Abstract
We report transport studies on the 5 nm thick Bi_{2}Se_{3} topological insulator films which are grown via molecular beam epitaxy technique. The angleresolved photoemission spectroscopy data show that the Fermi level of the system lies in the bulk conduction band above the Dirac point, suggesting important contribution of bulk states to the transport results. In particular, the crossover from weak antilocalization to weak localization in the bulk states is observed in the parallel magnetic field measurements up to 50 Tesla. The measured magnetoresistance exhibits interesting anisotropy with respect to the orientation of parallel magnetic field B_{//} and the current I, signifying intrinsic spinorbit coupling in the Bi_{2}Se_{3} films. Our work directly shows the crossover of quantum interference effect in the bulk states from weak antilocalization to weak localization. It presents an important step toward a better understanding of the existing threedimensional topological insulators and the potential applications of nanoscale topological insulator devices.
Introduction
Topological insulators (TIs), a new type of quantum materials characterized by the existence of a gap in the energy spectrum and the symmetryprotected surface states within the bulk gap, have attracted significant interest in recent years^{1,2,3}. As a result of the strong spinorbit coupling (SOC), the spinmomentum locked surface states always show weak antilocalization (WAL) effect^{4,5,6} due to the acquired π Berry phase when completing a timereversed selfcrossing path. Plentiful interesting behaviors of TIs, particularly in the topologically protected surface states, have been explored through electrical transport experiments^{7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22}. Whereas, it is known that the bulk states of the existing threedimensional (3D) TIs are not perfectly insulating even at low temperatures, and as a direct consequence, the bulk states can also influence the transport behaviors of TIs. In order to develop a comprehensive understanding on the exotic properties of TIs, it is important to systematically study the transport of TIs taking into account the effects from the bulk states.
Contrasting to the symmetry protected surface states, the TI bulk states with strong SOC can lead to either WAL or weak localization (WL) depending on the experimental conditions^{5,6,23}. Recently, the WL effect of bulk states has been studied in the ultrathin Bi_{2}Se_{3} films under perpendicular magnetic field^{24}. However, it is difficult to distinguish the bulk state features from the surface state behaviors by the perpendicular field transport measurements. In comparison, the parallel field magnetoresistance (MR) properties of TI films reveal more bulkstate information^{25,26}, and therefore, the parallel magnetic field transport measurements provide a powerful tool in investigating the quantum interference effects in the TI bulk states.
Here we comprehensively study the transport properties of 5 quintuple layers (QLs) Bi_{2}Se_{3} films grown on epiready αAl_{2}O_{3} (0001) substrates by molecular beam epitaxy (MBE). The in situ angleresolved photoemission spectroscopy (ARPES) result shows that two quantum well states of the conduction band, as well as the surface states, contribute to the density of states near the Fermi level. The MR is measured in pulsed high magnetic field (PHMF) up to 50 Tesla (T). When the external field is perpendicular to the film plane, linear MR is observed above 16 T. In parallel magnetic field, MR behaviors of the TI films exhibit interesting anisotropy when the field orientation is tuned between B_{//} ⊥ I and B_{//} // I configurations. Specifically, while the field is increased up to 50 T, the MR always exhibits a distinctive switch from positive to negative when B_{//} ⊥ I; whereas, when B_{//} // I, such switch either occurs at a much larger field, or does not occur at all within 50 T. The theoretical analysis and the quantitative fitting for the experimental results indicate that such parallel field MR behaviors of the ultrathin TI films can be well explained using the WALWL crossover mechanism in the TI bulk states. To be specific, as a consequence of the strong SOC effect in the TI films, the phase coherence time τ_{φ} generally presents a larger time scale than the intrinsic spinflip time τ_{SO}. As a result, the WAL effect always occurs when the magnetic field is relatively weak, whereas, the WL effect arises when the field becomes sufficiently strong. From this perspective, the MR switch from positive to negative can be understood as a manifestation of the WALWL crossover in the TI bulk states. In addition, we observe novel MR anisotropy with respect to the relative orientation of the parallel magnetic field and the current, which can be qualitatively explained using the SOC mechanism. Combining the ARPES data, the transport results and the theoretical analysis, we reveal the crossover of quantum interference effect, from WAL to WL, in the bulk states of the ultrathin Bi_{2}Se_{3} films.
