Abstract
The newly discovered threedimensional strong topological insulators (STIs) exhibit topologically protected Dirac surface states^{1,2}. Although the STI surface state has been studied spectroscopically, for example, by photoemission^{3,4,5} and scanned probes^{6,7,8,9,10}, transport experiments^{11,12,13,14,15,16,17} have failed to demonstrate the most fundamental signature of the STI: ambipolar metallic electronic transport in the topological surface of an insulating bulk. Here we show that the surfaces of thin (∼ 10 nm), lowdoped Bi_{2}Se_{3} (≈10^{17} cm^{−3}) crystals are strongly electrostatically coupled, and a gate electrode can completely remove bulk charge carriers and bring both surfaces through the Dirac point simultaneously. We observe clear surface band conduction with a linear Hall resistivity and a welldefined ambipolar field effect, as well as a chargeinhomogeneous minimum conductivity region^{18,19,20}. A theory of charge disorder in a Dirac band^{19,20,21} explains well both the magnitude and the variation with disorder strength of the minimum conductivity (2 to 5 e^{2}/h per surface) and the residual (puddle) carrier density (0.4×10^{12} to 4×10^{12} cm^{−2}). From the measured carrier mobilities 320–1,500 cm^{2} V^{−1} s^{−1}, the charged impurity densities 0.5×10^{13} to 2.3×10^{13} cm^{−2} are inferred. They are of a similar magnitude to the measured doping levels at zero gate voltage (1×10^{13} to 3×10^{13} cm^{−2}), identifying dopants as the charged impurities.
Main
Bi_{2}Se_{3}, as prepared, is observed to be ntype owing to Se vacancies. We find that mechanically exfoliated thin (thickness t≈10 nm) Bi_{2}Se_{3} on SiO_{2}/Si is invariably highly ndoped with sheet charge densities ≳10^{13} cm^{−2}, much greater than expected considering the bulk charge density (≈10^{17} cm^{−3}) in our lowdoped starting material^{22}, suggesting additional doping is induced by mechanical cleavage, reaction with ambient species^{14,23}, or substrate interaction. To remove this doping, we employed two types of ptype doping schemes on mechanically exfoliated thin Bi_{2}Se_{3} fieldeffect transistors on 300 nm SiO_{2}/Si backgate substrates^{24,25,26,27}: (1) chemical doping with 2,3,5,6tetrafluoro7,7,8,8tetracyanoquinodimethane (F4TCNQ) or (2) electrochemical doping with a polymer electrolyte top gate.
Figure 1a,b shows the schematics of the device structures and gating schemes. We exploit either the strong electron affinity (≈5.4 eV) of F4TCNQ molecules^{27} or the large capacitance (≈1 μF cm^{−2}) of the electrochemical double layer at the interface between accumulated ions and the sample surface^{24,25,26} to induce negatively charged ions near the surface and ptype doping of Bi_{2}Se_{3}. In both cases the dopant density was fixed after cooling to cryogenic temperature, but further tuning of the carrier density was possible using the back gate (see Methods).
Figure 1c,d shows the longitudinal resistivity ρ_{xx} and Hall carrier density n_{H}=1/(e R_{H}) (where R_{H}is the Hall coefficient and e is the elementary charge) of a representative device (F4TCNQdoped device 4) at various temperatures T from 2 to 50 K as a function of the backgate voltage V _{g}. The plot of ρ_{xx}(V _{g}) shows a peak at V _{g,0}≈−45 V, and n_{H} changes sign at a similar V _{g}, diverging positively (negatively) when approaching V _{g,0}=−45 V from above (below). There is no evidence of an energy gap: ρ_{xx}(T) is metallic (dρ_{xx}/dT>0) and saturates at low T, and n_{H}(T) shows little temperature dependence. The behaviour is strongly reminiscent of that seen for the twodimensional Dirac electronic system in graphene^{18}. Likewise, we identify the linear regions of n_{H} versus V _{g} for V _{g}>−35 V and V _{g}<−60 V as unipolar n and pdoped regimes respectively, and the region −35<V _{g}<−60 V as an inhomogeneous regime where electron and hole transport are both present.
