Observations of two-dimensional quantum oscillations and ambipolar transport in the topological insulator Bi2Se3 achieved by Cd doping
Zhi Ren, A. A. Taskin, Satoshi Sasaki, Kouji Segawa, Yoichi Ando
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A ug Observations of two-dimensional quantum oscillations and ambipolar transport in thetopological insulator Bi Se achieved by Cd doping Zhi Ren, A. A. Taskin, Satoshi Sasaki, Kouji Segawa, and Yoichi Ando
Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan (Dated: December 7, 2018)We present a defect-engineering strategy to optimize the transport properties of the topologicalinsulator Bi Se to show a high bulk resistivity and clear quantum oscillations. Starting with a p -type Bi Se obtained by combining Cd doping and a Se-rich crystal-growth condition, we were ableto observe a p -to- n -type conversion upon gradually increasing the Se vacancies by post annealing.With the optimal annealing condition where a high level of compensation is achieved, the resistivityexceeds 0.5 Ωcm at 1.8 K and we observed two-dimensional Shubnikov-de Haas oscillations composedof multiple frequencies in magnetic fields below 14 T. PACS numbers: 73.25.+i, 74.62.Dh, 72.20.My, 73.20.At
I. INTRODUCTION
The three-dimensional (3D) topological insulator (TI)realizes a novel quantum state of matter where a non-trivial Z topology of the wavefunction of the bulk va-lence band leads to the emergence of a “topological”surface state consisting of helically spin-polarized Diracfermions. The peculiar spin texture of the surface stateholds promise for novel spintronics and fault-toleranttopological quantum computing, so there is a rush of re-search to address this surface state.
However, most ofthe known TI materials are poorly insulating in the bulk,making it difficult to probe the surface state by transportexperiments. For example, Bi Se is considered to be apromising TI material because it has a relatively large( ∼ however, no matterwhether it is in the form of bulk crystal, nanoribbon, or epitaxial thin film, Bi Se always accompanies a lotof Se vacancies (usually ∼ cm − ) that act as electrondonors, and as a result, the residual bulk carriers hinderthe transport studies of the surface state of this material.To achieve a bulk-insulating state in Bi Se , dopingholes to compensate for the residual electrons is a vi-able strategy. While this was done through low-level sub-stitution of Ca for Bi , the resulting disorder wasso strong that no Shubnikov-de Haas (SdH) oscillationfrom the surface state was observed in Bi − x Ca x Se .A different strategy was to partially substitute Sb forBi, which apparently reduces the Se vacancies; indeed,with a relatively large ( ∼ n -typeBi − x Sb x Se , but a very high magnetic field ( ∼
60 T) wasrequired for the observation. It is to be noted that withthe Sb doping one can never cross the band gap to reachthe p -type regime, and hence the tuning of the chemicalpotential to the Dirac point is impossible. This is a pity,because Bi Se is attractive for its isolation of the Diracpoint from the bulk bands. Therefore, it is desirable tofind a suitable p -type dopant to access the Dirac pointwhile keeping the mobility to be sufficiently high for the surface state to be studied by the SdH oscillations.In this paper, we show that tactful defect engineer-ing in Bi Se employing Cd doping in combination withSe-vacancy tuning provides a useful means to controlthe chemical potential across the band gap. In theliterature, whereas Cd in Bi Se was shown to be-have as an acceptor, Cd-doped Bi Se crystals alwaysremained n -type due to the low solubility of Cd atomsin Bi Se ; however, it has been elucidated that in-creasing the Se content in the Bi-Se melt for the crystalgrowth can suppress the formation of Se vacancies andgreatly reduce the residual bulk carrier density to thelevel of ∼ cm − . Therefore, even though the solu-bility of Cd is low, one could achieve a p -type behaviorby combining Cd doping and a Se-rich growth condition.Actually, we obtained a p -type sample with this strat-egy and, furthermore, starting from the p -type sample,we could gradually increase the Se vacancies by carefulpost-annealing and achieve a high level of compensation,at which the sample becomes optimally bulk-insulatingand presents two-dimensional (2D) SdH oscillations be-low 14 T. II. EXPERIMENTAL DETAILS
