Appl. Phys. Lett. 117, 102108 (2020); https://doi.org/10.1063/5.0019081 117, 102108

© 2020 Author(s).

Shubnikov–de Haas oscillations and Rashbasplitting in Bi2Te3 epitaxial film

Cite as: Appl. Phys. Lett. 117, 102108 (2020); https://doi.org/10.1063/5.0019081Submitted: 21 June 2020 . Accepted: 28 August 2020 . Published Online: 11 September 2020

D. P. A. Holgado, K. Bolaños , S. de Castro , H. S. A. Monteiro, F. S. Pena, A. K. Okazaki , C. I. Fornari

, P. H. O. Rappl , E. Abramof , D. A. W. Soares , and M. L. Peres

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Shubnikov–de Haas oscillations and Rashbasplitting in Bi2Te3 epitaxial film

Cite as: Appl. Phys. Lett. 117, 102108 (2020); doi: 10.1063/5.0019081Submitted: 21 June 2020 . Accepted: 28 August 2020 .Published Online: 11 September 2020

D. P. A. Holgado,1 K. Bola~nos,1 S. de Castro,2 H. S. A. Monteiro,1 F. S. Pena,1 A. K. Okazaki,3 C. I. Fornari,4

P. H. O. Rappl,3 E. Abramof,3 D. A. W. Soares,1 and M. L. Peres1,a)

AFFILIATIONS1Instituto de F�ısica e Qu�ımica, Universidade Federal de Itajub�a, Itajub�a, MG CEP 37500-903, Brazil2Universidade do Estado de Minas Gerais, Divin�opolis, MG CEP 35501-170, Brazil3Laborat�orio Associado de Sensores e Materiais, Instituto Nacional de Pesquisas Espaciais, S~ao Jos�e dos Campos,SP CEP 12227-010, Brazil

4Experimentelle Physik VII, Universit€at W€urzburg, Am Hubland, 97074 W€urzburg, Germany

a)Author to whom correspondence should be addressed: marcelos@unifei.edu.br

ABSTRACT

This work presents the results of magnetotransport measurements performed on a 156 nm-thick Bi2Te3 epitaxial film in the temperaturerange of 1.9–300K, showing Shubnikov–de Haas oscillations for temperatures below 50K. A detailed analysis of oscillations as a function oftemperature provides the main transport parameters, including the Land�e g-factor and cyclotronic masses. A systematic analysis of fastFourier transform, performed on the oscillations, indicates that the origin of the oscillation pattern is not related to the topological surfacestates but from the Rashba splitting of the Bi2Te3 Fermi surface.

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Bi2Te3 is part of a material group classified as topological insula-tors (TIs) that presents natural spin-polarized currents composed ofDirac fermion particles that flow via topological surface states (TSS).Such properties make Bi2Te3 compounds potential candidates forapplication in spintronics and quantum computation, which led to anintense investigation of its optical and transport properties in the pastdecade.1–4 The TSS result from the spin-momentum locking due tothe strong spin–orbit coupling (SOC) intrinsic to these materials andtheir detection via transport measurements is mandatory for rapidimplementation in integrated circuits. However, this is a complex taskbecause of the Bi2Te3 strong degenerate nature, since transport viabulk and surface states is mixed due to the Fermi level resonance inthe bands. This is mainly due to the unintentional doping of crystaldefects (antisite or point defects).5 Magnetotransport measurementsare an important tool to investigate the existence of such states sincethe Shubnikov–de Haas (SdH) oscillations afford a significant role inidentifying the contribution of TSS conduction. From the SdH oscilla-tion angle dependence and the magnetic field dependence of theLandau levels (LLs), it is possible to identify the Dirac fermion pres-ence in most topological insulators. However, in the Bi2Te3 case, thebulk cylindrical Fermi surface can also give rise to 2D quantum

oscillations. In addition, due to the cylindrical Fermi surface, the SdHfrequency follows the dependency F / 1=cosh, also commonly attrib-uted to Dirac fermions.6 From LL analysis, the Dirac fermions areexpected to exhibit a non-zero Berry phase, while normal fermionshave a zero Berry phase. It has recently been shown that the Rashbasplitting of the cylindrical Fermi surface could also give rise to thenon-zero Berry phase7 that, in this case, has nothing to do with TSS.Despite the intensive investigation of the electrical and optical proper-ties carried out over the past few years, very few information regardingthe experimental investigation of the Rashba effect on Bi2Te3 basedstructures is found in the literature.

