ω0,6ℎ < and Γ-.* 9Γ'3 < are the center frequency and damping rate for intersubband transitions among the QWSs (A1u phonon), respectively. q is a dimensionless Fano asymmetry factor. The fitting parameter values are shown in Table 1. In our fitting, ∗ ',)** , ∗ ',-.* , Ω∗ ',-.* , and Ω∗ ','3 are fitting parameters, and so the values of dsurface and dbulk are not separately needed. Alternatively, the total optical conductance can be decomposed into surface and bulk contributions. The surface component consists of contributions from the TSSs. The QWSs and α phonon mode contribute to the bulk component. The contributions of free bulk carriers were neglected in the fitting. Here the α phonon contribution (Fig. 2) with a peak centered at about 70 cm-1 has an asymmetric Fano line shape due to the coupling between the TSSs and the phonon. Transport measurements. Electrical transport properties were measured by using a Quantum Design Physical Properties Measurement System (PPMS, San Diego, CA, USA). Before the measurements, all thin Bi2Se3 films were capped by 20 nm thick Al2O3 by using a conventional atomic layer deposition method. The Al2O3 capping layer is known to be very effective in preventing changes of the doping level by air exposure. All measurements were performed under a vacuum of ~10-6 Torr. The temperature dependence of conductance was obtained by using the Kelvin four-point probe configuration for the area of 100 µm × 100 µm at T = 2–300 K. The magneto-conductance was measured between -1 and 9 T at various temperatures, T=2, 3, 5, 7, 10, 20, 40 and 50 K. Ultraviolet photoelectron spectroscopy. To measure work function and surface electronic structure of the Bi2Se3 films on polyimide, we performed ultra-violet photoelectron spectroscopy (UPS) under a base pressure of 10-9 Torr. Since bending of the films cannot be realized in-situ environment, it was performed in a nitrogen purged glove box with 0.01% or less oxygen concentration as an alternative way. An aging effect was also measured in atmosphere (Fig. S2 in 6 ACS Paragon Plus Environment

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Supporting Information) in order to check on reliability of the glove-box environment. We found that 10 minutes in the glove-box environment provides similar aging effects to a few seconds in atmosphere. We used a PHI 5700 spectrometer with an un-polarized light source from helium gas (He I) with an energy of 21.22 eV. The spectrometer was calibrated with respect to the Fermi edge of a clean Au sample. Since thermal and instrumental broadening determines resolution of the system, we set the resolution such that the full-width at half maximum of the Au Fermi edge becomes 200 meV. The system resolution was considered in determining the spectral cutoff and onset. A sample bias of -8 V was applied to obtain secondary electron cutoff. Density-functional theory calculations. We used generalized gradient approximation for the exchange correlation functional42 and projector augmented wave (PAW) pseudopotentials43 within VASP44. Spin-orbit coupling (SOC) and van der Waals interaction45,46 were included selfconsistently within our DFT calculations. For the unbent 6-QL Bi2Se3 slab, we used experimental lattice constants (a = 4.143 Å, c = 28.636 Å) 47. For the 6-QL slabs under compressive and tensile stress, we first relaxed all atomic coordinates of bulk Bi2Se3 with a given c/a ratio, assuming that uniaxial 5% compressive or tensile strain was applied along the crystal c axis with a Poisson ratio (∆c/∆a) of 0.2423. Then we constructed a 6-QL Bi2Se3 film under the stress from the bulkrelaxed atomic coordinates. The atomic coordinates of the bulk unit cell were relaxed until the residual force is less than 0.01 eV/Å with 19 × 19 × 19 k points sampled. Upon the relaxation, we found that the vdW gap or distance between adjacent QLs decreases by 14% (increases by 8%) for the 5% compressive (tensile) strain, compared to the unbent slab. Once the slab geometry was constructed, no further geometry relaxation was carried out. We calculated electronic structures of the unbent 6-QL slab and the 6-QL slabs under the compressive and tensile stress, by considering a thick vacuum layer of 30 Å and k-point sampling in the range of 13 × 13 × 1 to 17 × 17 × 1. A finer k-point mesh than this would not change the electronic 7 ACS Paragon Plus Environment


structure. The polyimide substrate was not included in our DFT calculations. We identified surface states from electron-density profiles as a function of z coordinate (along the film thickness direction) shown in Fig. 4 e and g. For the unbent and bent 6-QL slabs, the identified surface states have electron density localized onto the topmost or bottommost QLs by more than 40%48, and they are marked by red symbols in Fig. 4a-c. A slight change in the criterion of the surface-state identification does not change the characteristics of the bands shown in Fig. 4a-c.

