Letter pubs.acs.org/NanoLett
Surface-Dominated Transport on a Bulk Topological Insulator Lucas Barreto,† Lisa Kühnemund,‡ Frederik Edler,‡ Christoph Tegenkamp,‡ Jianli Mi,¶ Martin Bremholm,¶ Bo Brummerstedt Iversen,¶ Christian Frydendahl,† Marco Bianchi,† and Philip Hofmann*,† †
Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark ‡ Institut für Festkörperphysik, Leibniz Universität Hannover, 30167 Hannover, Germany ¶ Center for Materials Crystallography, Department of Chemistry, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark S Supporting Information *
ABSTRACT: Topological insulators are guaranteed to support metallic surface states on an insulating bulk, and one should thus expect that the electronic transport in these materials is dominated by the surfaces states. Alas, due to the high remaining bulk conductivity, it is challenging to achieve surface-dominated transport. Here we use nanoscale four-point setups with a variable contact distance on an atomically clean surface of bulk-insulating Bi2Te2Se. We show that the transport at 30 K is two-dimensional rather than threedimensional, that is, surface-dominated, and we find a surface state mobility of 390(30) cm2 V−1 s−1 at 30 K at a carrier concentration of 8.71(7) × 1012 cm−2. KEYWORDS: Topological insulators, Bi2Te2Se, nanoscale four-point probe, angle-resolved photoemission, scanning tunneling spectroscopy
T
other scattering angles are not,19 such that transport could be strongly affected by impurity scattering and, at finite temperature, also by electron−electron and electron−phonon scattering. Indeed, the heavy elements in the topological insulators typically lead to a low Debye temperature, increasing the significance of phonon scattering.20 In the present work, the direct measurement of surface transport is achieved by combining high-quality bulk-insulating crystals of Bi2Te2Se16 with four-point transport measurements on the clean surface in ultrahigh vacuum and on a variable length scale. The transport measurements shown in Figure 1(a) were performed using the same piece of Bi2Te2Se on two instruments: a four tip scanning tunnelling microscope (4STM)21−23 and a collinear 12-point probe (12pp).24,25 These are shown in Figure 1b,c. For the 4STM, the scanning electron microscopy image is that of the four contacts placed on the actual surface of Bi2Te2Se. Typically, transport measurements were performed on large areas free of atomic steps (with lateral dimensions larger than 100 × 100 μm2) but this particular image has been chosen to show how such steps appear in the images (see magnified inset). The 4STM and 12pp transport measurements, as well as the photoemission
he most significant hurdle for reaching surface-dominated transport in a topological insulator (TI) is currently believed to be the high conductivity of the underlying bulk. In fact, most bulk TIs have a small band gap, are degenerately ndoped, and/or suffer from poor screening of impurities.1 Surface contributions to transport have so-far only been singled out indirectly via quantum oscillations,2,3 systematic doping change in thin films,4 or for devices based on gated and doped topological insulator thin films, a situation in which the surface carrier mobility could be limited by defect and interface scattering,5−10 or degrade rapidly because of surface contamination.11,12 An important goal of the field is therefore to achieve surface-dominated transport on a pristine surface and to establish the carrier mobility that can be reached under these circumstances.13,14 Only recently, materials with a semiconducting temperature dependence of the bulk resistivity dρ/dT have been synthesized,15,16 opening the road to surfacedominated transport even on bulk crystals. While the high bulk conductance is a well-recognized issue, it is by no means obvious that the surface conductance would be very high. For a one-dimensional (1D) edge state of a twodimensional (2D) TI (the quantum spin Hall effect), the spin texture provides a protection from back scattering and because this is the only possible scattering process in 1D, perfect quantum transport results at low temperature.17,18 For a 2D surface state, strict 180° backscattering is still forbidden but © 2014 American Chemical Society
Received: February 17, 2014 Published: June 18, 2014 3755
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Figure 1. (a) Four-point resistance measurements on a clean Bi2Te2Se surface taken at 300 and at 30 K (data points), together with the expected result for bulk dominated transport at these two temperatures (solid lines). Note that the statistical uncertainties are in some cases smaller than the markers (see Methods section for a discussion of this). The dimensionality of the transport can be read directly from the data as 2D for 30 K and 3D for 300 K. (b) Scanning electron microscopy (SEM) image of the four STM contacts used for the 30 K measurements on the surface of Bi2Te2Se. The inset shows how surface steps appear in the image (marked by an arrow). (c) SEM image of the 12 point probe used for the 300 K measurements. (d) Bulk resistivity of the Bi2Te2Se sample as a function of temperature. (e) Picture of a sample similar to that used in the experiment (but not identical) together with a measurement of the local Seebeck coefficient, showing a p-n transition across the sample, as well as the local variation in the n-type region close to the transition.