In this work, we present the analysis of the magnetoresistancemeasurements performed in an n-type Bi2Te3 epitaxial film, whichpresented SdH oscillations in the temperature range of 1.9–50K. Thedetailed investigation of the frequencies obtained from FFT (fastFourier transform) revealed two main peaks, which are attributed tothe Rashba effect that splits the bulk states leading to the oscillationpatterns observed in the experiments. This scenario corroborates theanalysis of the Fermi surface provided by the angle dependence ofSdH oscillations. From FFT analysis and SdH oscillation amplitude,we obtained the cyclotronic masses, the effective Land�e g-factor, and

Appl. Phys. Lett. 117, 102108 (2020); doi: 10.1063/5.0019081 117, 102108-1

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the Rashba splitting DkR and Rashba coefficient aR. The results showthat, even though the investigated sample presented the features oftransport via TSS, the complex form of the Bi2Te3 Fermi surface,together with the Rashba splitting, is the most likely cause of the quan-tum oscillations observed in the experiments. In addition, the highvalue of aR, when compared to similar structures, opens the possibilityof the application of a tunable Rashba effect by means of a disorderinduced by exposure to environmental conditions.

Sample preparation was performed on a Riber 32P MBE system,using a Bi2Te3 solid source, with nominal stoichiometry. The electriccontact preparation followed the van der Pauw geometry, using gold(Au) wires soldered with indium (In) contacts. Details about the MBEgrowth of Bi2Te3 epitaxial films on the BaF2 (111) substrates arepublished elsewhere.8 The magnetoresistance measurements wereperformed using a Physical Property Measurement System fromQuantum Design composed of a He-cooled superconducting systemwith a magnetic field of up to 9T and an operating temperature of1.9K–400K.

Figure 1(a) shows the longitudinal electrical resistance (Rxx) as afunction of temperature for the 156nm-thick Bi2Te3 epitaxial film inthe temperature range of 1.9–300K. According to this figure, the sam-ple exhibits a metallic behavior, which agrees with the highly degener-ate Bi2Te3 films reported in the literature.9 Figure 1(b) shows thecarrier mobility (left axis, open circles) and concentration (right axis,open squares), where it is possible to observe that carrier concentrationis nearly constant for T< 10K, indicating that the Fermi level energyis also constant. In the same temperature region, it is possible toobserve that carrier mobility saturates for T< 10K, indicating that noadditional scattering mechanism becomes effective in this temperatureregion. The inset in Fig. 1(b) shows the linear profile of the Hall resis-tance Rxy at 4.2K. Such linear behavior indicates that only a singleband contributes to the electrical transport.

Figure 2(a) shows Rxx as a function of the magnetic field appliedperpendicularly to the sample surface. In this figure, small-amplitudeoscillations are observed for magnetic fields above 6T and tempera-tures below 50K. Quantum oscillations can be better resolved if thesecond derivative, with relation to the magnetic field, is applied to Rxx .The curve of d2Rxx=dB2 as a function of the magnetic field is shown inthe inset of Fig. 2(a) for T¼ 4.2K, where the presence of theShubnikov–de Haas effect is clear. In Fig. 2(b), we plot d2Rxx=dB2 as a

function of the inverse of the magnetic field for different temperatures.As expected, the amplitude of the SdH oscillations decreases withincreasing temperature, and for T¼ 50K, the oscillations almost dis-appear. From this figure, it is possible to observe that the SdH oscilla-tions have at least two components with different frequencies since abeating pattern is visible. The frequencies responsible for the beatingpattern can be obtained by applying FFT analysis. The FFT curves aredisplayed in Fig. 3(a) showing the presence of two well-developedpeaks with frequencies f1 ¼ 59 T and f2 ¼ 75 T close to each other.From these frequencies, we can calculate the carrier concentrations bynSdH ¼ kF

3=3p2, where kF is the Fermi wave vector that can be calcu-lated using kF ¼ 2ef =�hð Þ1=2. We obtain nSdH ¼ 2:5� 1018 cm�3 andnSdH ¼ 3:7� 1018 cm�3 for f1 and f2, respectively. The carrier con-centration derived from Hall measurements was nHall ¼ ð2:16 0:1Þ�1018 cm�3 close to the values obtained from the SdH frequencies.