Results
The 5 QLs Bi_{2}Se_{3} films are epitaxially grown on sapphire (0001) substrates in an ultrahigh vacuum MBEARPESSTM (scanning tunneling microscope) combined system^{27}. Figure 1(a) shows the reflection highenergy electron diffraction (RHEED) pattern of a typical MBEgrown 5 QLs Bi_{2}Se_{3} film, where the sharp 1 × 1 streaks demonstrate that the film has good single crystal quality. The band map of the film taken in Γ–K direction is shown in Figure 1(b). In the ARPES measurement, photoelectrons are excited by an unpolarized HeI light (21.21 eV), and collected by a Scienta SES2002 analyzer. The topological surface states are observed within the bulk gap. A quite small gap is opened in the Dirac cone just below the Dirac point due to the coupling between the top and bottom surface states. Moreover, as shown in Figures 1(b) and (c), the quantum well states of the conduction band have a significant contribution to the Fermi surface. These observations indicate that our films are TIs with the Dirac surface states and the bulk states play a great role in the charge transport.
In order to explore the transport properties of the films by ex situ measurements, 20nmthick insulating amorphous Se is deposited on the TI films as a protection capping layer (Figure 1(d)). The Hall bars with channel dimensions of 600 × 400 μm^{2} are fabricated using standard photolithography method. An optical image of the typical Hall bar structure is shown in the inset of Figure 2(a). The transport properties of the films were measured mainly by using the standard fourelectrode method in a 16 T Quantum Design PPMS (physical property measurement system) and PHMF at the Wuhan National High Magnetic Field Center. The nondestructive pulsed magnet has a rise time of 15 ms and fall time of 135 ms. The field and current directions are reversed in the measurements to improve the precision of the results by eliminating the parasitic voltages. Typical results from the sample 1 (a 5 QLs Bi_{2}Se_{3} film) are shown in the main text. (The results are repeatable in a collection of samples.)
The dependence of the sheet longitudinal resistance R_{□} on the temperature was measured firstly (for the sample 1), which is shown in Figure 2(a). The resistance decreases almost linearly when the temperature decreases from 300 K to about 50 K. Whereas, when the temperature drops approximately below 12 K, the resistance develops an upturn. The upturn resistance, as shown in Figure 2(b), exhibits a logarithmic dependence on the temperature, which can be understood in terms of the quantum correction induced by the electronelectron interaction^{13}. The resistance upturn becomes larger at 8 T than that at 0 T, which is due to the suppression of the WAL effect in the presence of the perpendicular magnetic field resulting in enhanced resistance. The Hall trace of the sample 1 at 4.2 K is shown in Figure 2(c). Utilizing the slope at low fields, we calculate the sheet carrier density n_{s} ~ 1.89 × 10^{13} cm^{−2} and mobility μ ~ 316.6 cm^{2}/(V·s) at 4.2 K.
Next, the MR behavior of the sample 1 at relatively low perpendicular fields (<16 T) was measured in PPMS and PHMF, respectively. The results in both measurements are consistent, which are shown in Figure 2(d). Specifically, these MR curves show typical dips around 0 T at low temperatures as a result of the WAL effect in TIs^{7,12,13,14,15}, which can be clearly seen in the inset of Figure 2(d). In addition, a linear MR appears above 16 T at both 4.2 K and 77 K. This is consistent with the previous observation in a 5 QLs Bi_{2}Se_{3} film grown on the same substrate by MBE^{15}. Note that similar linear behavior of MR has been observed in many TI systems^{28,29,30,31,32,33,34,35}, yet, the underlying origin remains to be clarified. Some attribute such linear MR to a quantum origin, including the Abrikosov's quantum linear MR model which relates the linear MR to the linear energy dispersion of the gapless topological surface states^{28,29,30}, and the HikamiLarkinNagaoka theory which interprets the linearlike MR at high fields in terms of the WAL mechanism^{31,32}. Other theories associating the linear MR with a classical origin have also been proposed, such as the inhomogeneity model by Parish and Littlewood which stresses the influence from the sample inhomogeneity^{34,35}.
Interestingly, a different set of rich MR behavior is observed when a magnetic field parallel to the film plane is applied. In particular, as clearly shown in Figure 3, the normalized MR of sample 1 along the [110] direction in parallel field, exhibits a significant dependence on the relative orientation of B_{//} and I. The behavior of MR when the parallel field is oriented along B_{//} ⊥ I (the field increases up to 50 T) is shown in Figure 3(a). At 4.2 K, the MR first increases to a maximum at about 25 T, and then decreases as a downward paraboliclike curve. When the temperature is increased to 77 K, the MR slightly increases within 11 T and then decreases monotonically up to 50 T. In comparison, the MR behavior for the field orientation B_{//} // I (Figure 3(b)) is different, only showing positive MR within 50 T at both 4.2 K and 77 K.
