Atomic scale quantum anomalous hall effect in monolayer graphene/MnBi2Te4 heterostructure

The two-dimensional quantum anomalous Hall (QAH) effect is direct evidence of non-trivial Berry curvature topology in condensed matter physics. Searching for QAH in 2D materials, particularly with simplified fabrication methods, poses a significant challenge in future applications. Despite numerous theoretical works proposed for the QAH effect with C = 2 in graphene, neglecting magnetism sources such as proper substrate effects lacks experimental evidence. In this work, we propose the QAH effect in graphene/MnBi2Te4 (MBT) heterostructure based on density-functional theory (DFT) calculations. The monolayer MBT introduces spin-orbital coupling, Zeeman exchange field, and Kekulé distortion as a substrate effect into graphene, resulting in QAH with C = 1 in the heterostructure. Our effective Hamiltonian further presents a rich phase diagram that has not been studied previously. Our work provides a new and practical way to explore the QAH effect in monolayer graphene and the magnetic topological phases by the flexibility of MBT family materials.

Enhanced Photoresponse of High Crystalline Bi2Se3 Thin-Films Using Patterned Substrates

High-quality Bi₂Se₃ thin films with topological insulating properties at room temperature have recently attracted much attention as one of the promising materials for realizing innovative electronic and optoelectronic devices. Here, we report the high crystallinity growth of Bi₂Se₃ thin films on a patterned sapphire substrate (PSS) by using a vapor-phase transport deposition with minimizing thermal dissociation of Se atoms vaporized in Bi₂Se₃ powder. This PSS not only reduces the large dislocation of heterogeneously grown Bi₂Se₃ on a sapphire substrate but also induces enhanced light absorption in the visible to near-infrared (IR) ranges compared to Bi₂Se₃ on planar sapphire substrates. Thus, the Bi₂Se₃ thin film laterally grown on the PSS reveals uniform surface properties and high crystallinity in the rhombohedral lattice phase with a full width at half maximum of 0.06° for the XRD (003) peak. Also, the photoresponse of the fabricated IR conversion device using Bi₂Se₃/PSS heterostructure exhibits excellent performance and high reliability with no degradation after continuous switching. As a result, the device constructed with the Bi₂Se₃/PSS exhibits one order of magnitude higher NIR induced-photocurrent and 1-2 orders of magnitude faster photo-switching than that with Bi₂Se₃/Al₂O₃. Such an enhancement in the device performance of Bi₂Se₃/PSS is confirmed by the increased absorption spectra in visible and NIR ranges and the improved light absorption distribution.

Experimental Demonstration of a Magnetically Induced Warping Transition in a Topological Insulator Mediated by Rare-Earth Surface Dopants

Magnetic topological insulators constitute a novel class of materials whose topological surface states (TSSs) coexist with long-range ferromagnetic order, eventually breaking time-reversal symmetry. The subsequent bandgap opening is predicted to co-occur with a distortion of the TSS warped shape from hexagonal to trigonal. We demonstrate such a transition by means of angle-resolved photoemission spectroscopy on the magnetically rare-earth (Er and Dy) surface-doped topological insulator Bi₂Se₂Te. Signatures of the gap opening are also observed. Moreover, increasing the dopant coverage results in a tunable p-type doping of the TSS, thereby allowing for a gradual tuning of the Fermi level toward the magnetically induced bandgap. A theoretical model where a magnetic Zeeman out-of-plane term is introduced in the Hamiltonian governing the TSS rationalizes these experimental results. Our findings offer new strategies to control magnetic interactions with TSSs and open up viable routes for the realization of the quantum anomalous Hall effect.

Evolution of Dopant-Concentration-Induced Magnetic Exchange Interaction in Topological Insulator Thin Films

To date, the quantum anomalous Hall effect has been realized in chromium (Cr)- and/or vanadium(V)-doped topological insulator (Bi,Sb)₂Te₃ thin films. In this work, we use molecular beam epitaxy to synthesize both V- and Cr-doped Bi₂Te₃ thin films with controlled dopant concentration. By performing magneto-transport measurements, we find that both systems show an unusual yet similar ferromagnetic response with respect to magnetic dopant concentration; specifically the Curie temperature does not increase monotonically but shows a local maximum at a critical dopant concentration. We attribute this unusual ferromagnetic response observed in Cr/V-doped Bi₂Te₃ thin films to the dopant-concentration-induced magnetic exchange interaction, which displays evolution from van Vleck-type ferromagnetism in a nontrivial magnetic topological insulator to Ruderman-Kittel-Kasuya-Yosida (RKKY)-type ferromagnetism in a trivial diluted magnetic semiconductor. Our work provides insights into the ferromagnetic properties of magnetically doped topological insulator thin films and facilitates the pursuit of high-temperature quantum anomalous Hall effect.

Layer-Dependent Magnetic Structure and Anomalous Hall Effect in the Magnetic Topological Insulator MnBi4Te7

The intrinsic antiferromagnetic topological insulator (TI) MnBi₄Te₇ provides a capacious playground for the realization of topological quantum phenomena, such as the axion insulator states and quantum anomalous Hall (QAH) effect. In addition to nontrivial band topology, magnetism is another necessary ingredient for realizing these quantum phenomena. Here, we investigate signatures of thickness-dependent magnetism in exfoliated MnBi₄Te₇ thin flakes. We observe an obvious odd-even layer-number effect in few-layer MnBi₄Te₇. Noticeably, we show that in monolayer MnBi₄Te₇ the anomalous Hall effect exhibits a sign reversal. Compared with the case of MnBi₂Te₄, interlayer antiferromagnetic exchange coupling, which is essential for the realization of the QAH effect, is greatly suppressed in MnBi₄Te₇. The demonstration of thickness-dependent magnetic properties is helpful to further explore the topological quantum phenomena in MnBi₄Te₇.

