Strong surface scattering in ultrahigh-mobility Bi2Se3 topological insulator crystals

N. P. Butch,* K. Kirshenbaum, P. Syers, A. B. Sushkov, G. S. Jenkins, H. D. Drew, and J. PaglioneCenter for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, Maryland 20742, USA

Received 12 May 2010; published 1 June 2010

While evidence of a topologically nontrivial surface state has been identified in surface-sensitive measure-ments of Bi2Se3, a significant experimental concern is that no signatures have been observed in bulk transport.In a search for such states, nominally undoped single crystals of Bi2Se3 with carrier densities approaching1016 cm−3 and very high mobilities exceeding 2 m2 V−1 s−1 have been studied. A comprehensive analysis ofShubnikov-de Haas oscillations, Hall effect, and optical reflectivity indicates that the measured electricaltransport can be attributed solely to bulk states, even at 50 mK at low Landau-level filling factor, and in thequantum limit. The absence of a significant surface contribution to bulk conduction demonstrates that even invery clean samples, the surface mobility is lower than that of the bulk, despite its topological protection.

DOI: 10.1103/PhysRevB.81.241301 PACS numbers: 71.18.y, 72.20.My, 78.20.Ci, 78.30.j

Topological insulators are bulk insulators that feature chi-ral Dirac cones on their surface. This surface state, which isprotected by time-reversal symmetry, is of fundamental in-terest and may have potential for spintronics and quantumcomputation applications. A small group of semimetallicstoichiometric chalcogenides have been theoretically shownto have the properties of three-dimensional topological insu-lators: Bi2Se3, Sb2Te3, and Bi2Te3.1,2 The chiral surface statehas been investigated by surface probes, notably angle-resolved photoemission spectroscopy ARPES Refs. 2–4and scanning tunneling microscopy5,6 and similar studies ex-ist of the alloy Bi1−xSbx.

7,8 The observation of chiral Diraccones and forbidden backscattering in these experiments hasgenerated a great deal of excitement.

In principle, electrical conduction in topological insula-tors should occur only at the surface but, in practice, thesestoichiometric materials have been known for decades to below carrier density metals. Bi2Se3 is expected to have a 300meV direct band gap at zone center,1,2 yet is almost always ntype, long believed the result of charged Se vacancies. Itremains an open question whether a bulk insulating state canbe achieved in stoichiometric undoped Bi2Se3. This problemhas been recently sidestepped by counterdoping with Ca,2,9,10

although this procedure introduces further defects. Over arange of carrier densities, ARPES data show one conductionband at zone center,2,4 and bulk Shubnikov-de Haas SdHmeasurements indicate that the Fermi surface is ellipsoidal.11

There have been several recent studies of bulk transport inBi2Se3. A thorough study of angle-dependent SdH oscilla-tions on a sample with a moderate carrier density hasmapped the anisotropy of the Fermi surface.12 A comparativeinvestigation demonstrated that while ARPES may identify aFermi level in the band gap, SdH oscillations in similarsamples always show metallic behavior, suggesting that theFermi level may vary between bulk and surface in Bi2Se3.13

This raises questions about the correspondence between sur-face and bulk studies on the same material. While it is pos-sible to tune the Fermi level of Bi2Se3 into the gap via Cadoping, the resulting samples show unusual magnetoresis-tance MR fluctuations but no SdH oscillations from thesurface state.10 In contrast, field-dependent oscillations as-cribed to the surface state have been observed in tunneling

spectra measured on Bi2Se3 thin films14,15 and Aharonov-Bohm interferometry of the surface state is reported inBi2Se3 nanoribbons.16 Because SdH oscillations attributableto surface states were identified in intrinsically disorderedBi1−xSbx alloys,17 it is intriguing that analogous bulk trans-port phenomena have not been seen in stoichiometric Bi2Se3.

In order to look for signatures of the novel surface state inbulk nominally undoped Bi2Se3, single crystals were synthe-sized over a wide range of carrier concentrations. Their lon-gitudinal and transverse electrical resistivity were systemati-cally characterized as a function of field and temperature,and infrared reflection and transmission were studied. Thisinvestigation confirms that all measured transport propertiescan be ascribed to bulk electronlike carriers, despite thesamples having the lowest reported bulk carrier densities andhighest mobilities. Even at low Landau-level filling factorand in the quantum limit, no transport signature of surfacestates is apparent, placing firm constraints on the mobility ofsurface carriers in these high-quality samples.