To further understand the parallel field MR behavior, we also measured the parallel field MR along the [−110] direction of the sample 1. The results are shown in Figures 4(a) and (b). The quasifourelectrode method (insets of Figures 4(a) and (b)) is used only here due to the restriction of sample size. It is worth mentioning that such measurement method can introduce contact resistance that can lead to a weaker MR response without changing the curve shape (Supplementary Information). In this case, the MR switch from positive to negative is also clearly observed at 4.2 K and 77 K when B_{//} ⊥ I, but much weaker when B_{//} // I. For a fixed temperature, the switching field for B_{//} // I is larger than that for B_{//} ⊥ I. In order to explore the general dependence of the MR switch on the B_{//}I orientation, the parallel field MR of sample 1 with the current along the [110] direction under different position θ was measured (Figure 4(c)). The sample position θ refers to the angle between B_{//} and the normal direction of I along the film plane (the inset of Figure 4(c)). Here θ = 0° means B_{//} ⊥ I and θ = 90° means B_{//} // I. When the magnetic field increases up to 16 T, the MR at 100 K increases when B_{//} // I, but decreases when B_{//} ⊥ I. When θ = 45°, the MR seems to show a competition between positive and negative MR. Normalized MR at 100 K as a function of θ when B_{//} = 15 T is shown in Figure 4(d).
Discussion
A positivetonegative MR switch of the ultrathin Bi_{2}Se_{3} films is observed when the parallel magnetic field increases. The switch occurs in a broad range of temperature and exhibits anisotropy when the relative orientation of B_{//} and I is varied. The parallel field MR data exhibit tiny variation in the presence of a large magnetic field, indicating a quantum correction regime. Taking into account the fact that the Fermi level locates at the bulk conduction band, and that the film shows quite large carrier density and lower mobility compared to those reported for the surface states of TI^{10}, we conclude that the major contribution to the charge transport in our films comes from the bulk states instead of the surface states. We emphasize that, while similar negative MR behavior observed in Sndoping Bi_{2}Te_{3} films^{26} under parallel field was reported, a clear interpretation of the MR data and the comparison of different behaviors in Sndoping samples are still missing. In contrast, for our present experimental results, the parallel field MR switch phenomenon of Bi_{2}Se_{3} films can be well explained in terms of the quantum interference effects in the TI bulk states. In particular, as we shall describe in detail below, the positive and negative MR can be attributed to the presence of WAL and WL, respectively.
For a TI system with strong SOC, the correction to the MR behavior due to the effect of quantum interference^{6} is characterized by two time scales: the dephasing time τ_{φ} and the spinflip time τ_{SO}. In the regime τ_{φ} ≫ τ_{SO}, the spinorbit scattering is significant, which gives rise to frequent spin flips. As a result, the quantum interference between the time reversed trajectories is destructive, leading to the occurrence of WAL and a positive MR. In the regime where τ_{φ} is comparable to τ_{SO} or τ_{φ} < τ_{SO}, the spinorbit scattering effect is weak and the scattering process barely affects the spin orientation. In such case, negative MR occurs with increasing magnetic field as a WL feature. In the intermediate regime where τ_{φ} > τ_{SO}, MR first increases to a peak value and then decreases, signifying a crossover from WAL to WL. Overall, the quantum interference behavior of a system is crucially dependent on the ratio between τ_{φ} and τ_{SO}.
In our thin films, the mean free path l can be estimated according to , where k_{F} can be obtained through the sheet density n_{s}. For the sample 1 described here, l is approximately 20 nm, much larger than the thickness d = 5 nm. The parallel field transport thereby falls into the DugaevKhmelnitskii (DK) regime where the resistance change is given by^{36,37} Here ΔR = R(B) − R(B = 0). R can be regarded as the resistance in the absence of external magnetic field due to the quite small variation, and R_{□} is the sheet resistance. N_{i} is the number of channels contributing to the charge transport. In addition, three length scales are involved: L_{so} is the spinflip length (the distance travelled by an electron before its spin direction is changed by the scattering, which depends on the strength of SOC in the bulk states. Please see Supplementary Information.), L_{φ} is the phase coherence length, and with L_{B} being the magnetic length . By varying only two fitting parameters L_{φ} and L_{SO}, we present a quantitative fitting of the experimental data in Figure 3. In the case of B_{//} ⊥ I, we have L_{φ} ≈ 140 nm, L_{SO} ≈ 30 nm at 4.2 K and L_{φ} ≈ 40 nm, L_{SO} ≈ 20 nm at 77 K. And for B_{//} // I, L_{φ} ≈ 140 nm, L_{SO} ≈ 18 nm at 4.2 K. Based on these fitting results, L_{φ} ≈ 40 nm and L_{SO} ≈ 14 nm at 77 K when B_{//} // I can be obtained by calculation (see Supplementary Information for details). Substituting these calculated values into Equation (1), we quantitatively reproduce the MR result at 77 K in B_{//} // I configuration as shown in Figure 3(b). The tiny mismatches of the fitting MR curves may arise from the neglect of the electronelectron interaction^{13}, which can actually play a role in the MR behavior.
