Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit

Kou, Xufeng; Guo, Shengqun; Fan, Yabin; Pan, Lei; Lang, Murong; Jiang, Ying; Shao, Qiming; Nie, Tianxiao; Murata, Kouchi; Tang, Jianshi; Wang, Yong; He, Liang; Lee, Ting Kuo; Lee, Wei‐Li; Wang, Kang L.

doi:10.1103/physrevlett.113.137201

Cited by 528 publications

(406 citation statements)

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“…1e) shows the sign-reversal roughly at negative V G and in the 6-20 K region. Such a sign-reversal of σ A xy has not been observed in singlelayer CBST, which always gives a positive sign regardless of its E F position and temperature [11][12][13] , as exemplified in Fig. 2a.…”

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confidence: 83%

“…Recent advances in fabricating artificial structures of materials, however, enable the design of emergent phenomena considering both momentum and real spaces in a unified way. Here, we examined these geometric Hall effects in TI heterostructures composed of magnetic TI Cr x (Bi 1−y Sb y ) 2−x Te 3 (CBST) and non-magnetic TI (Bi 1−y Sb y ) 2 Te 3 (BST; refs [11][12][13][18][19][20][21][22], which were grown on InP(111) substrates using molecular-beam epitaxy [20][21][22] . By applying a field-effect transistor structure (FET, see Methods), the Fermi energy (E F ) of the TI heterostructures can be precisely controlled in a large energy range over the bulk bandgap.…”

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confidence: 99%

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Geometric Hall effects in topological insulator heterostructures

et al. 2016

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Geometry, both in momentum and in real space, plays an important role in the electronic dynamics of condensed matter systems. Among them, the Berry phase associated with nontrivial geometry can be an origin of the transverse motion of electrons, giving rise to various geometric e ects such as the anomalous 1 , spin 2 and topological Hall e ects 3-6 . Here, we report two unconventional manifestations of Hall physics: a sign-reversal of the anomalous Hall e ect, and the emergence of a topological Hall e ect in magnetic/non-magnetic topological insulator heterostructures, Cr x (Bi 1−y Sb y ) 2−x Te 3 /(Bi 1−y Sb y ) 2 Te 3 . The sign-reversal in the anomalous Hall e ect is driven by a Rashba splitting at the bulk bands, which is caused by the broken spatial inversion symmetry. Instead, the topological Hall e ect arises in a wide temperature range below the Curie temperature, in a region where the magnetic-field dependence of the Hall resistance largely deviates from the magnetization. Its origin is assigned to the formation of a Néel-type skyrmion induced by the Dzyaloshinskii-Moriya interaction.The geometry and topology in Hilbert space constitute a central issue in quantum physics, which has recently also shed a new light on the electronic states in solids. The wavefunctions are characterized by the Berry connection between two neighbouring points, in both momentum space and real space, which plays the role of the vector potential leading to the concept of emergent electromagnetic field (EEMF). Global topology of the manifold in Hilbert space is represented by topological integers. As integers cannot change continuously, it gives a certain stability to the system. For example, the Chern number, which is given by the integral of the emergent magnetic field over the first Brillouin zone, protects the surface or edge states supporting the dissipationless current flows (that is, bulk-edge correspondence). The one-dimensional chiral edge mode in the quantum Hall effect and the Dirac surface state in three-dimensional topological insulators (TI; refs 7,8) are the representative examples of this phenomenon. In addition, it has recently been proposed 9,10 and observed 11-14 that TI with doped magnetic ions-namely, Cr or V-produces the quantized version of the anomalous Hall effect (AHE) in the absence of an external magnetic field.Topology in real space, on the other hand, is exemplified by skyrmion spin texture 15-17 found in chiral-lattice magnets such as MnSi (ref. 15) or Fe 1−x Co x Si (ref. 16). Here, the solid angle subtended by the spins forms an emergent magnetic field in real space, and its integral over the two-dimensional space defines a topological integer called the skyrmion number. Namely, the skyrmion number counts the number of times the spin direction wraps around a unit sphere. This integer protects the skyrmion from annihilation and allows it to behave as a single particle.Thus far, the EEMF in momentum and real spaces have mostly been studied separately. Recent advances in fabricating artificial stru...

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Geometric Hall effects in topological insulator heterostructures

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“…These materials are chosen because they are indeed ferromagnetic (29,30), they exhibit topological surface states with a Dirac point E D near the Fermi energy E F (31), and they exhibit the QAHE (19)(20)(21)(22). Our SI-STM experiments are carried out in cryogenic ultrahigh vacuum at T = 4.5 K, well below the measured T C ∼ 18 K bulk ferromagnetic phase transition in these samples.…”

Section: Experimental Methodsmentioning

confidence: 99%

“…A plethora of new physics is then predicted, including σ xy = ±e 2 =h quantum anomalous Hall effects (QAHE) (7,8), topological surface-state magneto-electric effects (9)(10)(11)(12), related magneto-optical Kerr and Faraday rotations (10,13,14), axionic-like electrodynamics (15,16), and even E-field induced magnetic monopoles (17,18). As yet, none of these phenomena except the QAHE (19)(20)(21)(22) have been detected, and the QAHE itself is poorly understood because σ xy = ±e 2 =h is observed only at temperatures far below 1 K.…”

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confidence: 99%

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _x (Bi _0.1 Sb _0.9 ) _2-x Te ₃