Further analysis of the SdH oscillations allows us to extractimportant parameters. From the temperature dependence of the FFTamplitude, we can obtain the cyclotron masses according to the ther-modynamic term of the Lifshitz–Kosevich (LK) equation,

FIG. 1. (a) Temperature dependence of longitudinal resistance Rxx for the Bi2Te3film. The profile indicates metallic behavior. (b) Carrier mobility (left axis, opencircles) and concentration (right axis, open squares). The inset shows Hall resis-tance Rxy at 4.2 K as a function of B. The solid red curve is a linear fit to the data.

FIG. 2. (a) Longitudinal resistance Rxx as a function of the magnetic field appliedperpendicularly to the sample surface. Small-amplitude oscillations are observedfor magnetic fields above 6 T and temperatures below 30 K. Inset: d2Rxx=dB2 as afunction of the magnetic field at 4.2 K where quantum oscillations are clear. (b) SdHoscillations obtained by the second derivative of Rxx with respect to B as a functionof 1/B.

FIG. 3. (a) Fast Fourier transform (FFT) curves obtained from the SdH oscillationsat different temperatures. (b) Temperature dependence of the FFT amplitude ofeach frequency. The solid lines are fittings using the thermodynamic term of the LKequation.

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Appl. Phys. Lett. 117, 102108 (2020); doi: 10.1063/5.0019081 117, 102108-2

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AFFT ¼ A02p2kBe�h

mcT

B

� �=sinh

2p2kBe�h

mcT

B

� �; (1)

where A0 is a constant parameter, kB is the Boltzmann constant, e isthe elementary charge, �h is the reduced Planck constant, T is the tem-perature, B is the inverse of the mean value of the 1/B range used inthe FFT analysis, and mc is the cyclotron effective mass. The calcula-tions were carried out considering the interval of 0.11–0.35T�1. Theobtained cyclotron masses are mc=me ¼ 0:0466 0:003, for thepeak with f1 ¼ 59 T and mc=me ¼ 0:0326 0:003 for the peak withf2 ¼ 75 T. The fittings using Eq. (1) are shown in Fig. 3(b).

There are some explanations available in the literature concern-ing the two frequencies observed in Bi2Te3 films. The second har-monic or bulk states are possible causes. As discussed before, the twofrequencies are very close to each other and the second harmonic situ-ation is discarded. Another alternative is to consider that the surfacestates can contribute to transport. In this case, transport through thesample would be a composition of normal fermions, from bulk, andDirac fermions, from surface states. A more precise procedure wouldbe the use of the complete Lifshitz–Kosevich expression to fit the nor-malized oscillatory component DRxx/R0 to obtain the Berry phase,10

DRxx

R0¼ �hxc

2EF

� �12 vsinh vð Þ

e�vDcos 2pEF

�hxcþ 12þ b� d

� �� �; (2)

where EF is the Fermi energy given by EF ¼ �h2kF2=2mc, kF is the

Fermi wavevector, v ¼ 2p2kBT=�hxc, and vD ¼ 2p2kBTD=�hxc, thecyclotron frequency is given by xc ¼ eB=mc and TD is the Dingle tem-perature, which provides the low-temperature collision broadening ofelectron states at the Fermi level giving information about crystal qual-ity. The phase shift d gives the dimensionality of the Fermi surface. d¼ 0 indicates that the Fermi surface is 2D, while d ¼ �1/8 or þ1/8,the Fermi surface is 3D. The phase parameter b can assume values inthe range from 0 to 1. For b ¼ 0 or b ¼ 1, trivial fermions should bethe main carriers responsible for transport. For b¼ 1=2, Dirac fermionsshould give a more effective contribution for conductivity.