RESULTS AND DISCUSSION Structural Properties. Bi2Se3 films of 5 QLs, 6 QLs, and 20 QLs were grown on 500 µm polyimide sheets using molecular beam epitaxy (MBE) and a self-ordering process13,27,38-40 (see Methods), where 1 QL corresponds to about 1 nm. As shown in Fig. 1c, while the sample was supported by two holders, an upward (downward) force was gently applied at the center of the sample plane from below (above) by using a metal tweezer, in order to control the curvature direction. In the case of bending stress with positive curvature (Fig. 1b), the Bi2Se3 film undergoes compressive stress along the out-of-plane direction. For the bending stress with negative curvature (Fig. 1a), the Bi2Se3 film experiences tensile stress along the out-of-plane direction. Bent/flat atomic layers are schematically illustrated in Fig. 1c-d. We investigated structural properties of a 20-nm TI film on polyimide with compressive stress and tensile stress, and without stress using XRD, as shown in Fig. 1. In all three cases, the long-range order and c-axis orientation of the Bi2Se3 film were confirmed from the θ − 2θ method. All indexed large peaks correspond to (00?) peaks of hexagonal unit cell, which signifies that the Bi2Se3 film is perfectly oriented along that direction. Two small non-indexed peaks on the left and right hand sides of the (006) peak originate from the polyimide substrate. Diffraction intensities in Fig. 1a and 1b differ from each other due to differences in measurement 8 ACS Paragon Plus Environment

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technique (see Methods).

Insets of Fig. 1 show the main (003) peaks surrounded by several

small peaks for the Bi2Se3 film. The main peak positions without stress are almost the same as those observed after application of the compressive or tensile stress. This implies that there is little structural deformation in vertical distances between adjacent atomic layers under the stress. However, positions of the small secondary peaks near the (003) main peaks have noticeably changed under the stress (insets in Fig. 1). The oscillation period of the secondary peaks decreases (increases) under the tensile (compressive) stress in reciprocal space. Considering that those secondary peaks are due to multiple reflections between top and bottom surfaces, we estimate that the film thickness increases (decreases) by about 4.32% (-4.03%) (error 0.2%) under the tensile (compressive) stress. Since the interlayer distances have not changed, this result suggests that the significant changes in the film thickness are attributable to significant modification of the vdW gap in the Bi2Se3 film. To the best of our knowledge, this is the first direct experimental observation of changes in vdW gap in layered TIs under uniaxial stress. Terahertz Spectroscopy. We performed terahertz spectroscopy measurements on the 5-QL and 6-QL films on polyimide without stress and under the compressive stress within 20 min after the growth, because the Bi2Se3 films would exhibit a noticeable aging effect after 20 min13. (See Methods for a measurement sequence and reproducibility.) Figure 2 shows the real part (G1) of complex conductance (G) vs photon wavenumber for the Bi2Se3 films at room temperature. We fitted the observed conductance, G(ω), to a Drude-Lorentz model13, by considering contributions of topological surface states (TSSs) and QWSs as well as coupling between the TSSs and the α phonon peaked at about 70 cm-1. See Methods for the fitting procedure and Table 1. From the fitting, we obtained quasi-DC conductance, G(ω→0), which represents the total number of quantum conducting channels in units of G0 from the TSSs and QWSs crossing the Fermi level, where G0 is the quantum of conductance, A + /ℎ. For the 5-QL Bi2Se3 films (Fig. 2a-b), we 9 ACS Paragon Plus Environment