The single crystals of Cd-doped Bi Se were grown byusing elemental shots of Bi (99.9999%), Cd (99.99%) andSe (99.999%) as starting materials. To maximize theCd content in the crystal, excess Cd and a mixture ofBi and Se with a ratio of Bi:Se = 32:68 were meltedin a sealed evacuated quartz tube at 750 ◦ C for 48 hwith intermittent shaking to ensure a homogeneity, fol-lowed by cooling slowly to 550 ◦ C and then annealing atthe same temperature for one week. The resulting crys-tals are easily cleaved along the basal plane, revealing asilvery mirror-like surface. The X-ray diffraction mea-surements confirmed the crystal to be single phase withthe proper Bi Se structure. The actual Cd content wasdetermined by the inductively-coupled plasma atomic-emission spectroscopy (ICP-AES) to be 0.0020(2). Theas-grown crystals were examined by X-ray Laue analy-sis and cut into single-domain, thin bar-shaped sampleswith typical dimensions of 3 × × .For each annealing experiment, samples weighingabout 4.2 mg were sealed in evacuated quartz tubes andannealed at a given temperature for one week, followedby quenching into cold water. All the samples used in thiswork were taken from the same part of the same batch,and the variation of the Cd content was confirmed to benegligible by the ICP-AES analysis. To avoid possiblesurface contamination, the surface layer of the annealedcrystals were removed using adhesive tapes before trans-port measurements.It worth mentioning that in our annealing experi-ments, we took precautions to minimize the uncertaintyin the annealing temperature. For each annealing run,we placed the quartz tube at the same position of thesame furnace so that the temperature gradients in thefurnace as well as the thermocouple calibration errorsdo not affect the annealing result. Also, the environmenttemperature was kept constant during this experiment tominimize the temperature fluctuations between differentannealing runs. As a result, the annealing temperature T anneal was very reproducible and its variation betweendifferent runs with nominally the same T anneal was within ± ◦ C.The in-plane resistivity ρ xx and the Hall coefficient R H were measured in a Quantum Design Physical Prop-erties Measurement System (PPMS-9) down to 1.8 K,for which the electrical contacts were prepared by usingroom-temperature-cured silver paste. In addition, one ofthe high-resistivity samples was brought to a 14-T mag-net for detailed SdH-oscillation measurements using anac six-probe method, in which four lock-in amplifiers wereemployed to measure both the primary and the second-harmonic signals in the longitudinal and transverse chan-nels at a frequency of 19 Hz. The SdH-oscillation datawere taken by sweeping the magnetic fields between ±
14T with the rate of 0.3 T/min, during which the temper-ature was stabilized to within ± III. RESULTS AND DISCUSSIONSA. p -type Bi − x Cd x Se The temperature dependence of the in-plane resistiv-ity ρ xx of a Bi . Cd . Se crystal grown in the Se-rich condition is shown in Fig. 1(a), together with thedata for a pristine Bi Se sample grown with the sameBi/Se ratio. The pristine Bi Se crystal shows an es-sentially metallic behavior with a weak resistivity up-turn below ∼
30 K, which is typical for low-carrier-densityBi Se ; indeed, the Hall coefficient R H in this sam-ple at 1.8 K corresponds to the bulk electron density n e ∼ × cm − , which is very small for Bi Se . On theother hand, in Bi . Cd . Se the resistivity upturn isabsent and the ρ xx value is lower, suggesting a highercarrier density. In fact, as shown in Fig. 1(b), R H in the -5 0 5-0.50.00.5 Bi Se Bi Cd Se xx ( m c m ) (a) (b) H ( c m / V s ) R H ( c m / C ) T (K) T yx ( m c m ) B (T) =1.8 K FIG. 1: (Color online) (a) Temperature dependences of ρ xx of an as-grown Bi . Cd . Se crystal (solid line) and apristine Bi Se crystal (dash-dotted line) grown in the sameSe-rich condition. The pristine sample is n -type with n e ∼ × cm − , while the Cd-doped sample is p -type with n h ∼ × cm − . Note that the low-temperature resistivity up-turn in the pristine sample is absent in the Cd-doped sample.