Intrinsic valley-polarized quantum anomalous Hall effect in a two-dimensional germanene/MnI_(2) van der Waals heterostructure

Valley-polarized quantum anomalous Hall effect(VQAHE), combined nontrivial band topology with valleytronics,is of importance for both fundamental sciences and emerging applications. However, the experimental realization of this property is challenging. Here, by using first-principles calculations and modal analysis, we predict a mechanism of producing VQAHE in two-dimensional ferromagnetic van der Waals germanene/MnI_(2) heterostructure. This heterostructure exhibits both valley anomalous Hall effect and VQAHE due to the joint effects of magnetic exchange effect and spin–orbital coupling with the aid of anomalous Hall conductance and chiral edge state. Moreover interestingly, through the electrical modulation of ferroelectric polarization state in In_(2)Se_(3), the germanene/Mn I_(2)/In_(2)Se_(3) heterostructure can undergo reversible switching from a semiconductor to a metallic behavior. This work offers a guiding advancement for searching for VQAHE in ferromagnetic van der Waals heterostructures and exploiting energy-efficient devices based on the VQAHE.

Spin direction dependent quantum anomalous Hall effect in two-dimensional ferromagnetic materials

We propose a scheme for realizing the spin direction-dependent quantum anomalous Hall effect(QAHE)driven by spin-orbit couplings(SOC)in two-dimensional(2D)materials.Based on the sp^(3)tight-binding(TB)model,we find that these systems can exhibit a QAHE with out-of-plane and in-plane magnetization for the weak and strong SOC,respectively,in which the mechanism of quantum transition is mainly driven by the band inversion of p_(x,y)/p_(z)orbitals.As a concrete example,based on first-principles calculations,we realize a real material of monolayer 1T-SnN_(2)/PbN_(2)exhibiting the QAHE with in-plane/out-of-plane magnetization characterized by the nonzero Chern number C and topological edge states.These findings provide useful guidance for the pursuit of a spin direction-dependent QAHE and hence stimulate immediate experimental interest.

Quantum anomalous Hall effect in twisted bilayer graphene quasicrystal

The nontrivial topology is investigated in a dodecagonal quasicrystal made of 30° twisted bilayer graphene (TBG). Based on tight-binding model with both exchange field and Rashba spin–orbit coupling, the topological index, chiral edge states, and quantum conductance are calculated to distinguish its unique topological phase. A high Bott index (B = 4) quantum anomalous Hall effect (QAHE) is identified in TBG quasicrystal, which is robust to a finite perturbation without closing the nontrivial gap. Most remarkably, we have found that the multiple Dirac cone replicas in TBG quasicrystal are only a spectra feature without generating extra chiral edge states. Our results not only propose a possible way to realize the QAHE in quasicrystal, but also identify the continuity of nontrivial topology in TBG between crystal and quasicrystal.

Current carrying states in the disordered quantum anomalous Hall effect

In a quantum Hall effect,flat Landau levels may be broadened by disorder.However,it has been found that in the thermodynamic limit,all extended(or current carrying)states shrink to one single energy value within each Landau level.On the other hand,a quantum anomalous Hall effect consists of dispersive bands with finite widths.We numerically investigate the picture of current carrying states in this case.With size scaling,the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit,in a power law way.The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects.The number of current carrying states obeys similar scaling rules,so that the density of states of current carrying states is finite.Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.

Manipulation of intrinsic quantum anomalous Hall effect in two-dimensional MoYN_(2)CSCl MXene

Quantum anomalous Hall effect(QAHE)is an innovative topological spintronic phenomenon with dissipationless chiral edge states and attracts rapidly increasing attention.However,it has only been observed in few materials in experiments.Here,according to the first-principles calculations,we report that the MXene MoYN_(2)CSCl shows a topologically nontrivial band gap of 37.3 me V,possessing QAHE with a Chern number of C=1,which is induced by band inversion between d_(xz)and d_(yz)orbitals.Also,the topological phase transition for the MoYN_(2)CSCl can be realized via strain or by turning the magnetization direction.Remarkably,MoYN_(2)CSCl shows the nodal-line semimetal state dependent on the electron correlation U.Our findings add an experimentally accessible and tunable member to the QAHE family,which stands a chance of enriching the applications in spintronics.