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estimated the quasi-DC conductance to be 4 G0 (2 G0) for the unbent (compressive strain) case, of which top and bottom TSSs each contribute 1 G0 and the QWSs contribute the remainder. That implies zero QWSs (two QWSs) cross the Fermi level for the bent (unbent) 5-QL film. For the 6QL films (Fig. 2c-d), we found the quasi-DC conductance to be 6 G0 (4 G0) for the unbent (bent) case, of which the TSSs and QWSs contribute 2 G0 and 4 G0 (2 G0), respectively. Without stress, the observed increase in the number of conducting channels with increasing number of QL, is consistent with the result from a previous terahertz experiment13. With compressive stress, surprisingly, our terahertz measurements reveal that the number of QWSs crossing the Fermi level decreases from four to two for the 6-QL film and from two to zero for the 5-QL film. This decrease cannot be simply explained by the change of the film thickness due to the stress, since the overall film thickness has decreased only by 4.03% (Fig. 1b). We conjecture that this decrease is attributable to the substantial reduction in the vdW gap under the stress, assuming that an electron doping amount has not been significantly changed upon the stress. Later, we will present DFT calculations which support this conjecture and show pronounced changes in electronic structure under the stress. This result suggests that it is possible to tune the Fermi level and the number of QWSs crossing the Fermi level, by mechanical uniaxial stress. Transport Properties. We also measured conductivity in the range of 2-300 K, for several 6QL films (which were capped with Al2O3) on polyimide without stress, with compressive stress, and with tensile stress. Figure 3a shows the temperature dependence of quantum corrections to the conductivity, ∆σ(T, B=0) = σ(T) − σ(T0), without B field, where T0 is the temperature at which the conductivity reaches its maximum. In this study, we focus on a low-T range (2-10 K). Considering that the TI film is ultrathin, we applied 2D transport theory49-52 for fitting (Fig. 3b): ∆(7) =

C

DE C ℏ

J ) G−2I6 + 2 − + KLM N ln G) N Q


(1)

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Equation (1) consists of contributions from WAL (the first term) and from electron-electron interaction (EEI) (the second and third terms), where α is a constant depending on the relative strength between spin-orbit and magnetic scattering32,52, and p is a positive constant on the order of unity which varies with scattering mechanism49,51. Here KLM reflects static screening of electrons at the Fermi surface. For strong SOC, α is 0.5 per transport channel, while in the absence of both SOC and magnetic scattering, α becomes zero49,52. As shown in Fig. 3b, for both the unbent film and the film under the tensile stress, the observed conductivity fits well to a logarithmic T-dependence with a positive slope. The fitting alone cannot determine α, p, and KLM values independently. However, we conjecture from Eq. (1) that EEL or WAL contributes to a positive or negative slope in the log-T dependence, respectively, considering that α > 0 , p > 0, and KLM =0.15~0.5 applicable for unbent Bi2Se3 films49-50. Therefore, the observed log-T dependence mainly originates from EEI with different KLM values for the unbent and tensile

strain cases. Our result for the unbent film is consistent with previous reports49-50. However, for the compressive strain, unexpectedly, the log-T fitting is very poor (Fig. 3b). Therefore, we considered 3D transport theory50-51: ∆(7) =

R.J C

DE C ℏ

U Q GJ − + KLM N T) T+ℏ

# )

Q

D

J

)

Q

(2)

Here kB is the Boltzmann constant and D0 is the diffusion constant. Equation (2) consists of contributions from EEL only since EEI dominates the quantum correction at low temperatures, i.e. 2-10 K. The contribution from localization has a temperature dependence of Tp/2, where p is 3/2, 2, and 3 when the electron interactions are in the dirty and clean disorder limit, and for strong electron-phonon scattering, respectively51. As shown in Fig. 3c, the √7 dependence gives rise to an excellent fitting for the compressive strain, while the temperature dependence from localization does not agree with the observation for any possible p values. This change in



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effective transport dimensionality under compressive stress suggests that the diffusion length may be significantly reduced to less than the film thickness51, although the film thickness has changed only -4.03%. A search for direct sources of this reduction deserves a further study but that is beyond the scope of this work. Furthermore, we measured magneto-conductivity at 2 K when B field is applied along the out-of-plane direction, for the 6-QL films with and without stress. Figure 3 d-e shows the B-field dependence of the quantum corrections ∆(W) = (W) − (W = 0). For the unbent film, the quantum correction sharply decreases with increasing B field at low fields and continues to decrease until 9 T. This behavior is a typical WAL effect shown in TIs related to π Berry phase of the massless Dirac surface states. For the compressive stress, ∆(W) has the similar trend to the unbent case except for a slight upturn starting from about 4.5 T, and the overall magnitude drops by one-third. For the tensile stress, ∆(W) has a similar trend to the compressive stress but the small upturn starts from about 3.4 T, and the overall magnitude is just one-tenth of the compressive strain case. We fitted the observed data to the Hikami−Larkin−Nagaoka (HLN) equation52: ∆(W) = I