From the fitting performed in our data using Eq. (2) (see Fig. S1,in the supplementary material), the obtained parameters are b1 � d¼ 0.596 0.01 (f1 ¼ 59T), b2 � d ¼ 0.576 0.01 (f2 ¼ 75T), TD1¼ 44K, and TD2 ¼ 68K. We also extracted the values of mobility,l1¼ (10566 71) cm2 V�1 s�1 and l2 ¼ (9816 92) cm2 V�1 s�1,which are three times lower than the mobility found in the litera-ture.5,9,11 The values of b1 � d �0.59 and b2 � d �0.57 could suggestthe presence of transport via topological surface states. However, assaid before, the Rashba splitting of the Fermi surface of Bi2Te3 couldalso lead to a non-zero Berry phase. This will be discussed later in thetext.

Angular dependence measurements are usually performed toindicate the 2D nature of the oscillation and to infer the possible con-tribution of TSS. If the SdH oscillations originate from 2D Fermi sur-face states, the maximum and minimum oscillations must be alignedwith each other for different angles when the curves are plotted as afunction of the perpendicular component of the magnetic field(B? ¼ Bcosh). Figure 4(a) shows the SdH oscillations at 4.2K for dif-ferent angular orientations plotted as a function of 1=Bcosh. The sam-ple holder is rotated with tilt angles h, while the applied magnetic fieldis kept fixed in the z-direction (see the inset). At h ¼ 0, we choose twomaxima indicated by the dashed vertical lines to check how the

position of the peaks behaves as the angle changes. As h varies from 0�

to 66�, the maximum positions change from the original positions.This behavior indicates that the observed SdH oscillations cannot beoriginated from 2D Fermi surface states. In addition, in the case ofTSS, the frequencies obtained from FFT must follow the dependencef / 1=cosh, and f1 must increase as h increases, which is clearly notthe case, as indicated by the dashed line in Fig. 4(b). This behavior alsoindicates that the shape of the Fermi surface is not spherical nor cylin-drical and is in a transition from a closed ellipsoid to an open Fermisurface.6 The behavior of f2 cannot be verified since it disappears fortilt angles higher than 20�. The angular dependence deviation of f1from the 2D behavior indicates that the SdH oscillation with frequencyf1 originates from 3D bulk states. In fact, similar behavior wasobserved in Bi2Se3

12 and BiTeCl,13 which have the same layered struc-ture. In the case of BiTeCl, the anomalous behavior of f ðhÞ is due toits Fermi surface shape that varies from spindle torus to ring torus,depending on the carrier concentration. For Bi2Se3, the Fermi surfacecan change from pure ellipsoidal to the bag shaped surface, alsodepending on carrier concentration. The Fermi surface of Bi2Te3 hasbeen investigated and revealed a very complex structure,14 which caneven diverge from the surfaces allowed to Bi2Se3 and BiTeCl and leadto anomalous behavior of f ðhÞ.

As previously indicated in the text, the Rashba effect can alsobe responsible for the two peaks observed in the FFT transform[Fig. 3(a)] and can lead to a non-zero Berry phase. The appearance oftwo frequencies with the same profiles as those observed in Fig. 3(a)has been observed in several systems, including bulk BiTeCl,13 SnTeepilayer,15 InSb/In1�xAlxSb,

16 and HgTe quantum wells,17 and attrib-uted to the Rashba spin-splitting. For Bi2Te3 single crystals, a similarprofile has also been observed recently, but its origin has not beenaddressed.5 We consider that, for the analysis presented next, theRashba spin splitting is responsible for the frequency f2 obtained fromthe SdH oscillations.

In the absence of Rashba splitting, the cross-sectional area ofthe Fermi surface SF perpendicular to the applied magnetic fieldgives rise to a cyclotronic frequency according to Onsager relationf ¼ �h=2peð ÞSF [see Fig. S2(a), in the supplementary material]. If theRashba effect is present, the spin-splitting of Fermi surface producestwo apparent cross-sectional areas, an internal S1 and an external S2,

FIG. 4. (a) SdH oscillations at T¼ 4.2 K for different tilt angles h plotted as a func-tion of 1=Bcosh. The inset shows the measurement configuration. (b) FFT curvesof the respective oscillations in (a). The dashed line indicates the angular evolutionof the SdH frequency f1.