Clearly, the agreement is excellent and we find no indication of surface transport. The situation is entirely different for the measurements taken at 30 K. Here the measured R is approximately independent of s. Such a behavior is expected for pure 2D conductance where one finds that R = R2D = ln 2/(πσs) with σs being the 2D sheet conductance.26 If we assume the total four-point resistance to be the contribution of surface and bulk in parallel, that is, R−1 tot = −1 R−1 2D + R3D, it thus appears that bulk transport contribution is negligible at this temperature. When taking the average resistance at 30 K (dashed black line in Figure 1a), we obtain a sheet conductance of σs = 5.3(3) × 10−4 Ω−1. Again, we can calculate the expected behavior for bulkdominated transport. From Figure 1d, we find the bulk resistivity at 30 K to be ∼4 Ωcm, consistent with the highest values reported in the literature,15 and 2 orders of magnitude higher than at 300 K. Using this value, a calculation of the expected bulk behavior results in the blue line. The four-point
measurements reported below, were taken before the sample’s bulk properties were measured, such that there was no risk of contaminating the sample surfaces by the silver paste used to contact the sample for the bulk measurements. Figure 1a shows the key results of this paper, the corrected four-point resistance R as a function of the corrected contact spacing s at 300 and at 30 K (see Experimental Methods section for a detailed discussion of the corrected resistance and corrected contact spacing). The data points at 300 K have been collected with the 12pp whereas the 30 K data points have been measured with the 4STM. At 300 K, the four-point resistance R is observed to be inversely proportional to the contact distance s. This behavior is characteristic for four-point measurements on a 3D bulk crystal, where we expect that R = R3D = 1/ (2πsσb), with σb being the bulk conductivity.26 The red line through the data points shows the expected four-point probe resistance at room temperature, based on a macroscopic bulk resistivity measurement on the same crystal (see Figure 1d). 3756
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Figure 2. ARPES and scanning tunnelling spectroscopy characterization of the Bi2Te2Se samples used in this study. (a) Surface state dispersion along the M̅ −Γ̅ −M̅ direction. (b) Photoemission intensity at the Fermi energy. (c) Scanning tunnelling spectra taken at 300 and 30 K.
