Realize Quantum Anomalous Hall Research Articles

Interaction-driven Chern insulating phases in the [formula omitted] lattice with Rashba spin-orbit coupling

The magnetic interaction is a necessary ingredient to break the time-reversal symmetry in realizing quantum anomalous Hall, or Chern insulating phases. Here, we study topological phases in the model, a minimal theoretical model supporting the flat band, taking account of Rashba spin-orbit coupling and flat-band-induced spontaneous ferromagnetism. By analyzing the interaction-driven phase diagrams, band structures, topological edge states, and topological invariants, we demonstrate that this system offers a platform for realizing a wide range of phases, including normal insulators, semimetals, and Chern insulators. Uniquely, there exist both high-Chern-number insulators and valley-polarized Chern insulators. In the latter phase, edge channels exist in the single valley, leading to nearly valley polarization. These findings demonstrate the potential of interaction-driven systems in realizing exotic phases and their promising role in future applications in topology electronics and valleytronics.

A generic designing rule for realizing quantum anomalous Hall phase in a transition-metal trichalcogenide family

Different from introducing ferromagnetism in three-dimensional (3D) topological insulators, empowering nontrivial band topology with 2D ferromagnetic (2DFM) materials is another way to realize quantum anomalous Hall effect (QAHE). The recently discovered 2DFM insulators provide unprecedented opportunities for realizing such an intriguing quantum phenomenon. Here, by using first-principles approaches, we design a generic rule for realizing QAHE in the transition-metal trichalcogenide family materials of Cr2A2X6 (where A = Si, Ge, Sn; X = S, Se, Te), whose design principle is based on that a 2D topologically trivial magnetic insulator can be converted into a QAH system via proper surface modification. Taking silicene-passivated Cr2Sn2Se6 as an illustration, we show that the Cuire temperature of Cr2Sn2Se6 monolayer can be enhanced up to ∼92 K after silicene passivation. Most strikingly, such a heterostructure harbors QAHE with a band gap of ∼30 meV. Further low-effective model analyses reveal that the topologically nontrivial states are attributed to the honeycomb lattice of Cr atoms. All those results demonstrate that our proposal is general, which opens a new avenue to explore high-temperature QAHE.

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}.

Angle dependent field-driven reorientation transitions in uniaxial antiferromagnet MnBi2Te4 single crystal

MnBi2Te4, a two-dimensional magnetic topological insulator with a uniaxial antiferromagnetic structure, is an ideal platform to realize quantum anomalous Hall effects. However, the strength of magnetic interactions is not clear yet. We performed systematic studies on the magnetization and angle dependent magnetotransport on MnBi2Te4 single crystals. The results show that the direction of the magnetic field has significant effects on the critical field values and the magnetic structure of this compound, which lead to different magnetotransport behaviors. The field-driven reorientation transitions can be utilized to estimate the antiferromagnetic interlayer exchange interaction coupling Jc and uniaxial magnetic anisotropy D. The obtained Hamiltonian can well explain the experimental data by Monte Carlo simulations. Our comprehensive studies on the field-driven magnetic transition phenomenon in MnBi2Te4 provide a general approach for other topological systems with antiferromagnetism.

Chiral Majorana edge modes and vortex Majorana zero modes in superconducting antiferromagnetic topological insulator

The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetry . In this paper we investigate the effects of the s-wave superconducting pairings on the multilayers of AFTI, which breaks symmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern number C = ±2. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase, denoted by the hinged TSC, can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.

Evolution of Berry curvature and reentrant quantum anomalous Hall effect in an intrinsic magnetic topological insulator

Recently, the magnetic topological insulator MnBi$_2$Te$_4$ emerged as a competitive platform to realize quantum anomalous Hall (QAH) states. We report a Berry-curvature splitting mechanism to realize the QAH effect in the disordered magnetic TI multilayers when switching from an antiferromagnetic order to a ferromagnetic order. We reveal that the splitting of spin-resolved Berry curvature, originating from the separation of the mobility edge during the magnetic switching, can give rise to a QAH insulator even \emph{without} closing the band gap. We present a global phase diagram, and also provide a phenomenological picture to elucidate the Berry curvature splitting mechanism by the evolution of topological charges. At last, we predict that the Berry curvature splitting mechanism will lead to a reentrant QAH effect, which can be detected by tuning gate voltage. Our theory will be instructive for the studies of the QAH effect in MnBi$_2$Te$_4$ in future experiments.