First-principles prediction of quantum anomalous Hall effect in two-dimensional Co2Te lattice

The quantum anomalous Hall effect(QAHE) has special quantum properties that are ideal for possible future spintronic devices. However, the experimental realization is rather challenging due to its low Curie temperature and small non-trivial bandgap in two-dimensional(2D) materials. In this paper, we demonstrate through first-principles calculations that monolayer Co2Te material is a promising 2D candidate to realize QAHE in practice. Excitingly, through Monte Carlo simulations, it is found that the Curie temperature of single-layer Co2Te can reach 573 K. The band crossing at the Fermi level in monolayer Co2Te is opened when spin–orbit coupling is considered, which leads to QAHE with a sizable bandgap of Eg= 96 me V, characterized by the non-zero Chern number(C = 1) and a chiral edge state. Therefore, our findings not only enrich the study of quantum anomalous Hall effect, but also broaden the horizons of the spintronics and topological nanoelectronics applications.

Prediction of quantum anomalous Hall effect in CrI_(3)/ScCl_(2)bilayer heterostructure

Based on first-principles calculations,a two-dimensional(2D)van der Waals(vd W)bilayer heterostructure consisting of two topologically trivial ferromagnetic(FM)monolayers CrI_(3)and ScCl_(2)is proposed to realize the quantum anomalous Hall effect(QAHE)with a sizable topologically nontrivial band gap of 4.5 me V.Its topological nature is attributed to an interlayer band inversion between the monolayers and critically depends on the symmetry of the stacking configuration.We further demonstrate that the topologically nontrivial band gap can be increased nearly linearly by the application of a perpendicular external pressure and reaches 8.1 me V at 2.7 GPa,and the application of an external out-of-plane electric field can also modulate the band gap and convert the system back to topologically trivial via eliminating the band inversion.An effective model is developed to describe the topological phase evolution in this bilayer heterostructure.This work provides a new candidate system based on 2D vd W materials for realization of potential high-temperature QAHE with considerable controllability.

AlO_x/LiF composite protection layer for Cr-doped(Bi,Sb)_2Te_3 quantum anomalous Hall films

We have realized robust quantum anomalous Hall samples by protecting Cr-doped（Bi,Sb）2Te3 topological insulator films with a combination of LiF and A1Ox capping layers.The AlOx/LiF composite capping layer well keeps the quantum anomalous Hall states of Cr-doped（Bi,Sb）2Te3 films and effectively prevent them from degradation induced by ambient conditions.The progress is a key step towards the realization of the quantum phenomena in heterostructures and devices based on quantum anomalous Hall system.

Low-damage photolithography for magnetically doped(Bi,Sb)_(2)Te_(3) quantum anomalous Hall thin films

We have developed a low-damage photolithography method for magnetically doped(Bi,Sb)_(2)Te_(3)quantum anomalous Hall(QAH) thin films incorporating an additional resist layer of poly(methyl methacrylate)(PMMA). By performing control experiments on the transport properties of five devices at varied gate voltages(V_(g)s), we revealed that the modified photolithography method enables fabricating QAH devices with the transport and magnetic properties unaffected by fabrication process. Our experiment represents a step towards the production of novel micro-structured electronic devices based on the dissipationless QAH chiral edge states.

Room temperature quantum anomalous Hall insulator in honeycomb lattice, RuCS_(3), with large magnetic anisotropy energy

The quantum anomalous Hall(QAH) effect has attracted enormous attention since it can induce topologically protected conducting edge states in an intrinsic insulating material. For practical quantum applications, the main obstacle is the non-existent room temperature QAH systems, especially with both large topological band gap and robust ferromagnetic order. Here, according to first-principles calculations, we predict the realization of the room temperature QAH effect in a two-dimensional(2D) honeycomb lattice, RuCS_(3) with a non-zero Chern number of C = 1. Especially, the nontrivial topology band gap reaches up to 336 me V for RuCS_(3). Moreover, we find that RuCS_(3) has a large magnetic anisotropy energy(2.065 me V) and high Curie temperature(696 K). We further find that the non-trivial topological properties are robust against the biaxial strain. The robust topological and magnetic properties make RuCS_(3) have great applications in room temperature spintronics and nanoelectronics.

