Abstract
The experimental realization of the quantum anomalous Hall (QAH) effect in magneticallydoped (Bi, Sb)_{2}Te_{3} films stands out as a landmark of modern condensed matter physics. However, ultralow temperatures down to few tens of mK are needed to reach the quantization of Hall resistance, which is two orders of magnitude lower than the ferromagnetic phase transition temperature of the films. Here, we systematically study the band structure of Vdoped (Bi, Sb)_{2}Te_{3} thin films by angleresolved photoemission spectroscopy (ARPES) and show unambiguously that the bulk valence band (BVB) maximum lies higher in energy than the surface state Dirac point. Our results demonstrate clear evidence that localization of BVB carriers plays an active role and can account for the temperature discrepancy.
Introduction
The QAH effect^{1,2,3,4,5,6,7,8,9,10,11,12}, characterized by its dissipationless spinpolarized chiral edge states at zero magnetic field, provides opportunities for future applications in lowenergydissipation electronic and spintronics devices. Conceptually, the QAH effect in magneticallydoped topological insulator (TI) films is expected to arise from the interplay of magneticdopant exchange coupling and hybridization of the top and bottom surface Dirac cones, with both contributions inducing a mass gap at the Dirac point (DP)^{4,6}. If the exchangecoupling mediated Zeeman term dominates, the hybridized surface bands invert only for one spin orientation and induce a single chiral edge mode that spans the ‘2D bulk” gap of the thin film at the DP (Fig. 1c). This mechanism of exchangeinverted surface states (QAHESS) stands in contrast to the conventional quantum Hall (QH) effect which relies on Landau quantization of the electronic motion by an external magnetic field. While ferromagnetism sets in at Curie temperatures on the order of tens of Kelvins, the relevant transport energy scales are ultimately limited by the effective size of the band gap that is set by the exchange splitting at the Dirac point (DP). Therefore, in materials where the three dimensional (3D) bulk TI valence band maximum (VBM) lies well below the DP (Fig. 1b), the QAHESS effect upon magnetic doping should be observable below temperatures whose scale is set by the lesser of the Curie temperature and the exchangeinduced Dirac gap. Indeed, firstprinciples calculations for magneticallydoped Bi_{2}Se_{3} indicate that ferromagnetic ordering would induce an exchange splitting of approximately 40meV for 5 quintuple layers (QLs)^{6}, suggesting a significantly higher QAH temperature than observed in experiment for both Cr and Vdoped (Bi, Sb)_{2}Te_{3} films.
However, the relative energy of the VBM with respect to the DP (∆) remains unclear in magneticallydoped alloyed (Bi, Sb)_{2}Te_{3} films: as shown in Fig. 1, previous studies reveal positive ∆ in Bi_{2}Te_{3}^{13,14} and negative ∆ in Sb_{2}Te_{3}^{13,15}, with firstprinciples studies for V doping indicating a separate delectron impurity band located at the Fermi level^{6}. A detailed determination is crucial to understand the nature of the quantized Hall signatures: If ∆ is a small negative value, whose magnitude is comparable to the exchangeinduced gap, the total effective gap may be reduced. Conversely, if ∆ > 0 the effective gap should disappear entirely, naively suggesting an absence of quantized Hall signatures in these samples due to the transport contributions from the BVB (Fig. 1c).
Results
We use ARPES to reveal the band structure of a (Bi_{0.29}Sb_{0.71})_{1.89}V_{0.11}Te_{3} QAH film^{11} (Fig. 2a and Fig. S1). The QAH thin films were grown by custombuilt molecular beam epitaxy (MBE), and stem from the same batch of films previously used to observe the QAH effect in transport^{11}. Details of the sample can be found in the Methods section and ref. 11. The DP is 54 meV below the Fermi energy (E_{F}) (Supplementary Note 1 and Fig. 2a). No ferromagnetic exchange gap is resolved near the DP down to 7 K (while the Curie temperature T_{c} of the compound is 19 K), which is expected due to the limited energy resolution. Consistent with the theoretical calculation^{13}, the BVB (marked by the yellow arrows) along the Γ–M direction (Fig. S1a) is closer in energy to the DP than that along the Γ–K direction (Fig. S1b). However, it is still challenging to decide based on this spectrum whether the BVB crosses the energy of the DP (E_{D}): The intensity of a band in ARPES spectra could be weak due to the matrix element effect, and we therefore need a systematic way to accurately determine the location of the BVB maximum.