Interlayer ferromagnetic coupling and enhanced magnetism by biaxial strain in MnBi2Te4/VBi2Te4 heterojunction

The pristine anti-ferromagnetic interlayer coupling of even layers MnBi2Te4 greatly restricts the possibility of realizing quantum anomalous Hall (QAH) effect. In this work, based on first-principles calculations, we find that the interlayer coupling can be transformed into ferromagnetic order from anti-ferromagnetic by substituting cations with V atoms. Furthermore, when applying biaxial strain, a strong band inversion occurs around Fermi level, achieving quantum anomalous Hall effect. A gapless surface states can further confirm it. Meanwhile, the magnetic moment of Mn and V atoms increases with the increase of strain. We attribute this to the electron hopping to magnetic atoms from p orbitals of nonmagnetic Bi and Te atoms. Our work extends the range for designing and applying for spintronic devices with QAH effect.

Electric field induced topological phase transition and large enhancements of spin-orbit coupling and Curie temperature in two-dimensional ferromagnetic semiconductors

Tuning topological and magnetic properties of materials by applying an electric field is widely used in spintronics. In this work, we find a topological phase transition from topologically trivial to nontrivial states at an external electric field of about 0.1 V/A in MnBi$_2$Te$_4$ monolayer that is a topologically trivial ferromagnetic semiconductor. It is shown that when electric field increases from 0 to 0.15 V/A, the magnetic anisotropy energy (MAE) increases from about 0.1 to 6.3 meV, and the Curie temperature Tc increases from 13 to about 61 K. The increased MAE mainly comes from the enhanced spin-orbit coupling due to the applied electric field. The enhanced Tc can be understood from the enhanced $p$-$d$ hybridization and decreased energy difference between $p$ orbitals of Te atoms and $d$ orbitals of Mn atoms. Moreover, we propose two novel Janus materials MnBi$_2$Se$_2$Te$_2$ and MnBi$_2$S$_2$Te$_2$ monolayers with different internal electric polarizations, which can realize quantum anomalous Hall effect (QAHE) with Chern numbers $C$=1 and $C$=2, respectively. Our study not only exposes the electric field induced exotic properties of MnBi2Te4 monolayer, but also proposes novel materials to realize QAHE in ferromagnetic Janus semiconductors with electric polarization.

Large-proximity-induced anomalous Hall effect in Bi2−xSbxTe3−ySey/Cr2Ge2Te6 heterostructure prepared by film transfer method

The magnetic proximity effect is one of the powerful approaches to realize quantum anomalous Hall effect in topological insulators (TIs) targeting at high temperatures. Various TI/ferromagnetic-insulator (FMI) heterostructures have extensively been investigated by using a van der Waals epitaxial growth technique of TI films grown on FMI substrates. However, FMI materials which can be used as a substrate are strictly limited due to the lattice mismatching between TI and FMI, not succeeding to boost the quantization temperature to be higher. Here, we show that a large anomalous Hall effect, comparable to the best value so far reported for the heterostructure interfaces fabricated by epitaxial growth techniques, is realized for ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ (BSTS)/${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ (CGT) heterostructure by transferring an epitaxially grown BSTS thin film floating on a ultrapure water directly on a CGT substrate (wet transfer method). The fundamental discussions about the nature of magnetic proximity effect were given in the aspect of the quality of the CGT substrate and the atomic orientation of the TI/CGT interface. The large magnetic proximity effect shown in our present studies can be applicable for a variety of FMI substrates and therefore can pave a route for promoting magnetic TIs both in basic science and applications.

Topological Kagome Magnet Co3Sn2S2 Thin Flakes with High Electron Mobility and Large Anomalous Hall Effect.

Magnetic Weyl semimetals attract considerable interest not only for their topological quantum phenomena but also as an emerging materials class for realizing quantum anomalous Hall effect in the two-dimensional limit. A shandite compound Co3Sn2S2 with layered kagome-lattices is one such material, where vigorous efforts have been devoted to synthesize the two-dimensional crystal. Here, we report a synthesis of Co3Sn2S2 thin flakes with a thickness of 250 nm by chemical vapor transport method. We find that this facile bottom-up approach allows the formation of large-sized Co3Sn2S2 thin flakes of high-quality, where we identify the largest electron mobility (∼2600 cm2 V-1 s-1) among magnetic topological semimetals, as well as the large anomalous Hall conductivity (∼1400 Ω-1 cm-1) and anomalous Hall angle (∼32%) arising from the Berry curvature. Our study provides a viable platform for studying high-quality thin flakes of magnetic Weyl semimetal and stimulate further research on unexplored topological phenomena in the two-dimensional limit.