(b) Temperature dependences of R H (left axis) and µ H for theCd-doped sample; inset shows the magnetic field dependenceof ρ yx in this sample at 1.8 K. Bi . Cd . Se crystal is positive and its value at 1.8K corresponds to the hole density n h ∼ × cm − , im-plying that the Cd doping has created ∼ × cm − of holes ( ∼ The reason for thesmaller number of doped holes compared to the Cd con-centration is most likely that a small portion of Cd atomsoccupy the interstitial site and act as donors. In Fig.1(b), R H is only weakly dependent on temperature andthe Hall resistivity ρ yx is perfectly linear in B (as shownin the inset), reflecting the metallic nature of the as-grown Bi . Cd . Se sample which is due to a singletype of carriers ( i.e. , the bulk holes). The Hall mobility µ H (= R H / ρ xx ), also shown in Fig. 1(b), increases withdecreasing temperature, reaching ∼ /Vs at 1.8K. B. p -to- n -type conversion by post annealing Annealing the as-grown Bi . Cd . Se crystals inevacuated quartz tubes has a drastic effect on its trans-port properties. Figure 2(a) shows how the tempera-
573 C580 C 573 C
577 C575 C 580 C577 C590 C xx ( m c m ) As grown (a)
590 C
T (K)
575 C (b) R H ( c m C - ) T (K)
FIG. 2: (Color online) (a) Temperature dependences of ρ xx for Bi . Cd . Se crystals annealed at different tempera-tures in evacuated quartz tubes. The data for the as-growncrystal is also shown for comparison. The low-temperatureresistivity values span three orders of magnitude. (b) Tem-perature dependences of R H for the same series of samples.As the annealing temperature is increased, the crystal be-comes less p -type and is eventually converted to n -type. Thisconversion occurs with the annealing temperature of ∼ ◦ C. ture dependence of ρ xx changes upon annealing in a nar-row temperature window between 573 and 590 ◦ C. Onecan see that ρ xx ( T ) evolves nonmonotonically with theannealing temperature, T anneal ; namely, ρ xx initially in-creases with T anneal until T anneal exceeds 577 ◦ C, afterwhich ρ xx decreases as T anneal is further increased. No-tably, ρ xx of the sample annealed at 577 ◦ C show a highvalue of 0.5 Ωcm at 1.8 K, which is three orders of magni-tude larger than that of the as-grown sample. Figure 2(b)shows the typical temperature dependences of low-field R H data (defined as R H = ρ yx / B for B ≈
0) for differ-ent T anneal , which indicates that more and more electroncarriers are introduced as T anneal is increased, and thesign change from p -type to n -type occurs around T anneal = 577 ◦ C.Since the drastic change in the transport propertiesoccurs in a very narrow temperature window (573 – 580 ◦ C), one may wonder about the reproducibility of theresult. As a matter of fact, the observed change wasquite reproducible, as demonstrated in Figs. 3 and 4.Figures 3(a)-3(d) show the ρ xx ( T ) data for at least twosamples annealed at the same temperature, where onecan see that the behavior for each T anneal is essentiallyreproducible. Figures 4(a)-4(d) show the corresponding R H ( T ) data for the same sets of samples; here, exceptfor the case of T anneal = 577 ◦ C [Fig. 4(c)], we observedreasonable reproducibility [Figs. 4(a), 4(b), and 4(d)].For T anneal = 577 ◦ C, two of the three samples (A andB) showed a sign change in R H from negative to positiveupon lowering temperature from 300 K, whereas the R H of sample C remained negative in the whole temperature xx ( m c m ) T (K) T anneal =573 C (a) (b) BA xx ( m c m ) T (K) T anneal =575 C (c) xx ( m c m ) T (K) T anneal =577 CAB C (d) xx ( m c m ) T (K) T anneal =580 CA B FIG. 3: (Color online) (a-d) Reproducibility of the ρ xx ( T )data in samples annealed at the same temperature, demon-strated for four different values of T anneal indicated in eachpanel. range. Actually, this variation in the behavior of R H indicates that the T anneal = 577 ◦ C samples are at theverge of the p -to- n -type conversion.Figures 4(e)-4(h) show the ρ yx ( B ) curves measured insample “A” of each T anneal . One can clearly see that thecurve in Fig. 4(g) for T anneal = 577 ◦ C is nonlinear, in-dicating that there are at least two bands contributingto the transport. In topological-insulator samples with alarge bulk resistivity, this kind of nonlinear ρ yx ( B ) curvesare indications of the surface channels making noticeablecontributions. Therefore, the consistently high resis-tivity [Fig. 3(c)] together with the complex behaviorsof the Hall signal are likely to be a