Single crystals of Bi2Se3 were prepared by melting high-purity bismuth 6N and selenium 5N in sealed quartz am-poules. Multiple batches were prepared with varyingbismuth/selenium ratios and heating conditions, which wereresponsible for variations in the carrier concentrations of thesamples. Similar trends were reported decades ago18 andmore recently.13 The resultant crystals cleaved easily perpen-dicular to the c3 trigonal axis. Four-probe measurements oflongitudinal and transverse electrical transport between 1.8and 300 K were conducted using a commerical cryostat. Thecurrent flowed in the plane perpendicular to c3 in both lon-gitudinal and transverse geometries, and the magnetic field Hwas always applied perpendicular to applied current. Electri-cal transport measurements at lower temperatures were per-formed in a dilution refrigerator with a rotating sample stageand 15/17 T magnet. Optical measurements were performedusing a Bomem DA3 FTIR spectrometer. Carrier density nwas determined by measurements of Hall effect, SdH oscil-lations, and fits to optical reflectivity data, which alwaysyielded identical results within experimental uncertainty.

The temperature dependence of the longitudinal electricalresistivity T is summarized in Fig. 1a. The values of n inthese samples were estimated via analysis of the SdH oscil-

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lations in H and approximating the Fermi surface asspherical, which is sufficient for purposes of comparison atlow n.11 In sample vi, no SdH oscillations are observed up to14 T, and the estimated n=51016 cm−3 is based on Hallmeasurements on samples from the same batch Fig. 1b.For n1018 cm−3, the T data reflect good metallic con-ductivity and generally, as n decreases, the samples becomemore resistive. For n1017 cm−3, a negative slope developsabove 250 K, which reflects a crossover to activated behaviorat T300 K.19 For n1018 cm−3, the T data also de-velop a shallow local minimum at 30 K, which is associatedwith a relatively small upturn that saturates as T→0.

In Fig. 1b, the T dependence of the Hall carrier densitiesnH= RHe−1 is shown for a range of samples. Values of theHall coefficient RH were determined via linear fits to sym-metrized transverse magnetoresistance data, which are linearto 5 T over the entire T range, except for at lowest n wherelinearity extends to 2 T at low T. Generally, nHT has agentle T dependence, consistent with a gradual crossoverfrom extrinsic to intrinsic conduction Eg100 meV.19

However, metallic T Fig. 1a is always observed, indi-cating that phonon scattering dominates any increase in con-ductivity due to increasing carrier number for most of the Trange. A detailed comparison of T sample iii and nHTbetween two samples from the same batch is shown in Fig.2a. These data highlight two regimes: below 30 K, wherenH is constant and T exhibits an upturn, and between 150and 250 K, where there is a change in curvature in nHT andT. The magnitude of these latter features is greatest insamples with n1017 cm−3. The two T ranges are accentu-ated in a plot of the Hall mobility T=RHT /T

Fig. 2b, highlighting the substantial low-T mobility2 m2 V−1 s−1 in these samples, which is the highestvalue reported for Bi2Se3 and corresponds to a mean-freepath longer than 300 nm. A comparison to T of batcheswith n1016 cm−3 and n1019 cm−3 indicates that doesnot simply increase with decreasing n, although at low n itstill exceeds 1 m2 V−1 s−1.