The capability of mapping the constant energy contours (CEC) by ARPES provides an ideal way to explore the band structure of a material along different directions in momentum space, while at the same time helping to overcome matrix element effects. We demonstrate this with a Bi_{2}Te_{3} film. With a photon energy of 20.5 eV, the VBM of a five QL Bi_{2}Te_{3} film is highlighted, showing the DP located deeply below the VBM [the inset of Fig. 2b], consistent with literature^{14}. The first column of Fig. 2b shows data for a photon energy of 29.5 eV that highlights the surface state band (SSB) for more accurate determination of DP energy. Due to a weaker intensity from the BVB, it remains unclear in the energy dispersion along ΓMK whether the VBM is higher than DP. However, in the CEC map at E_{D}, the BVB still manifests itself as a sixfold flowershaped structure surrounding the Dirac cone (see the CEC at E_{D} = −376 meV in the second column and the schematic in the third column of Fig. 2b). The petals of the flower are along the Γ–M direction. Such a flowershaped CEC hence acts as a signature of the BVB in this family of TIs^{14,15,16}. Inspired by results on Bi_{2}Te_{3}, we carefully measured the CEC maps of the Vdoped (Bi, Sb)_{2}Te_{3} film. As shown in Fig. 2a, the SSB induces a small circular Fermi surface at E_{F}. The flowershaped CEC around the DP is already developed at E_{D} ~ −54 meV. At higher binding energy, the flowershaped structure gradually expands. The coexistence of the DP and the flowershaped structure in CEC provides direct evidence for the overlap of the DP and the BVB in this system.
Figure 3b shows the CEC map of the Vdoped (Bi, Sb)_{2}Te_{3} film at E_{D}. As discussed above, the flowershaped structure around the DP arises from the BVB. Along cut 1 (see Fig. S4 as well as the threedimensional illustration of the Dirac cone in Fig. 3a), the VBM is hard to determine due to the matrix element effect. A better angle to reveal the VBM is slightly off the Γ point, which directly cuts the two petals of the CEC (cut 2). As schematically shown in Fig. 3b, one expects a spectrum composed of petals of the flowershaped CECs (the yellow part) along the energy direction, centered with the intensity from SSB (the blue part). Figure 3c shows the band dispersion along cut 2, where two branches of the BVB clearly cross the E_{D} [also see the momentum distribution curve (MDC) at E_{D} that reveals a double peak structure]. Therefore, we unambiguously demonstrate that the VBM lies above E_{D}.
Discussion
Our observations clearly establish the absence of a thin film bulk band gap at the DP energy that would be expected for the QAHESS. The consequences are twofold: on one hand, RKKY interaction through BVB states can complement the V corelevel vanVleck contribution^{17} to ferromagnetism, to explain the observed robust magnetic order of V moments. Second and more importantly, the absence of a bulk band gap should entail a bulk contribution to transport, precluding the QAH effect. An essential next step is therefore to reconcile this result with the reported QAH phenomena and ultralow observing temperatures of few tens of mK, orders of magnitude lower than the Curie temperature or the expected exchangeinduced gap^{6,11,18,19}. Importantly, in the QAHESS scenario, a clear transport signature of the chiral edge mode and associated quantization of σ_{xy} necessitates that the BVB carriers are absent in transport.