Figure 2a shows the Hall resistivity of device 4 as a function of magnetic field ρ_{xy}(B) at various gate voltages in the unipolar n and pdoped regimes. The Hall resistivity in the unipolar regime is always linear over the entire range of magnetic field (±9 T), indicating all bands contributing to the transport have similar mobility and the same carrier sign. Specifically, we can rule out the possibility of both bulk and surface channels participating in conduction (previously observed to give a nonlinear ρ_{xy}(B); refs 11, 12, 28) or significant contribution to conduction by impurity bands, which should have much lower carrier mobilities (1–10 cm^{2} V^{−1} s^{−1}; ref. 17). The measured linear ambipolar Hall effect, with carrier mobility of >10^{3} cm^{2} V^{−1} s^{−1}, is therefore a strong indication that conduction in our samples is dominated by the surface states.
We note that a previous work on singlegated Bi_{2}Se_{3} of similar thickness, but heavily (0.5%) Cadoped^{17}, also showed a superficially similar resistivity peak, interpreted there as the transition from bulk to surface conduction. No region of unipolar ptype Hall effect was observed. The authors concluded that significant band bending in these highly doped crystals led to very different carrier densities on either side of the device as well as an effective reduction of the bulk gap^{11,13,17}. To determine whether band bending is important in our devices, we fabricated a further top gate on an F4TCNQdoped device (device 5), using hydrogen silsequioxane (HSQ) as a topgate dielectric.
Figure 2b shows the resistivity ρ_{xx} of dualgated device 5 as a function of applied displacement field to the top (D_{tg}) and bottom (D_{bg}) surfaces (see Methods). The data are presented as a polar plot of the normalized resistivity (ρ_{xx}/ρ_{max}) of the device as a function of total magnitude of displacement field D_{total}=D_{bg}+D_{tg}and asymmetry factor, defined by α=(4/π)tan^{−1}[(D_{tg}−D_{bg})/D_{total}]. We find that the measured resistivity depends only on the total displacement field, proportional to the total charge density in the Bi_{2}Se_{3} slab. We conclude from the observed azimuthal symmetry that both surfaces are gated simultaneously with either gate and their chemical potential lies at the same level. If the gates acted independently on top and bottom surfaces, then the maximum resistivity peak associated with the transition from n to pdoping in each surface should broaden or split with increasing asymmetry; no such effect is observed. Remarkably, we find that simultaneous gating can be achieved even with a singlegate electrode (α=±1). We ascribe this effect to (1) the strong electrostatic coupling of the surfaces due to the large intersurface capacitance provided by the thin, lightly doped Bi_{2}Se_{3}, which has a high relative dielectric constant κ≈100; and (2) the low density of states of the Dirac surface. The net result is that the electrostatic intersurface capacitance exceeds the quantum capacitance of each surface, in which case the two surface potentials become locked together (see Supplementary Information for a further discussion).
Having eliminated the possibilities of band bending or significant contribution to the conductivity by bulk or impurity states, we conclude that our measurement probes the conductance of the simultaneously gated ambipolar Dirac surfaces states. Our results therefore represent the first experimental demonstration of metallic, ambipolar, gapless electronic conduction of the topological surface state in Bi_{2}Se_{3} in the absence of bulk carriers; the defining quality of a topological insulator.
Below, we analyse in more detail the transport properties of the topological surface state as a function of carrier density per surface n estimated from n=(C_{g}/2e)(V _{g}−V _{g,0}), where V _{g,0}is the gate voltage at which R_{H}=0, which corresponds closely to the gate voltage of minimum conductivity. Figure 3a–c shows the conductivity per layer (σ), the Hall carrier density per layer (n_{H,layer}=1/2R_{H}e), and field effect mobility μ=σ/n eversus carrier density per layer n. Data are shown for devices 1–3, with electrolyte gating, and devices 4 and 5, chargetransferdoped with F4TCNQ. Several features are notable immediately in Fig. 3 and comprise the main experimental observations in this work. On tuning the carrier density: (1) σ and n_{H,layer} show clear ambipolar conduction with welldefined p and nregions, (2) n_{H,layer}shows a minimum value (n^{*}) for p and nconduction, (3) σ shows a roughly linear carrier density dependence for n^{*}<n<n_{bulk}, where n_{bulk}≈5×10^{12} cm^{−2} is the carrier density above which the bulk conduction band is expected to be populated, and (4) a minimum conductivity (σ_{min}=2e^{2}/h to 5e^{2}/h) is observed.