Moreover, the dominance of surface transport is also favored by an anisotropy of the bulk conductivity27,28 because the lower conductivity perpendicular to the van der Waals gap in the structure will diminish the penetration of the current into the bulk. In order to determine the surface state mobility from the sheet resistance, it is necessary to know the carrier concentration in the surface state. To this end, the surface electronic structure of the Bi2Te2Se is determined by angleresolved photoemission spectroscopy (ARPES), using again the same piece of sample as for the transport measurements. Figure 2a,b shows the results of such a measurement. The spectra clearly show the existence of the topological surface state with the Dirac point at a binding energy of approximately 360 meV and a considerable hexagonal warping of the constant energy contour at the Fermi energy. The distance from the hexagon’s edges to the center is found to be 0.0997(4) Å −1 , corresponding to a density of 8.71(7) × 1012 surface electrons per cm2 (the bulk carrier density at 30 K is ∼1 × 1018 cm−3, see Supporting Information). From this and σs determined above, we can evaluate the carrier mobility to be 390(30) cm2 V−1 s−1. This surface mobility is somewhat lower (by a factor of ∼3) than the low-temperature values reported for Bi2Se39 or Bi2Te2Se.15 Apart from the obvious reason for increased electron−phonon scattering at the higher temperature here (30 K instead of 1.6 K for the Bi2Te2Se results in ref 15), the lower mobility could be caused by the higher carrier density (8.71(7) × 1012 instead of 1.5 × 1012 in ref 15) and thereby increased phase space for scattering. When interpreting σs as solely originating from the topological surface state, it is important to exclude the contributions of two-dimensional electron gases (2DEGs) that can potentially form at the surfaces of TIs due to adsorbate-induced band bending.29,30 ARPES can identify both degenerately populated conduction band states near the surface
resistance can clearly not be reconciled with bulk behavior, not only because of the wrong dependence on the contact spacing, but also because the surface is much more conductive at small contact spacings than expected for the bulk solid. Interestingly, the blue line crosses the constant of the dashed line through the data points for a spacing of ∼20 μm. One should therefore expect a transition to bulk-dominated behavior around this spacing but such a trend is not observed. The surfacedominated transport is seen to persist to the largest measured spacing of ∼100 μm, suggesting that the actual bulk resistivity of the underlying sample in the probed surface area is larger than the value obtained from the macroscopic resistivity measurement. In fact, it is plausible that a macroscopic measurement for a not perfectly homogeneous sample will tend to give an average resistivity that is dominated by percolated regions of low resistance. This is consistent with previous transport measurements of Bi2Te2Se single crystals that show strong variations between individual samples.15 It is also supported by a recent study of the crystal structure and transport behavior of nominally stoichiometric Bi2Te2Se crystals grown by the Stockbarger method which showed strong concentration and structural variations over the resulting crystal.16 Figure 1e illustrates this for a sample similar to the one used in our experiment here. A photograph of the sample is shown together with highly resolved measurements of the local Seebeck coefficient and the observed considerable fluctuations are ascribed to local stoichiometric and structural variations. Indeed, the Seebeck coefficient even changes sign, illustrating the local p-n junction typically found in the region of highest bulk resistivity.16 It is thus not surprising that a given surface region might show a higher local bulk resistivity than obtained by a macroscopic resistivity measurement. Note in fact that the entire distance range of measurements report in Figure 1a fits into one pixel of the Seebeck measurements in Figure 1e. 3757