C

+E C ℏ

R

G−Ψ G+ +

XY X

X

ℏ

N + ln G Y NN, WZ = D"C , X

Y

(3)

where Ψ is the digamma function and lφ is the dephasing length. From the fitting shown in Fig. 3e, the extracted α value is 0.33 for the unbent film, 0.16 for the compressive strain, and 0.01 for the tensile strain, respectively. The value of lφ was obtained from a fitting to T-1/2 (Fig. 3f). We find that the dephasing length is approximately 145 nm (95 nm) for the unbent film (compressive strain). For the unbent film, the extracted α value is somewhat smaller than the expected value for a single transport channel, 0.5, but several experiments on thin Bi2Se3 films49-50,53-56 reported α values smaller than 0.5. The extracted α value likely arises from the top TSS only or one


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transport channel where the top and bottom surface states are indirectly coupled by bulk states, considering the thickness of the Bi2Se3 film. With the compressive strain, the substantial decrease in α value indicates that the WAL effect is significantly suppressed. This can be explained by transport theory on topological materials including bulk states57. The theory states that bulk states such as QWSs in the conduction band region contributes to quantum transport depending on the location of the Fermi level relative to the bulk band gap edge (conduction band minimum, CBM) for low-doped thin TI films when the films are thicker than the bulk mean free path and thinner than the dephasing length. When the Fermi level is very close to the CBM, the bulk states contribute to weak localization (WL). However, when the Fermi level is much higher than the CBM, WAL is expected from the bulk states. Based on this theory, we speculate that with the compressive strain, the Fermi level come much closer to the CBM than in the unbent film, which is consistent with our terahertz spectroscopy data and DFT calculations shown later. The extracted α value for the tensile strain (~0.01) is similar to that observed in 2~3-QL Bi2Se3 films54,58, where the Dirac cone has a gap on the order of 100 meV. Furthermore, we investigated the change in electrical properties upon reversible bending stress in 20nm-thick Bi2se3 film more than 1000 cycles as shown in (Fig. S3 in Supporting Information). Considering the continuous resistance change with bending strain and cycling endurance more than 1000, this data clearly represents the reproducibility of reversible bending experiments. DFT-based Computer Simulations. To understand the mechanism of our experimental findings, we performed DFT calculations on a 6-QL Bi2Se3(111) film without stress and under uniaxial 5% compressive and 5% tensile strain along the crystal c axis (see Methods). Upon geometry relaxation of bulk Bi2Se3 under the stress, we found that the vdW gap between adjacent QLs in the (111)-film structure decreases by 14% (increases by 8%) for the 5% compressive (tensile) strain, compared to the unbent film. See Fig. 4h and Table 2 for the relaxed interlayer 13 ACS Paragon Plus Environment


distances. This result agrees with the experimental data shown in Fig. 1a-b. Figure 4a-c shows DFT-calculated electronic structures for the 6-QL film with and without stress, where the charge neutrality point, EFDFT, is set to zero in energy. Surface states were identified as states localized at the topmost/bottommost QL (see Methods). The quantum-well states appearing in thin Bi2Se3 films are similar to those in conventional semiconducting films with strong spin-orbit coupling. One interesting feature obtained from DFT is that an N-QL Bi2Se3 film has (N-1) quantum well states in the bulk conduction band region. For the unbent case (compressive strain), a surfacestate Dirac cone has a gap of 2 meV (0.6 meV) at Γ. The experimental Fermi level, EFExp, is set such that the number of the QWSs crossing EFExp agrees with the terahertz data (Fig. 2a-b) for a fixed amount of doping in all three cases, assuming that the doping amount does not change upon bending. Two QWSs cross EFExp for the unbent slab, whereas one QWS or three QWSs cross EFExp for the 6-QL slab under the compressive or tensile stress, respectively (Fig. 4a-c). Consequently, EFExp is only at 0.016 eV above the CBM for the compressive strain, but it is at 0.102 eV above the CBM for the unbent slab (Table 2), where the CBM coincides with the lowest QWS energy in the conduction band region at Γ. Combining transport theory57 with our DFT result, we find that bulk states such as QWSs contribute to WL (WAL) for the compressive strain (unbent case). This supports the significant suppression of the WAL effect or α value for the compressive strain in the measured magneto-conductivity (Fig. 3d-e). For the tensile strain, the Dirac cone has a gap of 0.113 eV at Γ with reduction in SOC, which is consistent with a previous report23-24 and explains the experimental α value (~0.01). An additional effect of the compressive strain is a change in surface-bulk coupling. With the compressive strain, the Dirac point is pushed downward to about 0.109 eV below the charge neutrality point (Fig. 4a), and consequently the work function increases by 86 meV, compared to the unbent case. This result is consistent with the increase in work function observed by 14 ACS Paragon Plus Environment