Highly Tunable Beyond-Room-Temperature Intrinsic Ferromagnetism in Cr-Doped Topological Crystalline Insulator SnTe Crystals

The combination of topological phase and intrinsic beyond-room-temperature ferromagnetism is expected to realize the quantum anomalous Hall effect at a high temperature. However, no beyond-room-temperature intrinsic ferromagnetism has been reported in either topological insulator or topological crystalline insulator (TCI) so far. Here, we report Cr-doping in TCI-phase SnTe crystals which possess highly tunable beyond-room-temperature intrinsic ferromagnetism including T_c, magnetic moment, and coercivity by varying Cr contents and crystal thickness. With the increase of the Cr content, the T_c increases by 159 K from 221 to 380 K and the saturation magnetic moments increase by ∼23.6 times from 0.018 to 0.421 μ_B/f.u. This intrinsic beyond-room-temperature ferromagnetism is fully demonstrated by the anomalous Hall effect and magneto-optical Kerr effect in a single Cr_xSn_1-xTe nanosheet. Moreover, the room-temperature tunneling magnetoresistance effect has been realized by using a Cr_xSn_1-xTe flake, a Fe thin film, and a commercially compatible ultrathin AlO_x tunneling barrier. This work indicates a great potential of Cr_xSn_1-xTe crystals in room-temperature magnetoelectronic and spintronic devices.

Quantum Transport and Magnetism of Dirac Electrons in Solids

The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi_{2}Se_{3} and Bi_{2}Te_{3}. Topological insulators feature gapless surface states and, moreover, magnetic doping and resultant ferromagnetic ordering break time-reversal symmetry to realize quantum anomalous Hall and Chern insulators. Here, we focus on the bulk and investigate the mutual coupling of electronic and magnetic properties of Dirac electrons. Without carrier doping, spiral magnetic orders cause a ferroelectric polarization through the spin-orbit coupling. In a doped metallic state, the anisotropic magnetoresistance arises without uniform magnetization. We find that electric current induces uniform magnetization and conversely an oscillating magnetic order induces electric current. Our model provides a coherent and unified description of all those phenomena. The mutual control of electric and magnetic properties demonstrates implementations of antiferromagnetic spintronics. We also discuss the stoichiometric magnetic topological insulator MnBi_{2}Te_{4}.

Two-Dimensional Van Der Waals Topological Materials: Preparation, Properties, and Device Applications

Over the past decade, 2D van der Waals (vdW) topological materials (TMs), including topological insulators and topological semimetals, which combine atomically flat 2D layers and topologically nontrivial band structures, have attracted increasing attention in condensed-matter physics and materials science. These easily cleavable and integrated TMs provide the ideal platform for exploring topological physics in the 2D limit, where new physical phenomena may emerge, and represent a potential to control and investigate exotic properties and device applications in nanoscale topological phases. However, multifaced efforts are still necessary, which is the prerequisite for the practical application of 2D vdW TMs. Herein, this review focuses on the preparation, properties, and device applications of 2D vdW TMs. First, three common preparation strategies for 2D vdW TMs are summarized, including single crystal exfoliation, chemical vapor deposition, and molecular beam epitaxy. Second, the origin and regulation of various properties of 2D vdW TMs are introduced, involving electronic properties, transport properties, optoelectronic properties, thermoelectricity, ferroelectricity, and magnetism. Third, some device applications of 2D vdW TMs are presented, including field-effect transistors, memories, spintronic devices, and photodetectors. Finally, some significant challenges and opportunities for the practical application of 2D vdW TMs in 2D topological electronics are briefly addressed.

Unveiling the hybridization between the Cr-impurity-mediated flat band and the Rashba-split state of the α-Au/Si(111) surface

Adsorption of foreign atoms onto 2D materials can either lead to ordinary electron doping or the emergence of new electronic effects including topology, superconductivity, and quantum anomalous Hall and Kondo states. We have investigated the effect of Cr doping on the electronic structure of the α-Au/Si(111)- surface and its adsorbate-modified family. It has been found that below a critical coverage of ∼0.05 monolayer, Cr adatoms penetrate beneath the Au and topmost Si layers and induce the occupied resonance flat band in the electronic spectrum as revealed by angle-resolved photoelectron spectroscopy. Further deposition of Cr leads to the growth of the 3D islands spoiling the surface homogeneity. Using density functional theory calculations, we have disclosed the effects of Cr doping on the electronic band structure and revealed the nature of hybridization between the Cr-induced magnetic-split band and the Au-induced Rashba-split surface state. We believe that the synthesized 2D phases and electronic effects produced by magnetic atom doping in the ultimate two-dimensional limit will stimulate further investigations related to the highly correlated phases and will find practical applications in nanoelectronic devices.

Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states. It can be achieved by either sweeping the magnetic field or tuning the carrier density. The recent realization of the quantum anomalous Hall (QAH) insulators with tunable Chern numbers introduces the channel degree of freedom to the dissipation-free chiral edge transport and makes the study of the quantum phase transition between two topological states under zero magnetic field possible. Here, we synthesized the magnetic topological insulator (TI)/TI pentalayer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy. By performing transport measurements, we found a potential plateau phase transition between C=1 and C=2 QAH states under zero magnetic field. In tuning the transition, the Hall resistance monotonically decreases from h/e^{2} to h/2e^{2}, concurrently, the longitudinal resistance exhibits a maximum at the critical point. Our results show that the ratio between the Hall resistance and the longitudinal resistance is greater than 1 at the critical point, which indicates that the original chiral edge channel from the C=1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels appear to self-organize and form the second chiral edge channel in completing the plateau phase transition. Our study will motivate further investigations of this novel Chern number change-induced quantum phase transition and advance the development of the QAH chiral edge current-based electronic and spintronic devices.