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

Recently, the magnetic topological insulator(TI) MnBi2Te4 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 critical points during the magnetic switching, can give rise to a QAH insulator. 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 the gate voltage. Our theory will be instructive for the studies of the QAH effect in MnBi2Te4 in future experiments.

Quantum anomalous Hall effect in two-dimensional Cu-dicyanobenzene coloring-triangle lattice

Metrics details Abstract Magnetic two-dimensional(2D)topological insulators with spontaneous magnetization have been predicted to host quantum anomalous Hall effects(QAHEs).For organic topological insulators,the QAHE only exists in honeycomb or Kagome organometallic lattices based on theoretical calculations.Recently,coloring-triangle(CT)lattice has been found to be mathematically equivalent to a Kagome lattice,suggesting a potential 2D lattice to realize QAHE.Here,based on first-principles calculations,we predict an organometallic CT lattice,Cu-dicyanobenzene(DCB),to be a stable QAH insulator.It exhibits ferromagnetic(FM)properties as a result of the charge transfer from metal atoms to DCB molecules.Moreover,based on the Ising model,the Curie temperature of the FM ordering is calculated to be around 100 K.Both the Chern numbers and the chiral edge states of the semi-infinite Cu-DCB edge structure,which occur inside the spin-orbit coupling band gap,confirm its nontrivial topological properties.These make the Cu-DCB CT lattice an ideal candidate to enrich the family of QAH insulators.

Valley-polarized quantum anomalous Hall effect in van der Waals heterostructures based on monolayer jacutingaite family materials

We numerically study the general valley polarization and anomalous Hall effect in van der Waals(vdW)heterostructures based on monolayer jacutingaite family materials Pt2AX3(A=Hg,Cd,Zn;X=S,Se,Te).We perform a systematic study on the atomic,electronic,and topological properties of vdW heterostructures composed of monolayer Pt2AX3 and two-dimensional ferromagnetic insulators.We show that four kinds of vdW heterostructures exhibit valley-polarized quantum anomalous Hall phase,i.e.,Pt_(2)HgS_(3)/NiBr_(2),Pt_(2)HgSe_(3)/CoBr_(2),Pt_(2)HgSe_(3)/NiBr_(2),and Pt_(2)ZnS_(3)/CoBr_(2),with a maximum valley splitting of 134.2 meV in Pt_(2)HgSe_(3)/NiBr_(2) and sizable global band gap of 58.8 meV in Pt_(2)HgS_(3)/NiBr_(2).Our findings demonstrate an ideal platform to implement applications on topological valleytronics.

Design of sign-reversible Berry phase effect in 2D magneto-valley material

Manipulating sign-reversible Berry phase effects is both fundamentally intriguing and practically appealing for searching for exotic topological quantum states.However,the realization of multiple Berry phases in the magneto-valley lattice is rather challenging due to the complex interactions from spin-orbit coupling(SOC),band topology,and magnetic ordering.Here,taking single-layer spin-valley RuCl_(2)as an example,we find that sign-reversible Berry phase transitions from ferrovalley(FV)to half-valley semimetal(HVS)to quantum anomalous valley Hall effect(QAVHE)can be achieved via tuning electronic correlation effect or biaxial strains.Remarkably,QAVHE phase,which combines both the features of quantum anomalous Hall and anomalous Hall valley effect,is introduced by sign-reversible Berry curvature or band inversion of d_(xy)/d_(x^(2)-y^(2))and d_(z^(2))orbitals at only one of the K/K′valleys of single-layer RuCl_(2).And the boundary of QAVHE phase is the HVS state,which can achieve 100%intrinsically valley polarization.Further,a k·p model unveiled the valleycontrollable sign-reversible Berry phase effects.These discoveries establish RuCl_(2)as a promising candidate to explore exotic quantum states at the confluence of nontrivial topology,electronic correlation,and valley degree of freedom.

Unprotected quadratic band crossing points and quantum anomalous Hall effect in FeB_(2) monolayer

Quadratic band crossing points(QBCPs)and quantum anomalous Hall effect(QAHE)have attracted the attention of both theoretical and experimental researchers in recent years.Based on first-principle calculations,we find that the FeB_(2) monolayer is a nonmagnetic semimetal with QBCPs at K.Through symmetry analysis and k·p invariant theory,we find that the QBCP is not protected by rotation symmetry and consists of two Dirac points with the same chirality(Berry phase of 2π).Once introducing Coulomb interactions,we find that there is a spontaneous-time-reversal-breaking instability of the spinful QBCPs,which gives rise to a C=2 QAH insulator with orbital moment ordering.