signature of a highlevel of compensation achieved in the samples annealedat 577 ◦ C; in other words, in those samples the acceptorsand donors are nearly equal in number and their delicatebalance can easily change the sign of R H . It is to be em-phasized that our data demonstrate that this high levelof compensation is reproducibly achieved with T anneal =577 ◦ C. In samples annealed at other temperatures, the ρ yx ( B ) behavior is almost linear [Figs. 4(e), 4(f), and4(h)], suggesting that the contribution of the surface tothe transport properties is minor. In passing, the col-lection of ρ xx ( T ) and R H ( T ) data shown in Fig. 2 forvarying T anneal are for sample “A” of each T anneal shownin Figs. 3 and 4. C. Defect chemistry
The above observation that a drastic change in thetransport properties of Bi . Cd . Se occurs in avery narrow temperature window might seem surpris-ing. However, this behavior can be readily understoodby examining the defect chemistry associated with the R H ( c m / C ) T (K) T anneal =573 C (a) 0 100 200 30005101520 yx ( m c m ) yx ( m c m ) yx ( m c m ) yx ( m c m ) R H ( c m / C ) (b) B A T (K) T anneal =575 C R H ( c m / C ) (c) T (K) T anneal =577 C ABC 0 100 200 300-40-30-20-10 R H ( c m / C ) (d) T (K) T anneal =580 C AB-5 0 5-40-2002040 A (h) B (T) T =1.8 K T anneal =580 C -5 0 5-20-1001020 A (f) T =1.8 K B (T) T anneal =575 C -5 0 5-505 A (g) A T =1.8 K
B (T) T anneal =577 C -5 0 5-20-1001020 T anneal = (e) T =1.8 K B (T)
573 CA
FIG. 4: (Color online) (a-d) Reproducibility of the R H ( T ) data in samples annealed at the same temperature, demonstratedfor four different values of T anneal indicated in each panel. (e-f) Magnetic-field dependences of ρ yx measured in sample “A” ofeach T anneal . The solid line in (g) is the two-band-model fitting to the data. annealing. In the present system, there are mainly twodifferent types of charged defects, the aliovalent substi-tutional defect Cd ′ Bi and the vacancy defect V •• Se , theformer acts as an acceptor and the latter as a donor.Therefore, the effective charge-carrier density is deter-mined by their competition and can be expressed as n eff = [Cd ′ Bi ] − V •• Se ], where positive (negative) n eff denotesthe hole (electron) density. In an as-grown sample, theCd ′ Bi defects are dominant and n eff is positive; accord-ingly, the chemical potential lies in the valence band.When annealed in evacuated quartz tubes, a portion ofselenium goes into the gas phase Se in equilibrium withthe solid phase, resulting in the formation of more V •• Se defects while leaving Cd ′ Bi unaffected (because the T anneal employed in the present study is much lower than themelting temperature of 710 ◦ C). The equilibrated vaporpressure of Se increases with increasing T anneal , creat-ing more V •• Se and eventually changing n eff from positiveto negative.To be more quantitative, one may assume that the in-crease in the Se-vacancy concentration upon annealing,∆[ V •• Se ], is directly reflected in the increase in the numberof Se molecules in the quartz tube, which determines theSe vapor pressure P Se ; in constant volume, one expectsa linear relation between ∆[ V •• Se ] and P Se if the Se va-por behaves as an ideal gas. According to Ref. 23, theequilibrated Se vapor pressure P Se of Bi Se is relatedto the absolute temperature T vialog P Se [atm] = A − B/T [K] , (1)where A = 7.81 ± B = 10870 ±
640 for the tem-perature range of 527 to 627 ◦ C. From this T dependenceof P Se , one can infer that ∆[ V •• Se ] is very sensitive to the change in T anneal : For example, changing T anneal by just 1 ◦ C near 577 ◦ C results in a variation of ∼ V •• Se ];therefore, the expected change in ∆[ V •• Se ] upon changing T anneal from 575 to 580 ◦ C is as much as ∼ n eff occurs abruptly inthe vicinity of T anneal = 577 ◦ C where n eff ≈ ′ Bi ] ≈ [ V •• Se ]), and results in a drastic change in thetransport properties as we observed. D. Surface quantum oscillations