It is noted that N_{i} = 2 in the fitting is identical to the number of bulk bands at the Fermi surface shown in Figure 2(b). While we cannot fully determine whether the two channels are completely from the two subbands of the bulk state or from the hybridized channels of bulk state and surface state, it is evident that the bulk state plays dominant role in the emergence of crossover behavior reported here. All the values of parameters shown above are fitting results and reasonable. The phasecoherence length L_{φ} decreases with temperature and L_{φ} is much larger than the mean free path as reported earlier^{15}. Besides, the frequent scattering due to the edges in the ultrathin films makes L_{so} comparable to the mean free path. Based on the fitting results of experimental data, L_{SO} is affected by the relative orientation of the parallel magnetic field and the current.
Through the parallel field MR curves of the ultrathin Bi_{2}Se_{3} films, a clear image of the quantum interference effects with the WALWL crossover in the TI bulk states is depicted. Three cases are presented for the data in Figure 3 and 4. (I) For the B_{//} ⊥ I configuration, the system usually falls into the intermediate regime (τ_{φ} > τ_{SO}) at relatively low temperatures. As a result, WAL effect characteristically arises when the field is weak, whereas, when the magnetic field becomes sufficiently large, a crossover into WL occurs. The data of Figure 3(a) and 4(a) belong to this case and the crossover is observed within 50 T. (II) For the B_{//} // I configuration and relatively low temperatures, compared to (I), a weaker effect of the WALWL crossover is observed at a larger switching field due to a larger ratio τ_{φ}/τ_{SO} as shown in Figure 4(b). In Figure 3(b), only the WAL effect is observed at 4.2 K and 77 K. This may indicate that the switching fields from WAL to WL in both conditions are larger than 50 T. (III) For either of the two geometries, the MR may show only WL effect at high temperatures when τ_{φ} decreases and becomes comparable to τ_{SO}, even τ_{φ} < τ_{SO}. The θ = 0° data at 100 K in Figure 4(c) fall into this situation.
The observed anisotropy feature of MR can be related to many factors, including the band structure asymmetry, crystalline anisotropy, and the relative orientation of the parallel magnetic field and the current. However, generally speaking, both the band asymmetry and the crystal anisotropy could result in a MR behavior that varies along different crystal directions. Since the anisotropy of MR along the [−110] direction remains consistent with that of the [110] direction, we consider the relative directions of the parallel magnetic field and the current as the leading factor that contributes to the novel MR anisotropy reported here. The underlying physics can then be qualitatively understood in terms of the SOC mechanism. Consider a moving electron, which experiences an effective magnetic field B_{e} that is perpendicular to the electron momentum. When B_{//} ⊥ I, the main transport path of the electron is perpendicular to the external field, in which the spinflip process due to the SOC effect is strongly suppressed by the external magnetic field, leading to an effectively larger τ_{SO}. In distinct contrast, when B_{//} // I, the spinflip process is hardly affected. This anisotropy in the effective SOC effect provides a mechanism that leads to the observed anisotropic MR here. Such explanation is also supported by Figures 4(c) and (d), which show an intimate relation between the parallel field MR and the sample position θ. Particularly, the negative MR behavior when B_{//} ⊥ I is consistent with a larger effective τ_{SO}, while the positive MR when B_{//} // I agrees with a smaller τ_{SO}. For arbitrary θ, the effective τ_{SO} is given by the combination of both effects, which leads to the MRθ characteristics shown in Figure 4(d).
Interestingly, the anisotropy of the parallel field MR in thicker TI films (e.g. 45 QLs and 200 QLs Bi_{2}Se_{3})^{38} seems to be opposite to the experimental results of the 5 QLs Bi_{2}Se_{3} films. Additionally, there is one order of magnitude difference of the MR amplitudes for the thicker films^{38} between B_{//}⊥I and B_{//}//I, while it is not the case for the results presented here. In light of many different factors between the thick and ultrathin films, such as the thickness and the weight of bulk states at the Fermi surface, we are not able to achieve a unified understanding. Further theoretical investigations in this context would be valuable towards a quantitative comprehension of the anisotropic parallel field MR of TI films in various fieldcurrent orientations.