High-Yield Growth and Tunable Morphology of Bi2Se3 Nanoribbons Synthesized on Thermally Dewetted Au

The yield and morphology (length, width, thickness) of stoichiometric Bi₂Se₃ nanoribbons grown by physical vapor deposition is studied as a function of the diameters and areal number density of the Au catalyst nanoparticles of mean diameters 8–150 nm formed by dewetting Au layers of thicknesses 1.5–16 nm. The highest yield of the Bi₂Se₃ nanoribbons is reached when synthesized on dewetted 3 nm thick Au layer (mean diameter of Au nanoparticles ~10 nm) and exceeds the nanoribbon yield obtained in catalyst-free synthesis by almost 50 times. The mean lengths and thicknesses of the Bi₂Se₃ nanoribbons are directly proportional to the mean diameters of Au catalyst nanoparticles. In contrast, the mean widths of the Bi₂Se₃ nanoribbons do not show a direct correlation with the Au nanoparticle size as they depend on the contribution ratio of two main growth mechanisms—catalyst-free and vapor–liquid–solid deposition. The Bi₂Se₃ nanoribbon growth mechanisms in relation to the Au catalyst nanoparticle size and areal number density are discussed. Determined charge transport characteristics confirm the high quality of the synthesized Bi₂Se₃ nanoribbons, which, together with the high yield and tunable morphology, makes these suitable for application in a variety of nanoscale devices.

Visualization of the strain-induced topological phase transition in a quasi-one-dimensional superconductor TaSe3

Control of the phase transition from topological to normal insulators can allow for an on/off switching of spin current. While topological phase transitions have been realized by elemental substitution in semiconducting alloys, such an approach requires preparation of materials with various compositions. Thus it is quite far from a feasible device application, which demands a reversible operation. Here we use angle-resolved photoemission spectroscopy and spin- and angle-resolved photoemission spectroscopy to visualize the strain-driven band-structure evolution of the quasi-one-dimensional superconductor TaSe₃. We demonstrate that it undergoes reversible strain-induced topological phase transitions from a strong topological insulator phase with spin-polarized, quasi-one-dimensional topological surface states, to topologically trivial semimetal and band insulating phases. The quasi-one-dimensional superconductor TaSe₃ provides a suitable platform for engineering the topological spintronics, for example as an on/off switch for a spin current that is robust against impurity scattering.

Spacer-Layer-Tunable Magnetism and High-Field Topological Hall Effect in Topological Insulator Heterostructures

Controlling magnetic order in magnetic topological insulators (MTIs) is a key to developing spintronic applications with MTIs and is commonly achieved by changing the magnetic doping concentration, which inevitably affects the spin-orbit coupling strength and the topological properties. Here, we demonstrate tunable magnetic properties in topological heterostructures over a wide range, from a ferromagnetic phase with a Curie temperature of around 100 K all the way to a paramagnetic phase, while keeping the overall chemical composition the same, by controlling the thickness of nonmagnetic spacer layers between two atomically thin magnetic layers. This work showcases that spacer-layer control is a powerful tool to manipulate magneto-topological functionalities in MTI heterostructures. Furthermore, the interaction between the MTI and the Cr₂O₃ buffer layers also leads to a robust topological Hall effect surviving up to a record-high 6 T of magnetic field, shedding light on the critical role of interfacial layers in thin-film topological materials.

A magnetic topological insulator in two-dimensional EuCd2Bi2: giant gap with robust topology against magnetic transitions

Magnetic topological states open up exciting opportunities for exploring fundamental topological quantum physics and innovative design of topological spintronics devices. However, the nontrivial topologies, for most known magnetic topological states, are usually associated with and may be heavily deformed by fragile magnetism. Here, using a tight-binding model and first-principles calculations, we demonstrate that a highly robust magnetic topological insulator phase, which remains intact under both ferromagnetic and antiferromagnetic configurations, can emerge in two-dimensional EuCd₂Bi₂ quintuple layers. Because of spin-orbital coupling, an inverted gap with intrinsic band inversions occuring simultaneously for up and down spin channels is obtained, accompanied by a nonzero spin Chern number and a pair of gapless edge states, and remarkably the magnitude of the nontrivial band gap for EuCd₂Bi₂ reaches as much as 750 meV. Moreover, the robustness of the magnetic TI phase is further confirmed by rotating the magnetization directions, indicating that EuCd₂Bi₂ represents a promising material for understanding and utilizing the topological insulating states in two-dimensional spin-orbit magnets.

Tuning the Chern number in quantum anomalous Hall insulators

A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h/(Ce²) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an integer)^1,2. The QAH effect has been realized in magnetic topological insulators^3-9 and magic-angle twisted bilayer graphene^10,11. However, the QAH effect at zero magnetic field has so far been realized only for C = 1. Here we realize a well quantized QAH effect with tunable Chern number (up to C = 5) in multilayer structures consisting of alternating magnetic and undoped topological insulator layers, fabricated using molecular beam epitaxy. The Chern number of these QAH insulators is determined by the number of undoped topological insulator layers in the multilayer structure. Moreover, we demonstrate that the Chern number of a given multilayer structure can be tuned by varying either the magnetic doping concentration in the magnetic topological insulator layers or the thickness of the interior magnetic topological insulator layer. We develop a theoretical model to explain our experimental observations and establish phase diagrams for QAH insulators with high, tunable Chern number. The realization of such insulators facilitates the application of dissipationless chiral edge currents in energy-efficient electronic devices, and opens up opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects.

Criteria for Realizing Room-Temperature Electrical Transport Applications of Topological Materials

The unusual electronic states found in topological materials can enable a new generation of devices and technologies, yet a long-standing challenge has been finding materials without deleterious parallel bulk conduction. This can arise either from defects or thermally activated carriers. Here, the criteria that materials need to meet to realize transport properties dominated by the topological states, a necessity for a topological device, are clarified. This is demonstrated for 3D topological insulators, 3D Dirac materials, and 1D quantum anomalous Hall insulators, though this can be applied to similar systems. The key parameters are electronic bandgap, dielectric constant, and carrier effective mass, which dictate under what circumstances (defect density, temperature, etc.) the unwanted bulk state will conduct in parallel to the topological states. As these are fundamentally determined by the basic atomic properties, simple chemical arguments can be used to navigate the phase space to ultimately find improved materials. This will enable rapid identification of new systems with improved properties, which is crucial to designing new material systems and push a new generation of topological technologies.