Extending the theory of charge disorder in graphene^{19,20}, a recent theoretical study predicts the conductivity as being limited by chargedimpurity scattering in STI of the form (assuming a linear Dirac band)^{21},
where n_{imp}is the charged impurity density, C is a constant that depends on the Wigner–Seitz radius r_{s}, and n^{*} is identified as the residual carrier density in electron and hole puddles. For Bi_{2}Se_{3} on SiO_{2}(ref. 21) we expect 0.05<r_{s}<0.2 and 30<C<300. See Supplementary Information for a more detailed description of the theory. For n^{*}<n<≈5×10^{12} cm^{−2}, we fit σ(n) to equation (1a) (Fig. 3a, dashed lines), to obtain the fieldeffect mobility μ_{FE}=C e/n_{imp}h for each device. μ_{FE} ranges from 320–1,500 cm^{2} V^{−1},s^{−1}, reflecting different amounts of disorder in the samples. We identify the initial ntype dopants and defects induced by mechanical exfoliation as likely sources of the disorder. The decrease in μ_{FE} with further electrolytic gating (device 1 run 2) indicates electrochemical damage, probably solvation of Se ions. The observation of sublinear σ(n) at n<n_{bulk} in devices 3–5 may indicate that there are further types of disorder, for example neutral point defects, that should be considered.
The observed minimum conductivity of the Dirac electronic band can be understood well through equation (1b) as being due to the residual carrier density n^{*} in electron and hole puddles induced by the charged impurity potential at nominally zero carrier density: σ_{min}=n^{*}e μ, where n^{*} is calculated selfconsistently^{20} as a function of n_{imp}, r_{s} and d, the distance of the impurities to the Dirac surface. The selfconsistent theory predicts that n^{*}increases with increasing disorder and σ_{min} depends only weakly on disorder. Figure 4 shows the experimentally observed residual carrier density n^{*} per surface for each device (Fig. 4a) as well as σ_{min} per surface (Fig. 4b) as a function of the experimentally measured inverse mobility 1/μ_{FE}, which reflects the disorder strength. (For devices in which n^{*} could be measured for p and ntype conduction, both values are shown.) The shaded regions reflect the expectations of the selfconsistent theory using parameter ranges 0.05<r_{s}<0.2 and d=0.1 Å– 15 Å. We see a good agreement between experiment and theory in that (1) σ_{min} is weakly dependent on disorder strength (1/μ_{FE}) and (2) n^{*}increases with disorder strength (1/μ_{FE}). Particularly for increasing disorder in the same device (Device 1 run 1 versus run 2), n^{*} increases but σ_{min} is almost unchanged (arrows in Fig. 4a,b). The experimental data agree best with the upper range of the theoretical estimates, corresponding to small d=0.1 Å and large r_{s}=0.2. Assuming r_{s}=0.2, we infer an impurity density n_{imp} ranging from 0.5×10^{13} to 2.3×10^{13} cm^{−2}, much larger than for graphene exfoliated on similar SiO_{2} substrates^{29}, but comparable to the observed initial doping level of 1×10^{13} to 3×10^{13} cm^{−2}, suggesting that the dopants are the charged impurities responsible for limiting the mobility (see Supplementary Information).
The simple theory somewhat underestimates n^{*} and σ_{min}, but we expect that the theory can be refined to take into account the nonlinearity and asymmetry of the Bi_{2}Se_{3} surface state bands^{30}. Notably, the larger Fermi velocity for the electron band would increase the conductivity above the estimate in equation (1) for ntype conduction, indicating that the disorder strength is probably somewhat underestimated from the ntype mobility. Shifting the points to the right (to larger disorder strength) in Fig. 4 would indeed improve the agreement between experiment and theory.
Reducing the ntype doping of TI thin films by external agents provides an effective and simple way to probe topological surface transport properties in the absence of bulk conduction. For the present devices the level of charged impurity disorder is on the order of ∼10^{13} cm^{−2}, limiting the mobility to 320–1,500 cm^{2} V^{−1} s^{−1}. However, owing to the large dielectric constants in existing topological insulators, reduction of impurity concentrations to levels seen in the best bulk crystals (<10^{17} cm^{−3} corresponding to <10^{11} cm^{−2} in a 10 nm thick crystal^{22}) would allow mobilities exceeding 10^{5} cm^{2} V^{−1} s^{−1}. Hence understanding and eliminating the doping presently observed in all thin crystals and films is of central importance to increasing the mobility of the topological surface state.
Note added in proof: After submission of this work we became aware of a scanning tunnelling microscopy study^{10} that directly observed the screened potential fluctuations caused by charged impurity disorder in Bi_{2}Se_{3} and Bi_{2}Te_{3}, consistent with our interpretation of the minimum conductivity arising from charge inhomogeneity.