In Fig. 2c, H of sample iii is shown. In addition to thedramatic anisotropy, oscillations are readily apparent. Thenonoscillatory part is sufficiently well described by quadraticpolynomial or weak power-law functions. In contrast, samplevi exhibits no oscillations. The T dependence of SdH oscil-lations is shown in Fig. 3 in panels a and b for two dif-ferent field orientations cf. Fig. 2c. The SdH oscillationshave a frequency fSdH=20 T when H c3 and fSdH=25 Twhen Hc3, which correspond to an ellipsoidal Fermi sur-face with n=6.31017 cm−3. A Lifshitz-Kosevich fit to theT dependence of oscillation amplitude yields masses m

=0.141me and m=0.161me, where me is the bare elec-tron mass, consistent with other reports.12,13 In order to checkwhether lowering the temperature would uncover a secondfrequency of SdH oscillations arising from the surface state,measurements were performed at 50 mK on two sampleswith nH=41017–51017 cm−3 from the same batch assample iv. The field angle dependence of both longitudinaland transverse resistance are shown in Fig. 3 panels c andd. Figure 3c shows oscillations in the transverse magne-toresistance RxyH, whose frequencies range from 20 T withH c3 to 27 T with Hc3n=71017 cm−3. As expected,

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FIG. 1. Color online a Comparison of the electrical resistiv-ity T between samples of Bi2Se3. Carrier densities ncm−3 areestimated from SdH oscillations: i 11019, ii 5.31018, iii4.91017, iv 3.71017, v 3.31017, and vi 1016. Insamples with n1018 cm−3, a shallow minimum develops at 30 K.b Comparison of Hall carrier density nH between various samples.Low-temperature values span 3 orders of magnitude.

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FIG. 2. Color online a A comparison of electrical resistivityT iii from Fig. 1 and Hall carrier density nHT in two samplesfrom the same batch. The minimum in T coincides with thesaturation of nHT below 30 K. Despite increasing nH, increaseswith T up to 300 K. b The calculated mobility exceeds2 m2 V−1 s−1 at low T labeled 1017. The mobilities of sampleswith lower and higher n are compared. c Field orientation depen-dence of at 1.8 K. Compare to H of sample vi rescaled byfactor of 10, which exhibits no SdH oscillations.

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the magnitude of the effective Hall signal diminishes as Hrotates into the plane and the evolution of the oscillationfrequency reflects the expected Fermi-surface anisotropy.The longitudinal SdH oscillations are shown in Fig. 3d.The most prominent oscillations, with fSdH=15 Tn=31017 cm−3 occur with Hc3. In this field orientation, theelectrons are almost all in the first Landau level. Weak oscil-lations with H c3 have fSdH=11 T, yielding an anisotropyclose to that of the other two samples. The lack of bulk SdHoscillations in sample vi Fig. 2c having even lower n isdue to its low estimated fSdH=4 T, meaning that most of theaccessible field range is in the bulk quantum limit.

Samples were also characterized by infrared reflectionand transmission, which confirm the estimates of n based onHall and SdH data. Figure 4a shows an experimental re-flectivity spectrum of a sample from the same batch assample iv. Data were taken at 6 K and are presented with a fitto a sum of Lorentz oscillators to model the complex dielec-tric function. The fit shown in Fig. 4a includes only bulkcarriers as a Drude-type term together with two low-frequency phonons. A strong low-frequency phonon is cen-tered at 67 cm−1 with a plasma frequency of 640 cm−1 andrelaxation rate of 5 cm−1 and a second weaker phonon iscentered second at 124 cm−1 with a plasma frequency of76 cm−1 and a width of 2 cm−1. The calculated optical con-ductivity is shown in Fig. 4b together with two dc valuessample iv for rough comparison. This yields a bare plasmafrequency of free carriers to be 382 cm−1, corresponding ton=2.41017 cm−3 for 0.15me. The effective scattering rate

=8 cm−1=0.8 ps is unusually low for bulk carriers,consistent with a high mobility sample. Figure 4c showsthe real part of the dielectric function. The fit parameters arein agreement with those from the transmission spectra ofvery thin crystals. An important difference, however, is thatin transmission, a very broad Drude surface contribution=100 cm−1 is detected.

For small n, the competition between negative 1 of thefree carriers and the positive 1 from the phonons gives riseto an additional low-frequency plasma edge 1=0 thatleads to a transmission window near 30 cm−1. The strongbismuth-dominated low-frequency phonon produces a largestatic dielectric constant 10100 for Bi2Se3. This impliesa large reduction in the Coulomb potential and thus the scat-tering rate from ionized impurities, which can account forthe small scattering rate of the bulk carriers and the goodmetallic behavior of this doped semiconducting material, andprotecting against localization at low n. The Coulomb-mediated electron-electron interaction is also reduced20 and,along with the presence of low-frequency optical phonons,implies a dominance of the electron-phonon interaction bothfor the carrier mobility and for the electron-electron interac-tion.