As 2D electrons necessarily localize in the absence of a magnetic field and spinorbit coupling, the absence of BVB electrons in transport points, at first glance, to impuritydriven 2D Anderson localization (Fig. 3d and Fig. S5). Such a picture holds only if the thin film bulk falls into the unitary universality class. However, strong spinorbit coupling expected for a TI should place the bulk in the symplectic class, leading to antilocalization. The question then remains whether time reversal symmetry breaking due to magnetic impurities can still lead to localization. In principle, the QAH effect then should be determined by the temperature dependence of the localization length. If the insulating 2D bulk in the QAH phase indeed follows from Anderson localization, then samples with higher magnetic dopant concentration should naively suppress BVB contributions to σ_{xx} and push quantized Hall signatures to higher temperatures, up to the point where the disorder bandwidth is comparable to the exchangeinduced gap.
Another potential contribution follows from considering the internal magnetic field that arises from the ferromagnetic moments, ~13 mT for a fullypolarized domain of ~1.5 μ_{B}/V at 5.5% doping. In the absence of spinorbit coupling, a BVB effective mass ~0.18 m_{0} suggests a magnetizationinduced cyclotron frequency ω_{c} ~ 100 mK, above the temperature of observed quantized Hall signatures but well below the Curie temperature, and increasing to B_{int} ~ 200 mT and ω_{c} ~2 K for the pentalayer QAH samples^{20}. In theory, the internal magnetic field affects BVB electrons in two ways: First, the induced cyclotron gap can help quench bulk transport σ_{xx}, introducing the magnetic length as an extra scale in the localization problem. Second, extended states of the BVB Landau levels could conceivably provide a complementary QAH mechanism of a magnetic field driven “quantum Hall” σ_{xy} contribution. The latter scenario would require that no simultaneous exchangeinduced topological band inversion takes place for the SSBs and is rather unlikely due to the exceedingly low mobility of the samples. In experiments on V and Cr doped films, B_{int} is much smaller than the coercivity field: a clear counterindication then comes from magnetic hysteresis curves in which σ_{xy} does not disappear when the external field sweeps across B_{int}, cancelling the total magnetic field^{11}.
A third possibility for the absence of a bulk band contribution to transport arises if the chemical potential μ of the gated sample, tuned to the QAH regime, lies above the BVB maximum, inside the upper SSB. In this case, the BVB remains inert. Therefore, disorder and internal magnetic field must instead localize SSB electrons. While the TI surface state exhibits antilocalization in the absence of timereversal symmetry breaking, a transition to localization occurs as a function of μE_{D} and magnetic scattering^{21}. This scenario benefits from modulation doping of the pentalayer samples^{20}: as the Cr dopants are concentrated near the film surfaces, scattering is enhanced for the SSBs with peak amplitudes at the top and bottom surface, further aiding localization. On the other hand, the QAH edge modes would need to extend beyond the range of the exchangeinduced gap, far above E_{D}. However, given the Curie temperature and densityfunctionaltheory predictions of the QAH edge mode dispersion^{22}, this is unlikely.
In summary, among the three scenarios discussed, localization of the BVB appears to be the most likely explanation for the much lowerthanexpected temperatures of the QAH effect. Therefore, the solution might be searching for a system in which the Dirac point is well separated from BVB to avoid the bulk carriers, and not too far from E_{F} for easily gate tuning. Very recently, a bulk insulating TI has been realized in Sndoped Bi_{1.1}Sb_{0.9}Te_{2}S single crystals^{23}, which might be a good platform for further study of QAH. However, open questions remain. For example, recentlyreported experimental results on thicker (10 QL) films with negligible top and bottom SSB hybridization, which should naively reduce the temperature scale, nevertheless display the QAH effect at similar temperature^{9,10,12}. Furthermore, questions regarding the importance of localization come from Cr doped pentalayer QAH samples^{20}, where modulation doping conceivably reduces disorder in the thin film bulk, counteracting localization of a BVB while at the same time pushing QAH signatures to elevated temperatures. Given its potential importance for the QAH effect, a better understanding of the Anderson localization problem due to interplay of disorder, spinorbit coupling and the internal magnetic field will be essential. Given that the internal magnetizationinduced cyclotron frequency ω_{c} ~ 100 mK is well above the temperature of observed quantized Hall signatures, it is conceivable that impuritydriven Anderson localization for the bulk valence band and internal magnetic field induced Landau quantization may cooperate with each other to suppress bulk transport and while retaining chiral edge conduction. As transport properties are analogous for both V and Cr doping, it needs to be checked whether similar conclusions about the position of the BVB relative to E_{D} pertain to Cr doped thin films. Finally, direct detection of the exchangemediated gap of the SSBs as well as a systematic study of the role of disorder using magnetic and nonmagnetic dopants could further shed light on the microscopic mechanism that ultimately gives rise to the observed quantized transport signatures, as well as to delineate future directions towards a highertemperature QAH effect.