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ultraviolet photoelectron spectroscopy (UPS) (Fig. S1a in Supporting Information). The energy difference between the Dirac point and the lowest QWS in the conduction band region at Γ, increases with the compressive stress, which implies an increase in surface-bulk coupling (Table 2). This increase in the coupling and work function induces changes in characteristics of the band belonging to the upper Dirac cone at EFExp. Compare the electron-density profile for state u3 for the unbent case with that for state c3 for the compressive strain at EFExp (Fig. 4d-g). Although state u3 is localized at the surface (i.e., topmost QL) like state u1 and state c1, state c3 has a long tail into the film. Figure 4i-j shows DFT-calculated constant energy contours of the Dirac cone at EFExp for the compressive strain and unbent case. Bulk-like characteristics of the state near the ΓM directions (ky axis and five other equivalent directions) are clearly seen for the compressive strain case. This result supports the reduction in UPS intensity near the Fermi level (Fig. S1b), and provides an indirect clue in the observed 3D temperature dependence (Fig. 3c). An aging effect was also investigated (Fig. S2 in Supporting Information) in order to check the reliability in the glove-box environment. We found that the aging effect in the glove-box environment can be effectively suppressed within 10 minutes. We also find spin-momentum locking for all three cases (Fig. S4) and expect unique strain-induced quasiparticle interference patterns that can be observed by scanning tunneling microscopy.

CONCLUSION We investigated how the modification of vdW gap in ultrathin TI films influences the topological Dirac states by applying uniaxial compressive and tensile stress via mechanical bending to ultrathin Bi2Se3 films grown on flexible polyimide substrates. We demonstrated that the uniaxial stress mostly changed the vdW gap in the TI films and that it also tuned the Fermi level and work function. Furthermore, we found that the compressive stress can substantially 15 ACS Paragon Plus Environment


increase the surface-bulk coupling leading to the dimensional crossover and weakening of the WAL effect, while the tensile stress can induce a substantial gap at the Dirac cone which completely suppresses the WAL effect. Our set-ups allow one to directly explore the effects of vdW-gap modification on structural, optical and transport properties under compressive and tensile stress. Our findings will shed light in elucidating the mechanism of exotic topological properties in Cu-doped Bi2Se3 and other topological materials and their applications.

Figure 1

Figure 1. XRD measurements and bending process. a-b, XRD intensity vs 2θ for a 20-QL 16 ACS Paragon Plus Environment

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Bi2Se3 film on a polyimide substrate without stress (black) and under 4.32% tensile strain (red) and 4.03% compressive strain (blue) along the crystal c axis, or [0001] direction in hexagonal unit cell. All indexed large peaks correspond to (00?) peaks of hexagonal unit cell, which implies the orientation of the Bi2Se3 film. Small peaks corresponding to polyimide appear on the left and right hand sides of the (006) peak. Insets in a and b show zoomed-in (003) peaks and Laue oscillation patterns. c, Pictures showing the film supported by two holders under the tensile stress (with negative curvature), the flat film, and the film under the compressive stress (with positive curvature) from the left to the right. d, Schematic views of the atomic layer stacking and vdW gap for the unbent and bent films, where only two QLs are illustrated for simplicity.