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the Debye temperature in graphene is very high, such that the mobility is not very strongly temperature dependent. In the topological insulators, on the other hand, the presence of heavy atoms leads to a low Debye temperature and even lower values can be found at the surface.38 Finally, the filling of the topological state here is higher than for the graphene samples in refs.23,32 This increases the phase space for scattering and reduces the mobility. In conclusion, we have reported a direct surface statedominated transport measurement on the clean surface of bulkinsulating Bi2Te2Se. The surface mobility is found to be high, 390(30) cm2 V−1 s−1, at the measurement temperature of 30 K. Reaching the surface-dominated transport regime has been possible by the combination of a nanoscale four-point probe technique with high-quality bulk crystals. The results indicate that the bulk resistivity in a carefully chosen region of the crystal may significantly exceed the value measured from a macroscopic bulk crystal. This is not surprising in view of the fluctuations of physical properties observed in large bulk crystals16 and it suggests that pushing surface-dominated transport toward room temperature could be an achievable goal. Experimental Methods. Bi2Te2Se crystals were grown and characterized as described in ref 16. The surface transport measurements and ARPES measurements were performed on the same piece of sample that was cleaved several times in the different ultrahigh vacuum chambers in order to produce clean surfaces. The sample had a thickness of at least 300 μm. All experiments were performed within a few hours after cleaving such that all transport and ARPES experiments are comparable in terms of surface cleanliness. Nanoscale transport measurements with the 4STM were carried out using the four STM tips in a collinear and equidistant probe configuration (probe spacing s) with the current passed through the outer two probes and the voltage measured over the inner two. The position of the tips on the surface and the surface morphology was controlled using a scanning electron microscope. For transport measurements, the tips were approached individually to the sample until a tunnelling contact was established. From this position, the approach was further continued until an ohmic contact regime was reached. From a comparison between two-contact and four-contact measurements, the contact resistance can be estimated to be less than 100 Ω at all measured temperatures. The instrument is described in detail in ref 22. On the other hand, the 12pp measurements were taken with a monolithic collinear probe with different contact distances.24 These probes were approached to the sample until a measurable contact was established for all 12 tips. Because of possible misalignments of probe and sample, it was sometimes found necessary to retract and realign the probe in order to establish a contact of all tips. With a 12pp, it is not possible to vary the contact spacing but it is possible to effectively emulate an equidistant four-point probe measurement. To this end, one introduces the corrected resistance eq χ2DR4pp total and the corrected spacing S3D/χ2D. They correspond to the measured resistance R and contact spacing s for an equidistant four-point probe where the outer two contacts are used as current sources and the inner two as voltage probes, that is, to the situation in the 4STM measurements. This approach has been used to display the 12pp data points in Figure 1, whereas the 4STM data points in the figure are merely the uncorrected four-point resistance and contact spacing. For a detailed treatment of the concepts of corrected resistance and
as well as 2DEGs. Both give rise to features at the Fermi energy within the Fermi contour of the topological surface state. Bulk conduction band states appear as a broad feature that disperses with photon energy, while 2DEGs have a well-defined contour that does not show such dispersion. The data in Figures 2(a) and (b) have been taken with a photon energy that maximizes the sensitivity toward bulk states and 2DEGs and we can exclude the presence of a 2DEG. Only a very weak and diffuse enhancement of the photoemission intensity is seen around normal emission (k∥ = 0 Å−1) in Figure 2(b) (but not in Figure 2(a) because the color scaling of this figure is dominated by the intense states at higher binding energy). After several hours in vacuum, however, a small amount of adsorbate-induced band bending can be seen, leading to the observation of the bulk conduction band minimum at k∥ = 0 Å−1 but not to a distinct 2DEG. In fact, we find Bi2Te2Se surfaces to be much less sensitive to contamination-induced band bending than Bi2Se3 surfaces and no 2DEG formation is observed, unless the surface is doped with alkali atoms. The 2D character of the four-point resistance R at 30 K appears to rule out a significant contribution to the conductance from