Lee

Kim

Lee

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

233

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To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking timereversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr 0.08 (Bi 0.1 Sb 0.9 ) 1.92 Te 3 . Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship Δ(r) ∝ n(r) is confirmed throughout and exhibits an electron-dopant interaction energy J* = 145 meV·nm 2 . These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.ferromagnetic topological insulator | Dirac-mass gapmap | Dirac-mass disorder | magnetic dopant atoms T hat the surface states of 3D topological insulators (TIs) exhibit a "massless" Dirac spectrum EðkÞ = Zvk · σ with spinmomentum locking and protected by time-reversal symmetry is now firmly established. Opening a gap in this spectrum is key to the realization of several extraordinary new types of electronic phenomena. The prevalent approach to opening this "Dirac-mass gap" is to dope the materials with magnetic atoms (1-6). A plethora of new physics is then predicted, including σ xy = ±e 2 =h quantum anomalous Hall effects (QAHE) (7, 8), topological surface-state magneto-electric effects (9-12), related magneto-optical Kerr and Faraday rotations (10, 13, 14), axionic-like electrodynamics (15, 16), and even E-field induced magnetic monopoles (17,18). As yet, none of these phenomena except the QAHE (19-22) have been detected, and the QAHE itself is poorly understood because σ xy = ±e 2 =h is observed only at temperatures far below 1 K.Interactions between the TI surface electrons and the magnetic dopant atoms at random surface locations r i can be represented theoretically by a Hamiltonian of the type H DA = −J p P S i · sδðr − r i Þ. Here S i (s) is the spin of each dopant (surfacestate carrier) measured in units of Z, and J p is their exchangeinteraction energy scale. In the simple case of a homogenous ferromagnetic state with magnetization parallel to the surface normal z, the Hamiltonian becomes H = −J p n 0...

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“…When the Fermi level (E F ) lies within this gap, the only remaining conduction channel is the quasione-dimensional chiral edge state, which gives rise to quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field 3,14 . Up to date, the QAH effect has been observed in Cr or V doped (Bi,Sb) 2 Te 3 TI thin films with accurately controlled chemical composition and thickness grown by molecular beam epitaxy (MBE) [3][4][5][6] .…”

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Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator

Feng

et al. 2015

Phys. Rev. Lett.

119

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Quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) is a novel transport phenomenon in which theThe realization of QAH effect requires that a two-dimensional (2D) material must be FM, topological, and insulating simultaneously 9 . Magnetically doped TIs have been proposed 1, 2, 10-12 and experimentally proved 3-6 to be an ideal material system for fulfilling these stringent requirements. For a 3D TI, the inverted bulk band structure ensures topologically protected metallic surface states (SSs), which become 2D when the film is sufficiently thin 13 . The spontaneous FM order induced by magnetic doping not only leads to the anomalous Hall effect, but also opens an energy gap at the Dirac point. When the Fermi level (E F ) lies within this gap, the only remaining conduction channel is the quasione-dimensional chiral edge state, which gives rise to quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field 3, 14 . Up to date, the QAH effect has been observed in Cr or V doped (Bi,Sb) 2 Te 3 TI thin films with accurately controlled chemical composition and thickness grown by molecular beam epitaxy (MBE) 3-6 .The MBE-grown QAH insulator film studied here has a chemical formula Fig. 1a is a schematic drawing of the transport device, which is similar to that reported previously 3 .The film is manually scratched into a Hall bar geometry, and the SrTiO 3 substrate is used as the bottom gate oxide due to its large dielectric constant at low temperature. The Cr concentration, hence the density of local moment, is higher than that in the sample where the QAH effect was originally discovered 3 . As a result, the FM order forms at a higher Curie temperature T C = 24 K as determined by the temperature dependent anomalous Hall effect (supplementary Fig. S1). Another important consequence of higher Cr doping is that the sample becomes more disordered, which is crucial to the physics that will be discussed in this work.We first demonstrate the existence of QAH effect in this sample. Fig. 1b displays the gate voltage (V g ) dependence of the Hall resistance  yx (blue curve) and longitudinal resistance  xx (red curve) measured at T = 10 mK in a strong magnetic field B = 12 T applied perpendicular to the film. The  yx exhibits a plateau for -10 V < V g < 10 V with its maximum value close to 99.1% of the quantum resistance h/e 2 ~ 25.8 k. In the same V g range  xx shows a pronounced dip with its minimum value close to 0.1 h/e 2 . To show that the apparent Hall quantization in Fig. 1b is due to the QAH effect rather than conventional QH effect in high magnetic field, in Fig. 1c we display the field dependence of  yx measured at V g = -5 V, when  xx reaches a minimum in Fig. 1b. The Hall trace shows an abrupt jump at zero magnetic field, characteristic of the anomalous Hall effect.With increasing magnetic field, the  yx value increases gradually and approaches h/e 2 at 12 T. The  xx shown in Fig. 1d exhibits two sharp peaks at the coercive field H C , and decreases rapidly on b...

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Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit

Cited by 528 publications

References 52 publications

Geometric Hall effects in topological insulator heterostructures

Geometric Hall effects in topological insulator heterostructures

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _x (Bi _0.1 Sb _0.9 ) _2-x Te ₃

Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator

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Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit

Cited by 528 publications

References 52 publications

Geometric Hall effects in topological insulator heterostructures

Geometric Hall effects in topological insulator heterostructures

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr x (Bi 0.1 Sb 0.9 ) 2-x Te 3

Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator

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Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _x (Bi _0.1 Sb _0.9 ) _2-x Te ₃