Quantum Phases of Three-Dimensional Chiral Topological Insulators on a Spin Quantum Simulator

The detection of topological phases of matter has become a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our Letter paves the way toward the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions.

Single crystal growth and ferromagnetism of Cr-doped Sb4Te3

Here we report the single crystal growth, magnetic and transport properties of Cr-doped Sb₄Te₃, (Sb_1-x Cr _x )₄Te₃, with doping concentrations x  =  0.25%, 0.5%, 0.75%, and 1%. The samples with lower doping concentrations are paramagnetic, while ferromagnetism appears in higher doped samples with the highest Curie temperature of 7 K when x  =  1%. Anomalous Hall effect with clear hysteresis loop is observed in the samples with x  =  1%, indicating the intrinsic ferromagnetism in the system. Hall resistivity measurements show the dominant charge carriers are holes and the density of holes increases with the doping concentration. This work provides a possible single-crystalline platform for further experimental researches on the nontrivial band topology in Sb₄Te₃, and enriches the ferromagnetic members in the transition metal doped (Sb₂) _m -Sb₂Te₃ topological material series.

Competing Magnetic Interactions in the Antiferromagnetic Topological Insulator MnBi_{2}Te_{4}

The antiferromagnetic (AFM) compound MnBi_{2}Te_{4} is suggested to be the first realization of an AFM topological insulator. We report on inelastic neutron scattering studies of the magnetic interactions in MnBi_{2}Te_{4} that possess ferromagnetic triangular layers with AFM interlayer coupling. The spin waves display a large spin gap and pairwise exchange interactions within the triangular layer are long ranged and frustrated by large next-nearest neighbor AFM exchange. The degree of frustration suggests proximity to a variety of magnetic phases, potentially including skyrmion phases, which could be accessed in chemically tuned compounds or upon the application of symmetry-breaking fields.

Gap-like feature observed in the non-magnetic topological insulators

Non-magnetic gap at the Dirac point of topological insulators remains an open question in the field. Here, we present angle-resolved photoemission spectroscopy experiments performed on Cr-doped Bi₂Se₃ and showed that the Dirac point is progressively buried by the bulk bands and a low spectral weight region in the vicinity of the Dirac point appears. These two mechanisms lead to spectral weight suppression region being mistakenly identified as an energy gap in earlier studies. We further calculated the band structure and found that the original Dirac point splits into two nodes due to the impurity resonant states and the energy separation between the nodes is the low density of state region which appears to be like an energy gap in potoemission experiments. We supported our arguments by presenting photoemission experiments carried out with on- and off- resonant photon energies. Our observation resolves the widely debated questions of apparent energy gap opening at the Dirac point without long range ferromagnetic order in topological insulators.

Indirect exchange interaction between magnetic impurities in one-dimensional gapped helical states

We investigate theoretically indirect exchange interaction between magnetic impurities mediated by one-dimensional gapped helical states. Such states, containing massive Dirac fermions, may be realized on the edge of a two-dimensional topological insulator when time-reversal symmetry is weakly broken. We find that the indirect exchange interaction consists of Heisenberg, Dzyaloshinsky-Moriya, in-plane and out-of-plane Ising terms. These terms decay exponentially when the Fermi level lies inside the bandgap whereas the Dzyaloshinsky-Moriya term has smallest amplitude. Outside the bandgap, the massive helical states modify oscillatory behaviors of the range functions so that the period of oscillations decreases near the edge of band in terms of energy gap or Fermi energy. In addition, the out-of-plane Ising term vanishes in the case of zero-gap structure. Also, the oscillation amplitude of out-of-plane Ising term increases versus energy gap but it decreases as a function of Fermi energy. While the oscillation amplitudes of other components remain constant as functions of energy gap and Fermi energy. Analytical results are also obtained for subgap and over gap regimes. Furthermore, the effects of electron-electron interactions are analyzed.

Experimental Observation of the Gate-Controlled Reversal of the Anomalous Hall Effect in the Intrinsic Magnetic Topological Insulator MnBi2Te4 Device

Magnetic topological insulator, a platform for realizing quantum anomalous Hall effect, axion state, and other novel quantum transport phenomena, has attracted a lot of interest. Recently, it is proposed that MnBi₂Te₄ is an intrinsic magnetic topological insulator, which may overcome the disadvantages in the magnetic doped topological insulator, such as disorder. Here we report on the gate-reserved anomalous Hall effect (AHE) in the MnBi₂Te₄ thin film. By tuning the Fermi level using the top/bottom gate, the AHE loop gradually decreases to zero and the sign is reversed. The positive AHE exhibits distinct coercive fields compared with the negative AHE. It reaches a maximum inside the gap of the Dirac cone, and its amplitude exhibits a linear scaling with the longitudinal conductance. The positive AHE is attributed to the competition of the intrinsic Berry curvature and the extrinsic skew scattering. Its gate-controlled switching contributes a scheme for the topological spin field-effect transistors.

Sign Change in the Anomalous Hall Effect and Strong Transport Effects in a 2D Massive Dirac Metal Due to Spin-Charge Correlated Disorder

The anomalous Hall effect (AHE) is highly sensitive to disorder in the metallic phase. Here we show that statistical correlations between the charge-spin disorder sectors strongly affect the conductivity and the sign or magnitude of AHE. As the correlation between the charge and gauge-mass components increases, so does the AHE, achieving its universal value, and even exceeding it, although the system is an impure metal. The AHE can change sign when the anticorrelations reverse the sign of the effective Dirac mass, a possible mechanism behind the sign change seen in recent experiments.