bulk states and we can support this by further observations. Figure 2c shows scanning tunnelling spectra, taken with one of the tips of the 4STM at 30 and 300 K, around 4 h after cleaving the sample. While distinct signatures of the topological states are typically difficult to identify in such spectra, similar to the situation in ref 31, it is clear that the Fermi energy at the surface is placed well within the bulk band gap and the bulk states are therefore not expected to contribute significantly to the observed transport. Moreover, the in-gap differential conductance at 30 K is much lower than at 300 K, consistent with the resistivity change over this temperature range. A time-dependent near-surface band bending can be expected to increase the bulk carrier density near the surface and hence the conductance. However, we could not observe any systematic time-dependence of the measured σ2D within the first 30 h after the cleave. Indeed, no such change could be observed even when intentionally contaminating the surface with carbon monoxide at a partial pressure of ∼5 × 10−9 mbar for 2 h. From this we conclude that while a band bending might be present, the contribution of bulk states to the transport is still negligible, presumably because the band bending induced carrier density is still much smaller than that from the surface states. It is interesting to compare these results to those from epitaxial graphene grown on the silicon face of SiC, both because graphene is a similar Dirac-material but also because this system has been measured with the same 4STM23 and 12pp32 techniques. The reported results are remarkably similar. Not only do both techniques report a purely two-dimensional transport behavior, they also give nearly the same values for the measured resistance of ∼200 Ω at room temperature (note that ref 23 reports the sheet resistance which is equivalent to 1/σs here and in ref 32). The mobility was found to be 700 cm2 V−1 s−1 in ref 23 and 870 cm2 V−1 s−1 in ref 32 with the small difference being caused by different estimates of the carrier density. The (room temperature) mobility in graphene is thus somewhat higher than the 30 K mobility for the surface state of Bi2Te2Se as reported here. This is not very surprising: in weakly doped graphene, the electron phonon coupling strength is found to be exceedingly small,33,34 whereas the situation for the topological insulator surfaces is controversial.20,35−37 Moreover, 3758
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(3) Analytis, J. G.; McDonald, R. D.; Riggs, S. C.; Chu, J.-H.; Boebinger, G. S.; Fisher, I. R. Two-dimensional surface state in the quantum limit of a topological insulator. Nat. Phys. 2010, 6, 960−964. (4) Aitani, M.; Sakamoto, Y.; Hirahara, T.; Yamada, M.; Miyazaki, H.; Matsunami, M.; ichi Kimura, S.; Hasegawa, S. Fermi-Level Tuning of Topological Insulator Thin Films. Jpn. J. Appl. Phys. 2013, 52, 110112. (5) Steinberg, H.; Gardner, D.; Lee, Y.; Jarillo-Herrero, P. Surface State Transport and Ambipolar Electric Field Effect in Bi2Se3 Nanodevices. Nano Lett. 2010, 10. (6) Checkelsky, J. G.; Hor, Y. S.; Cava, R. J.; Ong, N. P. Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi2Se3. Phys. Rev. Lett. 2011, 106, 196801. (7) Cho, S.; Butch, N. P.; Paglione, J.; Fuhrer, M. S. Insulating Behavior in Ultrathin Bismuth Selenide Field Effect Transistors. Nano Lett. 2011, 11, 1925−1927. (8) Yuan, H.; Liu, H.; Shimotani, H.; Guo, H.; Chen, M.; Xue, Q.; Iwasa, Y. Liquid-Gated Ambipolar Transport in Ultrathin Films of a Topological Insulator Bi2Te3. Nano Lett. 2011, 11, 2601−2605. (9) Kim, D.; Cho, S.; Butch, N. P.; Syers, P.; Kirshenbaum, K.; Adam, S.; Paglione, J.; Fuhrer, M. S. Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3. Nat. Phys. 2012, 8, 460. (10) Xia, B.; Ren, P.; Sulaev, A.; Liu, P.; Shen, S.-Q.; Wang, L. Indications of surface-dominated transport in single crystalline nanoflake devices of topological insulator Bi1.5Sb0.5Te1.8Se1.2. Phys. Rev. B 2013, 87, 085442. (11) Kong, D.; Cha, J. J.; Lai, K.; Peng, H.; Analytis, J. G.; Meister, S.; Chen, Y.; Zhang, H.-J.; Fisher, I. R.; Shen, Z.-X.; et al. Rapid Surface Oxidation as a Source of Surface Degradation Factor for Bi2Se3. ACS Nano 2011, 5, 4698−4703. (12) Lang, M.; He, L.; Xiu, F.; Yu, X.; Tang, J.; Wang, Y.; Kou, X.; Jiang, W.; Fedorov, A. V.; Wang, K. L. Revelation of Topological Surface States in Bi2Se3 Thin Films by In Situ Al Passivation. ACS Nano 2011, 6, 295. (13) Brüne, C.; Liu, C. X.; Novik, E. G.; Hankiewicz, E. M.; Buhmann, H.; Chen, Y. L.; Qi, X. L.; Shen, Z. X.; Zhang, S. C.; Molenkamp, L. W. Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe. Phys. Rev. Lett. 2011, 106, 126803. (14) Kim, D. J.; Thomas, S.; Grant, T.; Botimer, J.; Fisk, Z.; Xia, J. Surface Hall Effect and Nonlocal Transport in SmB6: Evidence for Surface Conduction. Sci. Rep. 2013, 3. (15) Ren, Z.; Taskin, A. A.; Sasaki, S.; Segawa, K.; Ando, Y. Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se. Phys. Rev. B 2010, 82, 241306. (16) Mi, J.-L.; Bremholm, M.; Bianchi, M.; Borup, K.; Johnsen, S.; Søndergaard, M.; Guan, D.; Hatch, R. C.; Hofmann, P.; Iversen, B. B. Phase Separation and Bulk p-n Transition in Single Crystals of Bi2Te2Se Topological Insulator. Adv. Mater. 2013, 25, 889−893. (17) Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C. Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells. Science 2006, 314, 1757−1761. (18) Konig, M.; Wiedmann, S.; Brune, C.; Roth, A.; Buhmann, H.; Molenkamp, L. W.; Qi, X.-L.; Zhang, S.-C. Quantum Spin Hall Insulator State in HgTe Quantum Wells. Science 2007, 318, 766−770. (19) Nechaev, I. A.; Jensen, M. F.; Rienks, E. D. L.; Silkin, V. M.; Echenique, P. M.; Chulkov, E. V.; Hofmann, P. Hole dynamics in a two-dimensional spin-orbit coupled electron system: Theoretical and experimental study of the Au(111) surface state. Phys. Rev. B 2009, 80, 113402. (20) Hatch, R. C.; Bianchi, M.; Guan, D.; Bao, S.; Mi, J.; Iversen, B. B.; Nilsson, L.; Hornekær, L.; Hofmann, P. Stability of the Bi2Se3(111) topological state: Electron-phonon and electron-defect scattering. Phys. Rev. B 2011, 83, 241303. (21) Shiraki, I.; Tanabe, F.; Hobara, R.; Nagao, T.; Hasegawa, S. Independently driven four-tip probes for conductivity measuremtns in ultra-high vacuum. Surf. Sci. 2001, 493, 633. (22) Guise, O.; Marbach, H.; John T. Yates, J.; Jung, M.-C.; Levy, J.; Ahner, J. Development and performance of the nanoworkbench: A
corrected spacing, see refs 25 and 39. In some cases, single tips could not be brought into contact and then only measurement configurations not using these tips were employed. The vertical error bars on the points represent the uncertainty in the resistivity measurement and the horizontal error bars the uncertainty that arises from an in-line misplacement of the contacts. Note that the scatter in the data points is higher than what would be expected from the error bars. This is a wellknown effect and can be ascribed to sample inhomogeneity.25 After the completion of the surface transport and ARPES measurements, bulk transport measurements were performed on the millimeter-size crystal using a Quantum Design Physical Property Measurement System. This experiment requires contacting the sample with silver paste such that it is no longer possible to collect further ARPES or surface transport data from the same sample. A potential Seebeck microprobe40 was used to map Seebeck coefficient at room temperature with a resolution of 70 μm. Measurements were performed on crystal pieces with sizes and properties similar to that used for the other measurements reported in this paper. ARPES experiments were performed at the SGM-3 beamline of the synchrotron radiation source ASTRID.41 The sample temperature during the ARPES measurements was 70 K. The energy and angular resolution were better than 20 meV and 0.2°, respectively. The photon energy (17.5 eV) was chosen such that the photoemission intensity from the bulk conduction band minimum is maximized. This happens not because of the escape depth of the photoelectrons but because this photon energy causes a direct transition from the conduction band minimum to a final state that escapes the solid, that is, the choice of photon energy corresponds to the crystal momentum of the conduction band minimum in this material. The corresponding photon energy for Bi2Se3 is 19.2 eV and the observed dispersion of the conduction band minimum can be seen in Figure 1 of ref 42. The carrier density in the topological surface state was estimated from the size of the measured Fermi surface.
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ASSOCIATED CONTENT
S Supporting Information *
The supporting material contains a plot of the sample’s Hall coefficient as a function of temperature. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge support from the Carlsberg foundation, the VILLUM foundation, the Danish National Research Foundation (DNRF93) and Capres A/S.
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REFERENCES
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