From the above results, it is clear that the highest levelof compensation is achieved in samples annealed at 577 ◦ C. We therefore measured the sample C of T anneal = 577 ◦ C in a 14-T magnet using a rotation sample holder toinvestigate its SdH oscillations in detail. Before the high-field measurements, to protect the surface state from ag-ing, the top surface of the sample was covered with Al O in the following way: first, the crystal was cleaved onboth surfaces with adhesive tapes to reveal fresh sur-faces, mounted on a sample holder with GE varnish, andtransferred into the sputtering chamber; second, the topsurface was cleaned by bias-sputtering with Ar ions for 13minutes and then, without breaking the vacuum, a 540-nm-thick Al O film was deposited by the rf magnetronsputtering. After this process, gold wires were boundedto the side faces by spot welding. Probably because of thesample heating during the spot welding, the ρ xx value ofthis sample became even larger than that shown in Fig.3(c). Also, the sign of R H at low temperature changedto negative after the process, showing the Hall responsesimilar to that of the sample A. The R H ( T ) behavior of -10 -5 0 5 10-10010-10 -5 0 5 10-100-50050 - B d / dB (b) yx ( c m ) B (T) T =1.4 K (a) R H ( c m C ) T (K) B (T) xx ( c m ) xx ( c m ) (c) (d) B (T -1 ) xx xx , - B d xx / d B ( c m ) T=1.4 K (e) F (T) FT A m p . ( a r b . un i t )
33 T27 T
11 T
FIG. 5: (Color online) (a) R H ( T ) data of the sample C of T anneal = 577 ◦ C after the Al O -coverage process. (b) ρ yx ( B )data of the same sample measured at 1.4 K; the solid lineis the result of the two-band-model fitting. (c) Magnetic-field dependences of the primary signal ( ρ xx ) and the second-harmonic signal (∆ ρ xx ) measured at 1.4 K in magnetic fieldsalong the C axis. (d) Plots of ∆ ρ xx ( B ) and d ρ xx /dB vsthe inverse magnetic field 1 /B . Clear SdH oscillations can beseen in both data, and good agreements in the positions ofpeaks and dips between the two curves are evident. (e) TheFT spectrum of ∆ ρ xx showing three prominent frequencies. this sample C after the Al O -coverage process is shownin Fig. 5(a), and its ρ yx ( B ) curve at 1.4 K is shown inFig. 5(b).In our measurements using an ac lock-in technique,we simultaneously recorded the primary and the second-harmonic signals during the magnetic-field sweeps. Fig-ure 5(c) shows the magnetic-field ( B ) dependences of theprimary signal ( ρ xx ) and the second-harmonic signal (de-noted ∆ ρ xx ) measured at 1.4 K in magnetic fields alongthe C axis. One can see that the second-harmonic signal(∆ ρ xx ) shows pronounced oscillations, while in the pri-mary signal ( ρ xx ) the oscillations are hardly visible. Tounderstand the nature of the oscillations, we show in Fig.5(d) the plots of ∆ ρ xx and d ρ xx /dB (second derivativeof the primary signal) vs the inverse magnetic field 1 /B ;a comparison between the two curves indicates that theypresent essentially the same peak/dip positions. While o o xx ( c m ) B cos ) (T -1 ) o o o o o o = 0 o (a) F F (b) (deg) F ( T ) F FIG. 6: (Color online) (a) The ∆ ρ xx data for varyingmagnetic-field directions, plotted as a function of 1 / ( B cos θ );dashed lines mark the positions of the peaks. (b) The threeprominent frequencies in the FT spectra of the SdH oscilla-tions plotted as a function of θ . All the frequencies vary as1 / cos θ , as indicated by the solid lines. the waveforms are quite complicated, the Fourier trans-form (FT) spectrum of ∆ ρ xx ( B − ) shown in Fig. 5(e)presents three well-defined peaks at F = 11 T, F = 27T, and F = 33 T, indicating that the observed oscilla-tions are SdH oscillations with multiple frequencies.Note that the second-harmonic in ac measurements isa distortion of the input sine wave, and its occurrenceis an indication of a nonlinear response. In the presentcase, the SdH oscillations are apparently giving rise to apeculiar non-ohmicity. This makes the second-harmonicsignal to be useful for observing the SdH oscillations witha high sensitivity, although the detailed mechanism is notclear at the moment.Figure 6(a) shows how the SdH oscillations observedin ∆ ρ xx change when the magnetic field is rotated, byplotting ∆ ρ xx versus 1 / ( B cos θ ) where θ is the angle be-tween B and the C axis. One can see that the oscillatoryfeatures are essentially dependent on the perpendicularcomponent of the magnetic field. Also, as shown in Fig.6(b), the angular dependences of all three frequencies inthe FT spectra are consistent with 1 / cos θ . These resultsstrongly suggest that the present SdH oscillations signify2D Fermi surface(s). We note that the SdH oscillations inthis sample disappeared after keeping the sample in am-bient atmosphere for a week, which suggests that the SdHoscillations were coming from the surface. (This observa-tion also suggests that the Al O coverage, while usefulfor slowing the aging of the surface of Bi Se , does notprovide a perfect protection). Furthermore, one can esti-mate the bulk mobility of this sample to be ∼