Figure 2

Figure 2. Real part of complex conductance spectra G1. a-b, Measured G1 vs wavenumber at 17 ACS Paragon Plus Environment


room temperature for the 5-QL Bi2Se3 film on polyimide without stress and with the compressive stress, respectively. c-d, Measured G1 vs wavenumber at room temperature for the 6-QL Bi2Se3 film on polyimide without stress and with the compressive stress, respectively. G0 is the quantum of conductance. Each conductance spectrum was fitted to a Drude-Lorentz model13 (see Methods). The model consists of Drude components from the TSSs (dashed pale blue) and QWSs (magenta) and of Lorentz components from QWSs (broad green curve) and from the coupling between the TSSs and A1u phonon (dark blue curve centered at around 70 cm-1). The fitting parameter values are listed in Table 1. The real conductance value in the zero wavenumber limit indicates the total number of quantum conductance channels crossing the Fermi level which consists of two TSSs and some QWSs. For both 5-QL and 6-QL films on polyimide, the total number of quantum conductance channels crossing the Fermi level decreases by 2 G0 with the compressive stress.

Figure 3


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Figure 3. Transport measurements.

a, Measured quantum corrections to conductivity,

∆σ(T, B = 0) = σ(T) − σ(T0), versus temperature T in the absence of B field for the 6-QL Bi2Se3 film on polyimide without stress (black) and under the compressive (red) and tensile stress (blue). The circled region in a is emphasized in b and c for the fitting to 2D transport theory and 3D transport theory, respectively. Symbols and lines in b and c represent the experimental data and fitting models, respectively. Note that the horizontal scale in b is logarithmic, and the vertical scale in c is −∆σ2. Insets in b and c are zoomed-in quantum corrections for the tensile stress. d, Measured quantum corrections to conductivity, ∆(W) = (W) − (W = 0), versus B field for the 6-QL Bi2Se3 film on polyimide without stress (black) and under the compressive (red) and tensile stress (blue). e, Zoom-in of d in a low B-field region, where solid curves represent the fitting to the Hikami-Larkin-Nagaoka equation. The WAL effect is suppressed with either the 19 ACS Paragon Plus Environment


compressive or tensile stress. f, Temperature dependence of the dephasing length lφ. For the unbent film and compressive strain, lφ ~ T-1/2, but there is no temperature dependence for the tensile strain. g. Schematic view of a Kelvin four-point probe pattern for resistance measurement, where Al2O3 capped Bi2Se3 films on polyimide (PI) are indicated.

Figure 4

Figure 4: DFT-calculated results. a-c, Calculated band structures for the 6-QL Bi2Se3 slab 20 ACS Paragon Plus Environment

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under the compressive stress, without stress, and under the tensile stress, respectively, where red symbols represent surface states, and EFDFT and EFExp are the charge neutrality point and the experimental Fermi level, respectively. e and g, Electron-density profiles of states c1-c3 and u1u3 crossing EFExp marked by horizontal dashed lines in d and f for the 5% compressive strain and the unbent films, respectively. h, Calculated interlayer separations in units of Å for the (111)surface film with the 5% compressive strain along the c axis (normal to the surface). i-j Constant energy contours of the Dirac cone at EFExp for the compressive strain and unbent case, where the value of unity on the vertical color scale indicates 100% electron localization at either the topmost or bottommost QL. With the compressive stress, the Dirac cone has bulk-like characteristics along and nearby the Γ–M directions. Spin-momentum locking at the energy contours is shown in Fig. S4 in Supporting Information.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications Website.

UPS spectra of 6-QL Bi2Se3 on 500 µm polyimide sheet with and without strain; Resistance changes versus bending length for 10 cycles; Reversible bending test conducted more than 1000 times; DFT-calculated spin textures of the Dirac cone with and without strain.

AUTHOR INFORMATION Corresponding Authors Emails: M.-H. Cho ([email protected]) and K. Park ([email protected]). Phone: 1 540 231 5533. 21 ACS Paragon Plus Environment


Page 22 of 30

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS This research was supported by the National Research Foundation of Korea (NRF) grant funded by

the

Korea

government

(No.2015R1A2A1A01007560)

and

NRF

(Grant

No.2017R1A5A1014862, SRC program: vdWMRC center). The authors are grateful for the support in XRD measurements using the fs-THz spectroscopy beamlines at Pohang Light Source (PLS). The authors are also grateful to Junkyeong Jeong and YeonJin Yi for the support in UPS measurements, to Myung Wook Park for the support in drawing schematic atomic-scale figures, and to John W. Villanova for reading the manuscript. K. P. was supported by United States National Science Foundation Grant DMR-1206354 and computational support SDSC Comet under DMR060009N and Virginia Tech ARC.