Record High-Proximity-Induced Anomalous Hall Effect in (BixSb1-x)2Te3 Thin Film Grown on CrGeTe3 Substrate

Quantum anomalous Hall effect (QAHE) can only be realized at extremely low temperatures in magnetically doped topological insulators (TIs) due to limitations inherent with the doping process. In an effort to boost the quantization temperature of QAHE, the magnetic proximity effect in magnetic insulator/TI heterostructures has been extensively investigated. However, the observed anomalous Hall resistance has never been more than several ohms, presumably owing to the interfacial disorders caused by the structural and chemical mismatch. Here, we show that, by growing (Bi_xSb_1-x)₂Te₃ (BST) thin films on structurally and chemically well-matched, ferromagnetic-insulating CrGeTe₃ (CGT) substrates, the proximity-induced anomalous Hall resistance can be enhanced by more than an order of magnitude. This sheds light on the importance of structural and chemical matches for magnetic insulator/TI proximity systems.

Ferromagnetic Anomalous Hall Effect in Cr-Doped Bi2Se3 Thin Films via Surface-State Engineering

The anomalous Hall effect (AHE) is a nonlinear Hall effect appearing in magnetic conductors, boosted by internal magnetism beyond what is expected from the ordinary Hall effect. With the recent discovery of the quantized version of the AHE, the quantum anomalous Hall effect (QAHE), in Cr- or V-doped topological insulator (TI) (Sb,Bi)₂Te₃ thin films, the AHE in magnetic TIs has been attracting significant interest. However, one of the puzzles in this system has been that while Cr- or V-doped (Sb,Bi)₂Te₃ and V-doped Bi₂Se₃ exhibit AHE, Cr-doped Bi₂Se₃ has failed to exhibit even ferromagnetic AHE, the expected predecessor to the QAHE, though it is the first material predicted to exhibit the QAHE. Here, we have successfully implemented ferromagnetic AHE in Cr-doped Bi₂Se₃ thin films by utilizing a surface state engineering scheme. Surprisingly, the observed ferromagnetic AHE in the Cr-doped Bi₂Se₃ thin films exhibited only a positive slope regardless of the carrier type. We show that this sign problem can be explained by the intrinsic Berry curvature of the system as calculated from a tight-binding model combined with a first-principles method.

Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator

Inducing magnetic orders in a topological insulator (TI) to break its time reversal symmetry has been predicted to reveal many exotic topological quantum phenomena. The manipulation of magnetic orders in a TI layer can play a key role in harnessing these quantum phenomena toward technological applications. Here we fabricated a thin magnetic TI film on an antiferromagnetic (AFM) insulator Cr₂O₃ layer and found that the magnetic moments of the magnetic TI layer and the surface spins of the Cr₂O₃ layers favor interfacial AFM coupling. Field cooling studies show a crossover from negative to positive exchange bias clarifying the competition between the interfacial AFM coupling energy and the Zeeman energy in the AFM insulator layer. The interfacial exchange coupling also enhances the Curie temperature of the magnetic TI layer. The unique interfacial AFM alignment in magnetic TI on AFM insulator heterostructures opens a new route toward manipulating the interplay between topological states and magnetic orders in spin-engineered heterostructures, facilitating the exploration of proof-of-concept TI-based spintronic and electronic devices with multifunctionality and low power consumption.

Second-order topological insulators and loop-nodal semimetals in Transition Metal Dichalcogenides XTe2 (X = Mo, W)

Transition metal dichalcogenides XTe2 (X = Mo, W) have been shown to be second-order topological insulators based on first-principles calculations, while topological hinge states have been shown to emerge based on the associated tight-binding model. The model is equivalent to the one constructed from a loop-nodal semimetal by adding mass terms and spin-orbit interactions. We propose to study a chiral-symmetric model obtained from the original Hamiltonian by simplifying it but keeping almost identical band structures and topological hinge states. A merit is that we are able to derive various analytic formulas because of chiral symmetry, which enables us to reveal basic topological properties of transition metal dichalcogenides. We find a linked loop structure where a higher linking number (even 8) is realized. We construct second-order topological semimetals and two-dimensional second-order topological insulators based on this model. It is interesting that topological phase transitions occur without gap closing between a topological insulator, a topological crystalline insulator and a second-order topological insulator. We propose to characterize them by symmetry detectors discriminating whether the symmetry is preserved or not. They differentiate topological phases although the symmetry indicators yield identical values to them. We also show that topological hinge states are controllable by the direction of magnetization. When the magnetization points the z direction, the hinges states shift, while they are gapped when it points the in-plane direction. Accordingly, the quantized conductance is switched by controlling the magnetization direction. Our results will be a basis of future topological devices based on transition metal dichalcogenides.

Electric Polarization in Magnetic Topological Nodal Semimetal Thin Films

We theoretically study the electric polarization in magnetic topological nodal semimetal thin films. In magnetically doped topological insulators, topological nodal semimetal phases emerge once the exchange coupling overcomes the band gap. Changing the magnetization direction, nodal structure is modulated and the system becomes topological nodal point or line semimetals. We find that nodal line semimetals are characterized by non-linear electric polarization, which is not observed in nodal point semimetals. The non-linear response originates from the existence of the surface states. Screening effect is self consistently included within a mean field approximation and the non-linear electric polarization is observed even in the presence of screening effect.