Methods
Bi_{2}Se_{3} thin crystals were produced by micromechanical cleavage of bulk Bi_{2}Se_{3} single crystals and deposited on doped Si covered with 300 nm SiO_{2}. Thin crystals (thickness about 10 nm) were identified using atomic force microscopy (AFM). The thin film was patterned in a Hall bar geometry using an Ar plasma at a pressure of ≈6.7 Pa (5×10^{−2} torr). Au/Cr electrodes were defined by electronbeam lithography (see inset of Fig. 1d). A brief (≈10 s) selective surface treatment of the contact area with a N_{2} or Ar plasma before the deposition of metals was used to enhance the ohmic conduction of the contacts.
The ptype doping for devices 1–3 was achieved by applying a negative voltage to a polymer electrolyte consisting of LiClO_{4} and polyethylene oxide (PEO) in the weight ratio 0.12:1, as previously used for carbon nanotubes and graphene devices^{24,25,26}. Molecular charge transfer doping for device 4 and 5 was done by thermal evaporation of ≈15 nm of F4TCNQ molecules (Aldrich) on top of the samples^{27}. The devices were subsequently cooled down and further tuning of carrier density was done by sweeping the backgate voltage at cryogenic temperature. For electrolytegated measurements, the samples were cooled down to 250 K in less than 1 min after applying the topgate voltage to minimize electrochemical reactions^{25}.
As well as singlegated samples, we fabricated dualgated samples based on F4TCNQdoped samples (Fig. 2b). 60 nm of hydrogen silsequioxane (HSQ, XR1541, Dow Corning) was spincoated on an F4TCNQcoated Bi_{2}Se_{3} device and a topgate electrode was defined by electronbeam lithography. We found that further fabrication on predoped devices increased the ntype doping level (for example, ≈1.2×10^{13} cm^{−2} at zero gate field in Fig. 2b compared with ≈0.3×10^{13} cm^{−2} in Fig. 1d). From the Hall carrier density versus gate voltage, the bottomgate and topgate capacitances were determined to be ≈11 nF cm^{−2} and ≈33 nF cm^{−2}, respectively; reasonable values considering the dielectric constants of SiO_{2} (κ≈3.9) and HSQ (κ≈3).
Fourprobe measurements of longitudinal and transverse electrical resistances were conducted using Stanford Research Systems SR830 Lockin amplifiers and a commercial cryostat equipped with 9 T superconducting magnet. The Hall voltage was recorded in both polarities of the magnetic field (±1 T) and antisymmetrized to remove longitudinal voltage components. In the transport experiments a small and reproducible hysteresis in V _{g},_{0} (≈2 V) was observed during forward and backward gate voltage scans. As a consequence, resistivity and Hall data with the same V _{g} scan directions were compared in this work. Best fits to equation (1a) were determined using a least squares linear fit to σ(n) in the linear regime, determined by identifying the region of roughly constant slope dσ/dn. Thermal runs as described here were performed for more than ten different Bi_{2}Se_{3} samples of similar thickness, with qualitatively consistent results.
Note: certain commercial equipment, instruments or materials are identified in this paper to specify the experimental procedure adequately. Such an identification is not intended to imply any recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.
References
Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).
Zhang, H. J. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009).
Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009).
Chen, Y. L. et al. Experimental realization of a threedimensional topological insulator Bi2Te3 . Science 325, 178–181 (2009).
Xia, Y. et al. Observation of a largegap topologicalinsulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009).
Zhang, T. et al. Experimental demonstration of topological surface states protected by timereversal symmetry. Phys. Rev. Lett. 103, 266803 (2009).
Alpichshev, Z. et al. STM imaging of electronic waves on the surface of Bi2Te3: Topologically protected surface states and hexagonal warping effects. Phys. Rev. Lett. 104, 016401 (2010).
Hanaguri, T. et al. Momentumresolved Landaulevel spectroscopy of Dirac surface state in Bi2Se3 . Phys. Rev. B 82, 081305R (2010).
Cheng, P. et al. Landau quantization of topological surface states in Bi2Se3 . Phys. Rev. Lett. 105, 076801 (2010).
Beidenkopf, H. et al. Spatial fluctuations of helical Dirac fermions on the surface of topological insulators. Nature Phys. 7, 939–943 (2011).
Steinberg, H., Gardner, D. R., Lee, Y. S. & JarilloHerrero, P. Surface state transport and ambipolar electric field effect in Bi2Se3 nanodevices. Nano Lett. 10, 5032–5036 (2010).