40 cm /Vsfrom the values of ρ xx and R H , and such a mobility is toolow to give rise to SdH oscillations of the bulk carriersbelow 14 T. All told, one can reasonably conclude thatthe observed SdH oscillations are of the surface origin.From the SdH-oscillation data, the Fermi wave vec-tor k F can be calculated via the Onsager relation F =( ~ c/ πe ) πk F , yielding k F = 0.018, 0.029, and 0.032 ˚A − for F , F , and F , respectively. These are of the sameorder as the value k F = 0.031 ˚A − reported for the topo-logical surface state in n -type Bi − x Sb x Se . However,because of the multi-component nature of the oscillationsthat leads to complicated waveforms, it is difficult to re-liably extract the cyclotron mass m c nor the Dingle tem-perature for each component using the Lifshitz-Kosevichtheory. This makes it impossible to identify the originsof the three oscillation frequencies, but possible reasonsfor the multiple components in the present case include:(i) harmonics of a fundamental frequency are observed,(ii) chemical potentials of the top and bottom surfacesare not identical and give two frequencies associated withthe topological surface states, (iii) a trivial 2D electrongas created by the band bending at the surface presentsadditional SdH oscillations. Note that, in the case of thepresent sample used for the detailed SdH measurements,the top surface was covered by Al O and the bottomsurface was covered by the GE varnish, so the conditionsof the two surfaces were very different. To resolve theorigins of those multiple frequencies, an experiment in-volving the gate control of the surface chemical potentialto trace the energy dispersion of each branch (as wasdone for exfoliated Bi Se ) would be desirable. E. Nonlinear ρ yx ( B ) behavior Although we could not extract the surface mobilityfrom the SdH oscillations in the present case, we canstill estimate the relevant parameters of the surface andthe bulk transport channels by analyzing the nonlinear ρ yx ( B ) behavior [Fig. 5(b)] with the simple two-bandmodel described in Ref. 18. The solid line in Fig. 5(b) isthe result of the two-band-model fitting, from which weobtained the bulk electron density n b = 7 × cm − ,the bulk mobility µ b = 17 cm /Vs, the surface electrondensity n s = 1.8 × cm − , and the surface mobility µ s = 1.2 × cm /Vs. The observed frequencies of theSdH oscillations, 11, 27, and 33 T correspond to the sur- face carrier densities of 2.5 × , 6.7 × , and 8.1 × cm − in spin-filtered surface states, respectively, and itis interesting that the sum of these numbers, 1.7 × cm − , appears to be consistent with the n s value ob-tained from the two-band analysis. Also, it is assuringthat the surface mobility µ s obtained from the two-bandanalysis, ∼ /Vs, is reasonably large and is con-sistent with our observation of the SdH oscillations inmoderate magnetic fields.In passing, the ρ yx ( B ) data of the sample A shown inFig. 4(g) can also be fitted with the two-band model.The result of the fitting, shown by the solid line in Fig.4(g), yields the bulk electron density n b = 1.3 × cm − , the bulk mobility µ b = 15 cm /Vs, the surfaceelectron density n s = 2.0 × cm − , and the surfacemobility µ s = 1.0 × cm /Vs for this sample. IV. CONCLUSION
In conclusion, we demonstrate that with tactful de-fect engineering one can optimize the transport proper-ties of the topological insulator Bi Se to show a highbulk resistivity and clear quantum oscillations. Specifi-cally, by employing a Se-rich crystal-growth condition weachieved the p -type state in Bi Se by Cd-doping for thefirst time; we then employed careful post annealing totune the Se vacancies and achieved a high level of com-pensation, where the acceptors and donors nearly canceleach other and the sample presents a high ρ xx value ex-ceeding 0.5 Ωcm at 1.8 K and shows 2D SdH oscillationsconsisting of multiple components below 14 T. Acknowledgments
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