In summary, the crossover from WAL to WL in TI bulk states is revealed clearly by the parallel field MR behaviors of the 5 QLs ultrathin Bi_{2}Se_{3} films. The WALWL crossover is largely affected by the relative orientation of the parallel magnetic field and the current, which can be understood in terms of an orientationdependent effective spinflip time. To be specific, when B_{//} ⊥ I, the MR within 50 T always exhibits the crossover at 4.2 K and 77 K, whereas, the crossover for B_{//} // I occurs at a much higher magnetic field (possibly above 50 T), due to the anisotropic SOC effect under strong magnetic field. The novel transport properties of the ultrathin TI films demonstrated in this work are quite significant for a better understanding of the existing 3D TI materials and for the future potential magnetic applications of nanoscale TI devices.
Methods
Sample preparation
The high quality 5 QLs Bi_{2}Se_{3} films studied here were grown on αAl_{2}O_{3} (sapphire) (0001) substrates in an ultrahigh vacuum MBEARPESSTM combined system with a base pressure better than 2 × 10^{−10} mbar. Before sample growth, the sapphire substrates were first outgassed at 650°C for 90 min and then heated at 850°C for 30 min. Highpurity Bi (99.9999%) and Se (99.999%) were evaporated from standard Knudsen cells. To reduce Se vacancies in Bi_{2}Se_{3}, the growth was kept in Serich condition with the substrate temperature at ~220°C. For the transport measurement, 20 nm Se was capped on the TI film as protection layer.
Device fabrication and measurement
Hall bar structure with channel dimensions of 600 × 400 μm^{2} was fabricated using standard photolithography method. Positive photoresist S1813 was spun at 4000 rpm for 45 seconds on Bi_{2}Se_{3} film, followed by 110°C baking for 60 seconds. With a mask of Hall bar pattern, the photoresistcoated sample was exposed to ultraviolet light (365 nm wavelength) with exposure power of 8 mW/cm^{2} for 7 seconds. The exposed part of photoresist was removed after 40 seconds of developing (MFCD26 developer). Then, bared area of Bi_{2}Se_{3} film with no photoresist on was wetetched with 1 g of potassium dichromate in 10 ml of sulfuric acid and 20 ml of DI water. The expected etch rate for Bi_{2}Se_{3} was about 60 nm per minute, and DI water rinsing was needed. Via indium contacting, Au wires were attached as leads on samples at room temperature. Thus we were able to measure the transport properties of the fabricated devices by standard or quasi fourelectrode method. Transport measurements were performed in PPMS (16T) and PHMF up to 50 T.
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Acknowledgements
We thank Liang Li for helpful discussions about the pulsed magnetic field measurements. This work was financially supported by the National Basic Research Program of China (Grant Nos. 2013CB934600 & 2012CB921300), the National Natural Science Foundation of China (Nos. 11222434 & 11174007), and the Research Fund for the Doctoral Program of Higher Education (RFDP) of China.
Author information
Affiliations
International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People's Republic of China
 Huichao Wang
 , Haiwen Liu
 , Yanfei Zhao
 , Yi Sun
 , X. C. Xie
 & Jian Wang
Collaborative Innovation Center of Quantum Matter, Beijing, People's Republic of China
 Huichao Wang
 , Haiwen Liu
 , Yanfei Zhao
 , Yi Sun
 , Ke He
 , Xucun Ma
 , X. C. Xie
 , QiKun Xue
 & Jian Wang
State Key Laboratory of LowDimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
 CuiZu Chang
 , Ke He
 , Xucun Ma
 & QiKun Xue
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
 CuiZu Chang
 , Ke He
 & Xucun Ma
Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
 Huakun Zuo
 & Zhengcai Xia
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Contributions
J.W. and K.H. conceived and designed the study. H.W., Y.Z., Y.S. and J.W. carried on the transport measurements. C.C. did MBE growth and ARPES experiment. H.Z. and Z.X. helped in pulsed high magnetic field measurements. K.H., X.M. and Q.X. supervised the MBE growth and ARPES experiment. H.W., C.C., J.W., H.L. and X.C.X. analyzed the data. H.L. and X.C.X. did theoretical fittings. H.W., H.L. and J.W. wrote the manuscript.
Competing interests
The authors declare no competing financial interests.
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Discovery of highly spinpolarized conducting surface states in the strong spinorbit coupling semiconductor Sb2Se3
Physical Review B (2018)
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