TCNQ Physisorption on the Topological Insulator Bi2 Se3

Topological insulators are promising candidates for spintronic applications due to their topologically protected, spin-momentum locked and gapless surface states. The breaking of the time-reversal symmetry after the introduction of magnetic impurities, such as 3d transition metal atoms embedded in two-dimensional molecular networks, could lead to several phenomena interesting for device fabrication. The first step towards the fabrication of metal-organic coordination networks on the surface of a topological insulator is to investigate the adsorption of the pure molecular layer, which is the aim of this study. Here, the effect of the deposition of the electron acceptor 7,7,8,8-tetracyanoquinodimethane (TCNQ) molecules on the surface of a prototypical topological insulator, bismuth selenide (Bi₂ Se₃ ), is investigated. Scanning tunneling microscope images at low-temperature reveal the formation of a highly ordered two-dimensional molecular network. The essentially unperturbed electronic structure of the topological insulator observed by photoemission spectroscopy measurements demonstrates a negligible charge transfer between the molecular layer and the substrate. Density functional theory calculations confirm the picture of a weakly interacting adsorbed molecular layer. These results reveal significant potential of TCNQ for the realization of metal-organic coordination networks on the topological insulator surface.

Weyl nodes in periodic structures of superconductors and spin-active materials

Motivated by recent progress in epitaxial growth of proximity structures of s-wave superconductors (S) and spin-active materials (M), in this paper we show that certain periodic structures of S and M can behave effectively as superconductors with pairs of point nodes, near which the low-energy excitations are Weyl fermions. A simple model, where M is described by a Kronig-Penney potential with both spin-orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero-energy surface states in the form of open Fermi lines (Fermi arcs). As a second example, a lattice model with alternating layers of S and magnetic Z₂ topological insulators is solved. The calculated spectrum confirms previous predictions of Weyl nodes based on the tunnelling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors.This article is part of the theme issue 'Andreev bound states'.

Two-component anomalous Hall effect in a magnetically doped topological insulator

The anomalous Hall (AH) effect measurement has emerged as a powerful tool to gain deep insights into magnetic materials, such as ferromagnetic metals, magnetic semiconductors, and magnetic topological insulators (TIs). In Mn-doped Bi₂Se₃, however, the AH effect has never been reported despite a lot of previous studies. Here we report the observation of AH effect in (Bi,Mn)₂Se₃ thin films and show that the sign of AH resistances changes from positive to negative as the Mn concentration is increased. The positive and negative AH resistances are found to coexist in a crossover regime. Such a two-component AH effect and the sign reversal can also be obtained by electrical gating of lightly doped samples. Our results provide an important basis for understanding the puzzling interplay between the surface states, the bulk states, and various magnetic doping effects, as well as competing magnetic orders in magnetically doped TIs.

Disorder-Induced Topological State Transition in Photonic Metamaterials

The topological state transition has been widely studied based on the quantized topological band invariant such as the Chern number for the system without intense randomness that may break the band structures. We numerically demonstrate the disorder-induced state transition in the photonic topological systems for the first time. Instead of applying the ill-defined topological band invariant in a disordered system, we utilize an empirical parameter to unambiguously illustrate the state transition of the topological metamaterials. Before the state transition, we observe a robust surface state with well-confined electromagnetic waves propagating unidirectionally, immune to the disorder from permittivity fluctuation up to 60% of the original value. During the transition, a hybrid state composed of a quasiunidirectional surface mode and intensively localized hot spots is established, a result of the competition between the topological protection and Anderson localization.

Atomically Abrupt Topological p-n Junction

Topological insulators (TI's) are a new class of quantum matter with extraordinary surface electronic states, which bear great potential for spintronics and error-tolerant quantum computing. In order to put a TI into any practical use, these materials need to be fabricated into devices whose basic units are often p-n junctions. Interesting electronic properties of a 'topological' p-n junction were proposed theoretically such as the junction electronic state and the spin rectification. However, the fabrication of a lateral topological p-n junction has been challenging because of materials, process, and fundamental reasons. Here, we demonstrate an innovative approach to realize a p-n junction of topological surface states (TSS's) of a three-dimensional (3D) topological insulator (TI) with an atomically abrupt interface. When a ultrathin Sb film is grown on a 3D TI of Bi₂Se₃ with a typical n-type TSS, the surface develops a strongly p-type TSS through the substantial hybridization between the 2D Sb film and the Bi₂Se₃ surface. Thus, the Bi₂Se₃ surface covered partially with Sb films bifurcates into areas of n- and p-type TSS's as separated by atomic step edges with a lateral electronic junction of as short as 2 nm. This approach opens a different avenue toward various electronic and spintronic devices based on well-defined topological p-n junctions with the scalability down to atomic dimensions.

Magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 driven by the Stark effect

The recent experimental observation of the quantum anomalous Hall effect has cast significant attention on magnetic topological insulators. In these magnetic counterparts of conventional topological insulators such as Bi₂Te₃, a long-range ferromagnetic state can be established by chemical doping with transition-metal elements. However, a much richer electronic phase diagram can emerge and, in the specific case of Cr-doped Bi₂(Se_xTe_1-x)₃, a magnetic quantum phase transition tuned by the actual chemical composition has been reported. From an application-oriented perspective, the relevance of these results hinges on the possibility to manipulate magnetism and electronic band topology by external perturbations such as an electric field generated by gate electrodes-similar to what has been achieved in conventional diluted magnetic semiconductors. Here, we investigate the magneto-transport properties of Cr-doped Bi₂(Se_xTe_1-x)₃ with different compositions under the effect of a gate voltage. The electric field has a negligible effect on magnetic order for all investigated compositions, with the remarkable exception of the sample close to the topological quantum critical point, where the gate voltage reversibly drives a ferromagnetic-to-paramagnetic phase transition. Theoretical calculations show that a perpendicular electric field causes a shift in the electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and, in turn, a magnetic phase transition.