ARPES measurements show that surface states in Bi2Se3always have a larger Fermi surface than the bulk and that theareal difference increases as the chemical potentialdecreases.4 Quantum oscillations arising from the surfaceshould have an easily identifiable higher frequency of about300 T kF=0.1 Å−1 when the chemical potential is near thebottom of the conduction band. However, no higher-frequency oscillation is ever observed in our measurements,even in the quantum limit, where no bulk SdH oscillationsexist to obscure surface signal. As the existence of the sur-face states is not in doubt, the absence of their transportsignature can only arise from very high scattering rates. Aconservative assumption that the chemical potential is thesame at the surface and bulk, consistent with ARPES surfaceaging data,4 yields nsurf1013 cm−2. In our samples, thebulk areal carrier density is about 100 times that of the sur-

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FIG. 3. Color online Temperature dependence of SdH oscilla-tions with a H c3 trigonal axis and b Hc3. Oscillation fre-quencies fSdH=20 T and 25 T, respectively, and the mass mSdH

0.15me. SdH oscillations from two different samples at 50 mK inthe c transverse and d longitudinal MR. The largest amplitudeand smallest frequency in c is observed with H c3 and the fre-quency ranges from 20 to 27 T. In d the largest amplitude isobserved with Hc3 and fSdH=15 T. Only one SdH frequency isobserved in each measurement.

FIG. 4. Color online Spectra of a reflectivity, b optical con-ductivity, and c dielectric constant. Curves b and c were cal-culated from the fit to the reflectivity data in a. For comparison,the blue circle and red square in b are dc values from sample ivfor 6 K and room temperature, respectively.

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face, while the peak-to-noise ratio in the Fourier transform ofthe SdH oscillations is greater than 500, so the surface mo-bility has to be at least five times worse than the bulk mo-bility for SdH oscillations to be below our detection thresh-old. We calculate scattering times bulk=2 ps and surf0.4 ps. The latter value is generous compared to an upperlimit of surf0.05 ps determined from our transmissionmeasurements. These estimates indeed indicate substantialsurface scattering, yet are entirely consistent with ARPESdata, which show significant surface band broadening, with=0.02 ps Ref. 2 or 0.04 ps Ref. 21 even for samplescleaved in high vacuum.

It is clear that topological protection does not guaranteehigh surface mobility so increasing the surface conductionwill require considerable effort. Reducing sample thicknessis one possibility but bulk transport properties appear to beinsensitive to sample thickness down to 5 m.13 Even in50-nm-thick nanoribbons, the observed fSdH=70 and 110 TRef. 16 are well below 300 T and are not likely due tosurface states. Relative surface conduction may alternativelybe improved by further reducing bulk n. Attempts to do sovia chemical doping yield no surface SdH oscillations,10 pos-sibly due to even further decreased mobility. On the other

hand, doping may improve the surface signal if it preferen-tially decreases the bulk mobility without reducing surfacemobility, which may be possible considering the already highsurface scattering rate. A cleaner approach is to instead pref-erentially improve the surface mobility via controlled surfacepreparation. Such a task will be challenging, as it is difficultto improve upon the vacuum cleaving employed in ARPESstudies, which yields broad surface-state linewidths. None-theless, high surface mobility is a prerequisite for precisionexperiments such as optical Kerr rotation and future applica-tions potential of topological insulators.

We note a recent report of the observation of surface SdHoscillations in pulsed fields.22 The cleaved surfaces of theSb-doped Bi2Se3 were minimally exposed, yet the require-ment of high magnetic fields, up to 55 T, points to strongsurface scattering even under controlled conditions.

We thank M. S. Fuhrer, S. K. Goh, R. M. Lutchyn, and M.L. Sutherland for helpful discussions. This work was sup-ported in part by the National Science Foundation MRSECunder Grant No. DMR-0520471. N.P.B. is supported byCNAM.

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