Qu, D., Hor, Y. S., Xiong, J., Cava, R. J. & Ong, N. P. Quantum oscillations and Hall anomaly of surface states in the topological insulator Bi2Te3 . Science 329, 821–824 (2010).
Xiu, F. et al. Manipulating surface states in topological insulator nanoribbons. Nature Nanotech. 6, 216–221 (2011).
Analytis, J. G. et al. Twodimensional surface state in the quantum limit of a topological insulator. Nature Phys. 6, 960–964 (2010).
Peng, H. et al. Aharonov–Bohm interference in topological insulator nanoribbons. Nature Mater. 9, 225–229 (2010).
Chen, J. et al. Gate–voltage control of chemical potential and weak antilocalization in Bi2Se3 . Phys. Rev. Lett. 105, 176602 (2010).
Checkelsky, J. G., Hor, Y. S., Cava, R. J. & Ong, N. P. Surface state conduction observed in voltagetuned crystals of the topological insulator Bi2Se3 . Phys. Rev. Lett. 106, 196801 (2010).
Novoselov, K. S. et al. Twodimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).
Hwang, E. H., Adam, S. & Das Sarma, S. Carrier transport in twodimensional graphene layers. Phys. Rev. Lett. 98, 186806 (2007).
Adam, S., Hwang, E. H., Galitski, V. M. & Das Sarma, S. A selfconsistent theory for graphene transport. Proc. Natl Acad. Sci. USA 104, 18392–18397 (2007).
Culcer, D., Hwang, E. H., Stanescu, T. D. & Das Sarma, S. Twodimensional surface charge transport in topological insulators. Phys. Rev. B 82, 155457 (2010).
Butch, N. P. et al. Strong surface scattering in ultrahighmobility Bi2Se3 topological insulator crystals. Phys. Rev. B 81, 241301 (2010).
Kong, D. et al. Rapid surface oxidation as a source of surface degradation factor for Bi2Se3 . ACS Nano 5, 4698–4703 (2011).
Das, A. et al. Monitoring dopants by Raman scattering in an electrochemically topgated graphene transistor. Nature Nanotech. 3, 210–215 (2008).
Efetov, D. K. & Kim, P. Controlling electron–phonon interactions in graphene at ultrahigh carrier densities. Phys. Rev. Lett. 105, 256805 (2010).
Lu, C. G., Fu, Q., Huang, S. M. & Liu, J. Polymer electrolytegated nanotube fieldeffect carbon transistor. Nano Lett. 4, 623–627 (2004).
Coletti, C. et al. Charge neutrality and bandgap tuning of epitaxial graphene on SiC by molecular doping. Phys. Rev. B 81, 235401 (2010).
Bansal, M., Kim, Y. S., Brahlek, M., Eliav, E. & Oh, S. Thicknessindependent surface transport channel in topological insulator Bi2Se3 thin films. Preprint at http://arxiv.org/abs/1104.5709 (2011).
Chen, J. H. et al. Charged impurity scattering in graphene. Nature Phys. 4, 377–381 (2008).
Adam, S., Hwang, E. H. & Sarma, S. D. 2D transport and screening in topological insulator surface states. Preprint athttp://arxiv.org/abs/1201.4433 (2012).
Acknowledgements
The study of electronic transport in novel materials during electrochemical modification is supported as part of the Science of Precision Multifunctional Nanostructures for Electrical Energy Storage, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DESC0001160. Additional support was provided by the National Science Foundation (NSF) DMR1105224. Preparation of Bi_{2}Se_{3} was supported by NSF MRSEC (DMR0520471) and Defense Advanced Research Projects Agency (DARPA) MTO award (N6600109c2067). N.P.B. was partially supported by the Center for Nanophysics and Advanced Materials. The authors acknowledge useful conversations with S. Das Sarma, E. Hwang and D. Culcer.
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D.K. conceived the ptype doping schemes. D.K. and S.C. fabricated devices, performed the electrical measurements with K.K. and analysed the data. N.P.B., P.S. and J.P. prepared single crystal Bi_{2}Se_{3} starting material. S.A. assisted with the theoretical analysis. D.K., S.C. and M.S.F. wrote the manuscript.
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Kim, D., Cho, S., Butch, N. et al. Surface conduction of topological Dirac electrons in bulk insulating Bi_{2}Se_{3}. Nature Phys 8, 459–463 (2012). https://doi.org/10.1038/nphys2286
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DOI: https://doi.org/10.1038/nphys2286
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