Emergence of charge density waves and a pseudogap in single-layer TiTe2

Two-dimensional materials constitute a promising platform for developing nanoscale devices and systems. Their physical properties can be very different from those of the corresponding three-dimensional materials because of extreme quantum confinement and dimensional reduction. Here we report a study of TiTe₂ from the single-layer to the bulk limit. Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy and spectroscopy, we observed the emergence of a (2 × 2) charge density wave order in single-layer TiTe₂ with a transition temperature of 92 ± 3 K. Also observed was a pseudogap of about 28 meV at the Fermi level at 4.2 K. Surprisingly, no charge density wave transitions were observed in two-layer and multi-layer TiTe₂, despite the quasi-two-dimensional nature of the material in the bulk. The unique charge density wave phenomenon in the single layer raises intriguing questions that challenge the prevailing thinking about the mechanisms of charge density wave formation.

Due to reduced dimensionality, the properties of 2D materials are often different from their 3D counterparts. Here, the authors identify the emergence of a unique charge density wave (CDW) order in monolayer TiTe₂ that challenges the current understanding of CDW formation.

Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.

Above 400-K robust perpendicular ferromagnetic phase in a topological insulator

The quantum anomalous Hall effect (QAHE) that emerges under broken time-reversal symmetry in topological insulators (TIs) exhibits many fascinating physical properties for potential applications in nanoelectronics and spintronics. However, in transition metal-doped TIs, the only experimentally demonstrated QAHE system to date, the QAHE is lost at practically relevant temperatures. This constraint is imposed by the relatively low Curie temperature (T_c) and inherent spin disorder associated with the random magnetic dopants. We demonstrate drastically enhanced T_c by exchange coupling TIs to Tm₃Fe₅O₁₂, a high-T_c magnetic insulator with perpendicular magnetic anisotropy. Signatures showing that the TI surface states acquire robust ferromagnetism are revealed by distinct squared anomalous Hall hysteresis loops at 400 K. Point-contact Andreev reflection spectroscopy confirms that the TI surface is spin-polarized. The greatly enhanced T_c, absence of spin disorder, and perpendicular anisotropy are all essential to the occurrence of the QAHE at high temperatures.

Theory of topological insulator waveguides: polarization control and the enhancement of the magneto-electric effect

Topological insulators subject to a time-reversal-symmetry-breaking perturbation are predicted to display a magneto-electric effect that causes the electric and magnetic induction fields to mix at the material's surface. This effect induces polarization rotations of between ≈1-10 mrad per interface in an incident plane-polarized electromagnetic wave normal to a multilayered structure. Here we show, theoretically and numerically, that by using a waveguide geometry with a topological insulator guide layer and magneto-dielectric cladding it is possible to achieve rotations of ≈100 mrad and generate an elliptical polarization with only a three-layered structure. This geometry is beneficial, not only as a way to enhance the magneto-electric effect, rendering it easier to observe, but also as a method for controlling the polarization of electromagnetic radiation.

New Class of 3D Topological Insulator in Double Perovskite

We predict a new class of 3D topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate band gap. Band gap of conventional TI is mainly limited by two factors, the strength of SOC and, from electronic structure perspective, the band gap when SOC is absent. While the former is an atomic property, the latter can be minimized in a generic rock-salt lattice model in which a stable crossing of bands at the Fermi level along with band character inversion occurs in the absence of SOC. Thus large-gap TIs or TIs composed of lighter elements can be expected. In fact, we find by performing first-principles calculations that the model applies to a class of double perovskites A₂BiXO₆ (A = Ca, Sr, Ba; X = Br, I) and the band gap is predicted up to 0.55 eV. Besides, surface Dirac cones are robust against the presence of dangling bond at boundary.

Tuning the transport and magnetism in a Cr–Bi2Se3topological insulator by Sb doping

High-quality crystalline (Cr,Sb)-doped Bi₂Se₃(Cr-BSS) films were synthesized using molecular beam epitaxy (MBE).

Enhancing the Spin-Orbit Coupling in Fe3O4 Epitaxial Thin Films by Interface Engineering

By analyzing the in-plane angular dependence of ferromagnetic resonance linewidth, we show that the Gilbert damping constant in ultrathin Fe₃O₄ epitaxial films on GaAs substrate can be enhanced by thickness reduction and oxygen vacancies in the interface. At the same time, the uniaxial magnetic anisotropy due to the interface effect becomes significant. Using the element-specific technique of X-ray magnetic circular dichroism, we find that the orbital-to-spin moment ratio increases with decreasing film thickness, in full agreement with the increase in the Gilbert damping obtained for these ultrathin single-crystal films. Combined with the first-principle calculations, the results suggest that the bonding with Fe and Ga or As ions and the ionic distortion near the interface, as well as the FeO defects and oxygen vacancies, may increase the spin-orbit coupling in ultrathin Fe₃O₄ epitaxial films and in turn provide an enhanced damping.

Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators

The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity σ(yx) = e2/h without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.

Observation of Zeeman effect in topological surface state with distinct material dependence

Manipulating the spins of the topological surface states represents an essential step towards exploring the exotic quantum states emerging from the time reversal symmetry breaking via magnetic doping or external magnetic fields. The latter case relies on the Zeeman effect and thereby we need to estimate the g-factor of the topological surface state precisely. Here, we report the direct observations of the Zeeman effect at the surfaces of Bi₂Se₃ and Sb₂Te₂Se by spectroscopic-imaging scanning tunnelling microscopy. The Zeeman shift of the zero mode Landau level is identified unambiguously by appropriately excluding the extrinsic effects arising from the nonlinearity in the band dispersion of the topological surface state and the spatially varying potential. Surprisingly, the g-factors of the topological surface states in Bi₂Se₃ and Sb₂Te₂Se are very different (+18 and −6, respectively). Such remarkable material dependence opens up a new route to control the spins of the topological surface states.

The knowledge of how electrons behave under magnetic field provides inherent information for exotic quantum states. Here, Fu et al. find different g-factors of topological surface states in Bi₂Se₃ and Sb₂Te₂Se, which suggests possible control of such states in spin-related applications.