Quantum anomalous Hall effect and giant Rashba spin-orbit splitting in graphene system co-doped with boron and 5d transition-metal atoms

Quantum anomalous Hall effect （QAHE） is a fundamental quantum transport phenomenon in con- densed matter physics. Until now, the QAHE has only been experimentally realized for Cr/V-doped （Bi, Sb）2We3 but at an extremely low observational temperature, thereby limiting its potential appli- cation in dissipationless quantum electronics. By employing first-principles calculations, we study the electronic structures of graphene co-doped with 5d transition metal and boron atoms based on a com- pensated n-p co-doping scheme. Our findings are as follows： i） The electrostatic attraction between the n- and p-type dopants effectively enhances the adsorption of metal adatoms and suppresses their undesirable clustering, ii） Hf-B and Os-B co-doped graphene systems can establish long-range ferro- magnetic order and open larger nontrivial band gaps because of the stronger spin-orbit coupling with the non-vanishing Berry curvatures to host the high-temperature QAHE. iii） The calculated Rashba splitting energies in Re-B and Pt-B co-doped graphene systems can reach up to 158 and 85 meV, re- spectively, which are several orders of magnitude higher than the reported intrinsic spin-orbit coupling strength.

Realization of quantum anomalous hall effect at tens of kelvin by n-p codoping of topological insulators

With the support by the National Natural Science Foundation of China,the research teams led by Prof.Xu Xiaohong（许小红）at the School of Chemistry and Materials Science,Shanxi Normal University and Prof.Zhang Zhenyu at ICQD,University of Science and Technology of China used vanadium-iodine（Ⅴ-Ⅰ）codoped Sb2Te3 to realize high-temperature quantum anomalous Hall effect（QAHE）,which was

Electronic property and topological phase transition in a graphene/CoBr_(2) heterostructure

Recently,significant experimental advancements in achieving topological phases have been reported in van der Waals(vdW)heterostructures involving graphene.Here,using first-principles calculations,we investigate graphene/CoBr_(2)(Gr/CoBr_(2))heterostructures and find that an enhancement of in-plane magnetic anisotropy(IMA)energy in monolayer CoBr_(2) can be accomplished by reducing the interlayer distance of the vdW heterostructures.In addition,we clarify that the enhancement of IMA energy primarily results from two factors:one is the weakness of the Co-d_(xy) and Co-d_(x^(2)-y^(2)) orbital hybridization and the other is the augmentation of the Co-d_(yz) and Co-d_(z)2 orbital hybridization.Meanwhile,calculation results suggest that the Kosterlitz–Thouless phase transition temperature(TKT)of a 2D XY magnet Gr/CoBr_(2)(23.8 K)is higher than that of a 2D XY monolayer CoBr_(2)(1.35 K).By decreasing the interlayer distances,the proximity effect is more pronounced and band splitting appears.Moreover,by taking into account spin–orbit coupling,a band gap of approximately 14.3 meV and the quantum anomalous Hall effect(QAHE)are attained by decreasing the interlayer distance by 1.0 A.Inspired by the above conclusions,we design a topological field transistor device model.Our results support that the vdW interlayer distance can be used to modulate the IMA energy and QAHE of materials,providing a pathway for the development of new low-power spintronic devices.

Chiral edge state coupling theory of transport in quantum anomalous Hall insulators

The quantum anomalous Hall effect is characterized by a quantized Hall resistance with a vanishing longitudinal resistance.Many experiments reported the quantization of the Hall resistance,which is always accompanied by a non-vanishing longitudinal resistance that is several k?.Meanwhile,the non-vanishing longitudinal resistance exhibits a universal exponential decay with the increase in magnetic field.We propose that the coupling of chiral edge states,which has not been properly evaluated in the previous theories,can give rise to the non-vanishing longitudinal resistance.The coupling between the chiral edges states along the opposite boundaries can be assisted by magnetic domains or defects inside the sample bulk,which has been already identified in recent experiments.Our theory provides a potential mechanism to understand the experimental result in both magnetic topological insulator and moirésuperlattice systems.