Ab initio identification of two-dimensional square-octagonal bismuthene doped with 3d transition metals as potential spin gapless semiconductor, bipolar magnetic semiconductor, and quantum anomalous Hall insulator

The electronic structures and magnetic properties of square-octagonal bismuthene embedded with 3 d transition elements were studied systematically by the first-principles calculations. The formation energies of all the cases are negative, indicating the feasibility and practicability for these doped monolayer bismuthene. No considerable spin splitting appears in Sc-, Co-, and Zn-doped compounds. After doping, Sc- and Co-doped compounds are semiconductors while Zn-doped compound is metal. Ti-, V-, Cr-, Mn-, Fe-, Ni-, and Cu-doped systems behave as magnetic semiconductors. Among them, Cu-doped system exhibits both desirable spin gapless and bipolar magnetic semiconducting characteristics. In addition, Fe-doped system is a wonderful candidate for realizing quantum anomalous Hall insulating state. • Sc- and Co-doped square-octagonal bismuthene are nonmagnetic semiconductors. • Zn-doped square-octagonal bismuthene is nonmagnetic metal. • Fe-doped square-octagonal bismuthene is a ferromagnetic Chern insulator for realizing quantum anomalous Hall insulating state. • Cu-doped square-octagonal bismuthene is either spin gapless or bipolar magnetic semiconductor.

Intrinsic quantum anomalous Hall phase induced by proximity in the van der Waals heterostructure germanene/ Cr2Ge2Te6

A van der Waals heterostructure combined with intrinsic magnetism and topological orders have recently paved attractive avenues to realize quantum anomalous Hall effects. In this work, using first-principles calculations and effective model analysis, we propose that the robust quantum anomalous Hall states with sizable band gaps emerge in the van der Waals heterostructure of germanene/Cr$_2$Ge$_2$Te$_6$. This heterostructure possesses high thermodynamic stability, thus facilitating its experimental fabrication. Furthermore, we uncover that the proximity effect enhances the coupling between the germanene and Cr$_2$Ge$_2$Te$_6$ layers, inducing the nontrivial band gaps in a wide range from 29 meV to 72 meV. The chiral edge states inside the band gap, leading to Hall conductance quantized to $-e^2/h$, are clearly visible. This findings provide an ideal candidate to detect the quantum anomalous Hall states and realize further applications to nontrivial quantum transport at a high temperature.

Quantum anomalous Hall effect by coupling heavy atomic layers with CrI3

We explored the possibility of realizing quantum anomalous Hall effect by placing heavy-element atomic layer on top of monolayer CrI$_{3}$ with a natural cleavage surface and broken time-reversal symmetry. We showed that CrI$_{3}$/X (X = Bi, Sb, or As) systems can open up a sizable bulk gap to harbour quantum anomalous Hall effect, e.g., CrI$_{3}$/Bi is a natural magnetic insulator with a bulk gap of 30~meV, which can be further enlarged via strain engineering or adjusting spin orientations. We also found that the ferromagnetic properties (magnetic anisotropic energy and Curie temperature) of pristine CrI$_{3}$ can be further improved due to the presence of heavy atomic layers, and the spin orientation can be utilized as a useful knob to tune the band structure and Fermi level of CrI$_{3}$/Bi system. The topological nature, together with the enhanced ferromagnetism, can unlock new potential applications for CrI$_{3}$-based materials in spintronics and electronics.

Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator MnBi2Te4

$\mathrm{MnBi_2Te_4}$ has recently been established as an intrinsic antiferromagnetic (AFM) topological insulator and predicted to be an ideal platform to realize quantum anomalous Hall (QAH) insulator and axion insulator states. We performed comprehensive studies on the structure, nontrivial surface state and magnetotransport properties of this material. Our results reveal an intrinsic anomalous Hall effect arising from a non-collinear spin structure for the magnetic field parallel to the $c$-axis. We also observed remarkable negative magnetoresistance under arbitrary field orientation below and above the Neel temperature (T$_N$), providing clear evidence for strong spin fluctuation-driven spin scattering in both the AFM and paramagnetic states. Further, we found that the nontrivial surface state opens a large gap (~85 meV) even at temperatures far above T$_N$ = 25K. These findings demonstrate that the bulk band structure of $\mathrm{MnBi_2Te_4}$ is strongly coupled to the magnetic structure and that a net Berry curvature in momentum space can be created in a canted AFM state. In addition, our results imply that the gap opening in the surface states is intrinsic, likely caused by the strong spin fluctuations near the surface layers.

Stanene on a SiC(0001) surface: a candidate for realizing quantum anomalous Hall effect.

Stanene, a cousin of graphene, has pz-orbital Dirac states, owing to its hexagonal symmetry. Nevertheless, stanene has to be obtained through growing on substrates with strong interfacial interactions, which generally damages their intrinsic π(pz)-orbital Dirac states. Fortunately, we find that the quadratic topological states are derived from the px,y orbitals rather than pz orbitals in stanene on 4H-SiC(0001), which survive even the strong interfacial interactions. We also find that the spin-orbital coupling simultaneously with the exchange field gives rise to an observable band gap of 22.97 meV. Berry curvature and edge state calculations further demonstrate the nontrivial topological phase of such quadratic topological states with a Chern number C = 2, showing its potential to realize quantum anomalous Hall effect at near room temperature. Finally, we construct a simple effective model to reveal the low-energy physics in this system. It is hoped this finding will be applicable to other two-dimensional materials, which should be useful for future investigations.