To recap, our presented results clearly establish the absence of a thin film bulk gap at E_{D}, which suggests that the observed of QAH is a consequence of a chiral edge state in the presence of bulk carriers. This points towards possible origins why the temperature of quantized transport signatures is significantly lower than expected for an exchange mediated SSB inversion of topological insulator.
Methods
The 4QL Vdoped (Bi, Sb)_{2}Te_{3} QAH thin films were grown by custombuilt molecular beam epitaxy (MBE) with a base pressure better than 5 × 10^{−10} Torr^{11}. 5 nm Te was evaporated on the top as a capping layer for exsitu ARPES measurements. The Te capping layers were removed by heating the films with a filament behind the sample holder in ultrahigh vacuum (UHV) chamber before ARPES measurements. The decapping procedure was monitored by RHEED and the decapping temperature was optimized (Supplementary Note 2). The ARPES measurements were performed at the Stanford Synchrotron Radiation Lightsource (SSRL) Beamline 5–4 at 22 K. The photon energies of 29.5 eV and 20.5 eV were selected to highlight the SSB and the BVB, respectively. The energy resolution was set at 10.5 meV.
Additional Information
How to cite this article: Li, W. et al. Origin of the low critical observing temperature of the quantum anomalous Hall effect in Vdoped (Bi, Sb)_{2}Te_{3} film. Sci. Rep. 6, 32732; doi: 10.1038/srep32732 (2016).
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Acknowledgements
We would like to acknowledge very helpful discussions with Xi Dai, Shoucheng Zhang, Xiaoliang Qi, Naoto Nagaosa and Dunghai Lee. ARPES experiments were supported by the Office of Basic Energy Science, Division of Materials Science, and were performed at the Stanford Synchrotron Radiation Lightsource, which is operated by the Office of Basic Energy Sciences, U.S. Department of Energy.
Author information
Author notes
 W. Li
 , M. Claassen
 & CuiZu Chang
These authors contributed equally to this work.
Affiliations
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
 W. Li
 , M. Claassen
 , B. Moritz
 , T. Jia
 , C. Zhang
 , S. Rebec
 , J. J. Lee
 , R. G. Moore
 , T. P. Devereaux
 & Z.X. Shen
Francis Bitter Magnet Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
 CuiZu Chang
 & J. S. Moodera
Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
 T. Jia
 , S. Rebec
 , J. J. Lee
 , T. P. Devereaux
 & Z.X. Shen
Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
 M. Hashimoto
 & D.H. Lu
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
 J. S. Moodera
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Contributions
W.L. and Z.X.S. conceived the project. W.L. took the ARPES measurements with assistance from T.J., C. Z., S.R. and J.J.L. C.Z.C. grew the samples. W.L., M.C. and B. M. analyzed the data. M.H., R.G.M. and D.H.L. assisted in ARPES measurements at Stanford Synchrotron Radiation Lightsource. J.S.M., T.P.D. and Z.X.S. supervised the project. W.L., M.C., C.Z.C., B.M., T.P.D. and Z.X.S. wrote the paper with input from all coauthors.
Competing interests
The authors declare no competing financial interests.
Corresponding authors
Correspondence to T. P. Devereaux or Z.X. Shen.
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Further reading

1.
Zerofield edge plasmons in a magnetic topological insulator
Nature Communications (2017)
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