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Tables

Table 1. Fitting Parameter Values in the Drude-Lorentz Model13 for the Terahertz 26 ACS Paragon Plus Environment

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Parameters

Flat (5QLs)

Bent (5QLs)

Flat (6QLs)

Bent (6QLs)

∗ ',[\\ (]^_R/+ )

27(±2.5)

30(±2.3)

29(±5.4)

30(±3.7)

∗ ',-.* (]^_R/+ )

52.9(±2.7)

N/A

68.4(±4.4)

48(±5.2)

,)** (]^_R )

6.8(±1.3)

6.7(±1.7)

6.8(±1.6)

6.7(±1.4)

,-.* (]^_R )

20(±1.8)

N/A

20(±2.1)

19(±2.3)

Ω∗',-.* (]^_R/+ )

154(±5.2)

101.9(±5.9)

195.1(±11)

184.8(±8.6)

Ω∗','` (]^_R/+ )

116.4(±6.4)

119.4(±12)

55.43(±5.9)

36(±3.5)

Ω ,-.* (]^_R )

44.9(±1.5)

30(±2.1)

48.1(±2.5)

45.2(±2.7)

Ω ,'` (]^_R )

74.5(±0.2)

75.3(±0.4)

72.6(±0.3)

72.5(±0.4)

Γ-.* (]^_R )

107.3(±4.9)

80(±8.0)

130(±12)

150(±13)

Γ'` (]^_R )

16.3(±0.6)

17.1(±0.9)

13.9(±0.8)

18.8(±1.0)

2

-2.1(±0.05)

-2.1(±0.1)

-2.8(±0.1)

-3.3(±0.1)

Spectroscopy Data on the 5-QL and 6-QL Bi2Se3 Films on Polyimide (Fig. 2)a

∗ ',)** 9∗ ',-.* < is the plasma frequency of the TSSs (QWSs) multiplied by a square root

a

of the thickness of surface dsurface (the TI film thickness dbulk), and ,)** 9,-.* < is the scattering rate of the TSSs (QWSs). Ω∗ ',-.* 9Ω∗ ','3 < is the oscillator strength for intersubband transitions among the QWSs (A1u phonon) multiplied by a square root of dbulk, and Ω ,-.* 9Ω ,'3 < and Γ-.* 9Γ'3 < are the center frequency and damping rate for 27 ACS Paragon Plus Environment


Page 28 of 30

intersubband transitions among the QWSs (A1u phonon), respectively. q is a dimensionless Fano asymmetry factor. Table 2.

Experimental and DFT-calculated Lattice Constants, DFT-calculated Band Gaps

and Work Functions for Bi2Se3b Parameters

unstrained

5% compressive strain

5% tensile strain

a (Å)

4.1430

4.1927

4.0933

c (Å)

28.6360

27.2042

30.0678

z1 (Å)

1.5511

1.5499

1.6302

z2 (Å)

1.9320

1.8760

1.9911

z3 (Å)

2.5791

2.2163

2.7799

Dirac cone gap at Γ [6 QLs]

0.002

< 0.001

0.113

Bulk band gap edge from

0.377

0.218

N/A

0.016

0.102

0.175

5.162

5.076

4.934

Dirac point at Γ [6 QLs] EFExp from bulk band gap edge [6 QLs] Work function [6 QLs]

b

Here a and c are in-plane and out-of-plane lattice constants and z1, z2, z3 are interlayer

separations illustrated in Fig. 4h for the experimental Bi2Se3 bulk and (111) films47 and for the DFT-calculated bulk and films under the stress. The other DFT-calculated quantities are in units of eV. The other DFT-calculated quantities are in units of eV. The uncertainties of the in-plane and out-of-plane lattice parameters are 0.005 and 0.020, respectively47. The uncertainties of the DFT-calculated work functions are about 10 meV, and those of the DFT-calculated band edges 28 ACS Paragon Plus Environment

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are about 1 meV.



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Tuning of Topological Dirac States via Modification of van der Waals

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