Reversible 2D Phase Transition Driven By an Electric Field: Visualization and Control on the Atomic Scale

We report on a reversible structural phase transition of a two-dimensional system that can be locally induced by an external electric field. Two different structural configurations may coexist within a CO monolayer on Cu(111). The balance between the two phases can be shifted by an external electric field, causing the domain boundaries to move, increasing the area of the favored phase controllable both in location and size. If the field is further enhanced new domains nucleate. The arrangement of the CO molecules on the Cu surface is observed in real time and real space with atomic resolution while the electric field driving the phase transition is easily varied over a broad range. Together with the well-known molecular manipulation of CO adlayers, our findings open exciting prospects for combining spontaneous long-range order with man-made CO structures such as "molecule cascades" or "molecular graphene". Our new manipulation mode permits us to bridge the gap between fundamental concepts and the fabrication of arbitrary atomic patterns in large scale, by providing unprecedented insight into the physics of structural phase transitions on the atomic scale.

Route towards Localization for Quantum Anomalous Hall Systems with Chern Number 2

The quantum anomalous Hall system with Chern number 2 can be destroyed by sufficiently strong disorder. During its process towards localization, it was found that the electronic states will be directly localized to an Anderson insulator (with Chern number 0), without an intermediate Hall plateau with Chern number 1. Here we investigate the topological origin of this phenomenon, by calculating the band structures and Chern numbers for disordered supercells. We find that on the route towards localization, there exists a hidden state with Chern number 1, but it is too short and too fluctuating to be practically observable. This intermediate state cannot be stabilized even after some "smart design" of the model and this should be a universal phenomena for insulators with high Chern numbers. By performing numerical scaling of conductances, we also plot the renormalization group flows for this transition, with Chern number 1 state as an unstable fixed point. This is distinct from known results, and can be tested by experiments and further theoretical analysis.

Aqueous oxidation reaction enabled layer-by-layer corrosion of semiconductor nanoplates into single-crystalline 2D nanocrystals with single layer accuracy and ionic surface capping

A controllable aqueous oxidation reaction enabled layer-by-layer corrosion has been proposed to prepare high-quality two-dimensional (2D) semiconductor nanocrystals with single layer accuracy and well-retained hexagonal shapes.

Carrier-mediated ferromagnetism in the magnetic topological insulator Cr-doped (Sb,Bi)2Te3

Magnetically doped topological insulators, possessing an energy gap created at the Dirac point through time-reversal-symmetry breaking, are predicted to exhibit exotic phenomena including the quantized anomalous Hall effect and a dissipationless transport, which facilitate the development of low-power-consumption devices using electron spins. Although several candidates of magnetically doped topological insulators were demonstrated to show long-range magnetic order, the realization of the quantized anomalous Hall effect is so far restricted to the Cr-doped (Sb,Bi)₂Te₃ system at extremely low temperature; however, the microscopic origin of its ferromagnetism is poorly understood. Here we present an element-resolved study for Cr-doped (Sb,Bi)₂Te₃ using X-ray magnetic circular dichroism to unambiguously show that the long-range magnetic order is mediated by the p-hole carriers of the host lattice, and the interaction between the Sb(Te) p and Cr d states is crucial. Our results are important for material engineering in realizing the quantized anomalous Hall effect at higher temperatures.

Magnetically doped topological insulators may exhibit exotic transport phenomena such as the quantum anomalous Hall effect, however the underlying mechanisms of ferromagnetic order are currently debated. Here, the authors reveal stabilized ferromagnetism in Cr-doped (Sb,Bi)₂Te₃ mediated by Te and Sb p-hole carriers.

Charge-Induced Spin Torque in Anomalous Hall Ferromagnets

We demonstrate that spin-orbit coupled electrons in a magnetically doped system exert a spin torque on the local magnetization, without a flowing current, when the chemical potential is modulated in a magnetic field. The spin torque is proportional to the anomalous Hall conductivity, and its effective field strength may overcome the Zeeman field. Using this effect, the direction of the local magnetization is switched by gate control in a thin film. This charge-induced spin torque is essentially an equilibrium effect, in contrast to the conventional current-induced spin-orbit torque, and, thus, devices using this operating principle possibly have higher efficiency than the conventional ones. In addition to a comprehensive phenomenological derivation, we present a physical understanding based on a model of a Dirac-Weyl semimetal, possibly realized in a magnetically doped topological insulator. The effect might be realized also in nanoscale transition materials, complex oxide ferromagnets, and dilute magnetic semiconductors.

High-Mobility Sm-Doped Bi2 Se3 Ferromagnetic Topological Insulators and Robust Exchange Coupling

High-mobility (Smx Bi1-x )2 Se3 topological insulators (with x = 0.05) show a Curie temperature of about 52 K, and the carrier concentration and Fermi wave vector can be manipulated by intentional Te introduction with no significant influence on the Curie temperature. The origin of the ferromagnetism is attributed to the trivalent Sm dopant, as confirmed by X-ray magnetic circular dichroism and first-principles calculations. The carrier concentration is on the order of 10(19) cm(-3) and the mobility can reach about 7200 cm(2) V(-1) s(-1) with pronounced Shubnikov-de Haas oscillations.

Domain wall of a ferromagnet on a three-dimensional topological insulator

Topological insulators (TIs) show rich phenomena and functions which can never be realized in ordinary insulators. Most of them come from the peculiar surface or edge states. Especially, the quantized anomalous Hall effect (QAHE) without an external magnetic field is realized in the two-dimensional ferromagnet on a three-dimensional TI which supports the dissipationless edge current. Here we demonstrate theoretically that the domain wall of this ferromagnet, which carries edge current, is charged and can be controlled by the external electric field. The chirality and relative stability of the Neel wall and Bloch wall depend on the position of the Fermi energy as well as the form of the coupling between the magnetic moments and orbital of the host TI. These findings will pave a path to utilize the magnets on TI for the spintronics applications.