Realizing both giant magnetic anisotropy and quantum anomalous Hall effect in graphene with adsorbed Te-Co dimer

To realize quantum anomalous Hall state at higher temperature, it needs to search for the magnetic topological insulators with giant magnetic anisotropy. We have studied the structural, magnetic and topological properties of graphene with adsorbed Te-A (A Co, Rh, Ir) dimers by first-principles calculations and Wannier technique. Our results reveal that the system of Te-Co@G is an excellent magnetic topological insulator with both perpendicular magnetic anisotropy of 61.7 meV and large topological band-gap of 35.8 meV. Both the magnetic anisotropy and the band-gap can be effectively tuned by the applied electric field. The dimers are stably adsorbed onto the graphene and the systems are robust against thermal fluctuation. Topological analysis reveals that the adsorption system is the Chern insulator with .

Penta-AlN2 monolayer: A ferromagnetic insulator

Abstract A ferromagnetic insulating behavior is necessary to realize quantum anomalous Hall effect. Here we study, using first-principles calculations and a Monte Carlo simulation, the electronic structure and magnetism of AlN2 monolayer. Our results show that the AlN2 monolayer has a ferromagnetic insulating behavior. By using the crystal field analysis, we find that the axes of the neighboring N2 dimers are perpendicular, and the superexchange between them accounts for the ferromagnetic (FM) order in the AlN2 monolayer. We also carried out a Monte Carlo simulation, which shows that the AlN2 monolayer remains FM with Curie temperature (Tc) ∼ 22 K. Moreover, the tensile strain would make a stronger overlap between the neighboring N2 dimers, and steadily enhances the FM stability. As a result, the Tc can be increased with the tensile strain.

Topological Dirac States beyond π-Orbitals for Silicene on SiC(0001) Surface.

The discovery of intriguing properties related to the Dirac states in graphene has spurred huge interest in exploring its two-dimensional group-IV counterparts, such as silicene, germanene, and stanene. However, these materials have to be obtained via synthesizing on substrates with strong interfacial interactions, which usually destroy their intrinsic π(pz)-orbital Dirac states. Here we report a theoretical study on the existence of Dirac states arising from the px,y orbitals instead of pz orbitals in silicene on 4H-SiC(0001), which survive in spite of the strong interfacial interactions. We also show that the exchange field together with the spin-orbital coupling give rise to a detectable band gap of 1.3 meV. Berry curvature calculations demonstrate the nontrivial topological nature of such Dirac states with a Chern number C = 2, presenting the potential of realizing quantum anomalous Hall effect for silicene on SiC(0001). Finally, we construct a minimal effective model to capture the low-energy physics of this system. This finding is expected to be also applicable to germanene and stanene and imply great application potentials in nanoelectronics.

Realization of quantum anomalous Hall effect in graphene from n−p codoping-induced stable atomic adsorption

Using first-principles calculation methods, we study the possibility of realizing quantum anomalous Hall effect in graphene from stable 3\textit{d}-atomic adsorption via charge-compensated \textit{n}-\textit{p} codoping scheme. As concrete examples, we show that long-range ferromagnetism can be established by codoping 3\textit{d} transition metal and boron atoms, but only the Ni codopants can open up a global bulk gap to harbour the quantum anomalous Hall effect. Our estimated ferromagnetic Curie transition temperature can reach over 10 Kelvin for various codoping concentrations.

Quantum anomalous Hall effect in magnetically modulated topological insulator/normal insulator heterostructures

We theoretically study how magnetic modulation can be used to manipulate the transport properties of heterostructures formed by a thin film of a three-dimensional topological insulator sandwiched between slabs of a normal insulator. Employing the k ∙ p scheme, in the framework of a continual approach, we argue that electron states of the system are spin-polarized when ultrathin magnetic insertions are incorporated into the film. We demonstrate that (i) the spin-polarization magnitude depends strongly on the magnetic insertion position in the film and (ii) there is the optimal insertion position to realize quantum anomalous Hall effect, which is a function of the material parameters, the film thickness and the topological insulator/normal insulator interface potential. For the heterostructure with a pair of symmetrically placed magnetic insertions, we calculate a phase diagram that shows a series of transitions between distinct quantum regimes of transverse conductivity. We provide consistent interpretation of recent experimental findings in the context of our results.