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as illustrated in Fig. S2(b) of the supplementary material. These twoFermi pockets S1 and S2 can be related to the frequencies f1 and f2. Ageneral circular cross-sectional area is given by SF ¼ pk2F . Usingthe frequencies f1 and f2, we derive the Fermi wave vectors andobtain kF1 ¼ 0:0423 A

�1e kF2 ¼ 0:0477 A

�1. The Fermi velocities

obtained from these values are vF1 ¼ 1:07� 106 m=s and vF2¼ 1:73� 106 m=s, which are one order higher than the values foundin the literature for bulk Bi2Te3 films.1,5,9 The Rashba splitting inmomentum space, DkR, can be calculated from geometric consider-ations taking into account the distance between the center of the twocircles indicated in Fig. S2(b) of the supplementary material, leadingto the value of DkR � 0:009 A

�1. The Rashba energy can be calcu-

lated from ER ¼ �h2DkR2=2mc, which gives ER ¼ 6:8 meV. From

these values, we can calculate the Rashba parameter aR ¼ 2ER=DkR,which gives aR ¼ 1.58 eV A. Similar investigations were performedon bismuth tellurium chloride (BiTeCl) and potassium dopedBi2Se3 single crystals. For BiTeCl, the Rashba parameters wereDkR � 0:030 A

�1and aR ¼ 1.2 eV A;13 while for Bi2Se3:K, DkR

� 0:066�0:08 A�1 with aR ¼ 0.79� 0.35 eV A:18

The observed Rashba splitting may be related to the intrinsic dis-order present in the Bi2Te3 film or due to surface oxidation of the sam-ple. It is well known that Bi2Te3 undergoes surface oxidation whenexposed to an ambient environment due to the weak interlayer inter-action.11 Bando et al.19 investigated the Bi2Te3 surface oxidation incontrolled air conditions (30% relative humidity and 24 �C) andreported that an oxidized layer with a thickness of one quintuple layer(1 nm) is formed on the Bi2Te3 surface just after 50 h of air exposure.Therefore, as the Bi2Te3 film investigated here was exposed to air for aperiod of years before performing the magnetotransport measure-ments, we can assure that its surface is oxidized. A theoretical investi-gation showed that the adsorbed atoms from the atmosphere, such asNa and O, alter the surface states by inducing the Rashba splitting dueto the charge transfer from the adsorbed atoms to the sample sur-face.20 The Rashba parameters found in this work are summarized inTable I and compared to the data available in the literature.

We can also extract the Land�e g factor from the oscillations if themagnetic field is sufficiently high to show the Landau level separation(see Fig. S3 in the supplementary material). Using the cyclotron massvalues obtained from the FFT analysis, we obtained g ¼ 21 andg ¼ 33, for mc ¼ 0:046me and mc ¼ 0:032me, respectively. Thesevalues are close to the values found in the literature (see Table I).

In summary, we presented the magnetotransport measurementsperformed on a 156nm-thick Bi2Te3 epitaxial film. From the analysisof the data, we suggest that SdH oscillations originate from the bulkstates rather than surface states since the angular dependence of the

FFT amplitudes does not follow the expected 2D Fermi surface statebehavior. In addition, the non-zero Berry phase is attributed to theRashba splitting that breaks the spin degeneracy, giving rise to the twofrequencies observed in the FFT graphics. We also found that theRashba parameter aR is very high when compared to similar structuresas BiTeCl and potassium doped Bi2Se3. This opens the possibility ofthe application of a tunable Rashba effect, via environmental exposure,to the development of spintronic devices based on Bi2Te3.

See the supplementary material for the detailed procedure usedto obtain the Berry phases, the Land�e g-factor, and the schematic rep-resentation of the Rashba splitting of the Fermi surfaces.

We would like to thank CAPES and CNPq (No. 307933/2013)for their financial support.

DATA AVAILABILITY

The data that support the findings of this study are availablefrom the corresponding author upon reasonable request.

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TABLE I. The cyclotronic masses, Lande g-factors, and Rashba parameters found inthis work compared to the data available in the literature.

This work References

mc2 (units of me) 0.032 0.058; 0.07521

mc1 (units of me) 0.046 0.08;5 0.0922

g g1 ¼ 33:3; g2 ¼ 23 17,22 10–253

DkR (A)�1 0.009 0:03013 ð0:066� 0:08Þ18aR eV Að Þ 1.58 1.213 (0.35 � 0.79)18

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