Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators

Light-Induced Topological Phase Transition with Tunable Layer Hall Effect in Axion Antiferromagnets

The intricate interplay between light and matter provides effective tools for manipulating topological phenomena. Here, we theoretically propose and computationally show that circularly polarized light holds the potential to transform the axion insulating phase into a quantum anomalous Hall state in MnBi2Te4 thin films, featuring tunable Chern numbers (ranging up to ±2). In particular, we reveal the spatial rearrangement of the hidden layer-resolved anomalous Hall effect under light-driven Floquet engineering. Notably, upon Bi2Te3 layer intercalation, the anomalous Hall conductance predominantly localizes in the nonmagnetic Bi2Te3 layers that hold zero Berry curvature in the intact state, suggesting a significant magnetic proximity effect. Additionally, we estimate variations in the magneto-optical Kerr effect, giving a contactless method for detecting topological transitions. Our work not only presents a strategy to investigate emergent topological phases but also sheds light on the possible applications of the layer Hall effect in topological antiferromagnetic spintronics.

High spin axion insulator

Axion insulators possess a quantized axion field θ = π protected by combined lattice and time-reversal symmetry, holding great potential for device applications in layertronics and quantum computing. Here, we propose a high-spin axion insulator (HSAI) defined in large spin-s representation, which maintains the same inherent symmetry but possesses a notable axion field θ = (s + 1/2)2π. Such distinct axion field is confirmed independently by the direct calculation of the axion term using hybrid Wannier functions, layer-resolved Chern numbers, as well as the topological magneto-electric effect. We show that the guaranteed gapless quasi-particle excitation is absent at the boundary of the HSAI despite its integer surface Chern number, hinting an unusual quantum anomaly violating the conventional bulk-boundary correspondence. Furthermore, we ascertain that the axion field θ can be precisely tuned through an external magnetic field, enabling the manipulation of bonded transport properties. The HSAI proposed here can be experimentally verified in ultra-cold atoms by the quantized non-reciprocal conductance or topological magnetoelectric response. Our work enriches the understanding of axion insulators in condensed matter physics, paving the way for future device applications.

Lossless Spin-Orbit Torque in Antiferromagnetic Topological Insulator MnBi_{2}Te_{4}

We formulate and quantify the spin-orbit torque (SOT) in intrinsic antiferromagnetic topological insulator MnBi_{2}Te_{4} of a few septuple-layer thick in charge-neutral condition, which exhibits pronounced layer-resolved characteristics and even-odd contrast. Contrary to traditional current-induced torques, our SOT is not accompanied by Ohm's currents, thus being devoid of Joule heating. We study the SOT-induced magnetic resonances, where in the tri-septuple-layer case we identify a peculiar exchange mode that is blind to microwaves but can be exclusively driven by the predicted SOT. As an inverse effect, the dynamical magnetic moments generate a pure adiabatic current, which occurs concomitantly with the SOT and gives rise to an overall reactance for the MnBi_{2}Te_{4}, enabling a lossless conversion of electric power into magnetic dynamics.

Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi_{2}Te_{4}

We propose an intrinsic mechanism to understand the even-odd effect, namely, opposite signs of anomalous Hall resistance and different shapes of hysteresis loops for even and odd septuple layers (SLs), of MBE-grown MnBi_{2}Te_{4} thin films with electron doping. The nonzero hysteresis loops in the anomalous Hall effect and magnetic circular dichroism for even-SLs MnBi_{2}Te_{4} films originate from two different antiferromagnetic (AFM) configurations with different zeroth Landau level energies of surface states. The complex form of the anomalous Hall hysteresis loop can be understood from two magnetic transitions, a transition between two AFM states followed by a second transition to the ferromagnetic state. Our model also clarifies the relationship and distinction between axion parameter and magnetoelectric coefficient, and shows an even-odd oscillation behavior of magnetoelectric coefficients in MnBi_{2}Te_{4} films.

Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators

The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.

Progress on the antiferromagnetic topological insulator MnBi2Te4

Topological materials, which feature robust surface and/or edge states, have now been a research focus in condensed matter physics. They represent a new class of materials exhibiting nontrivial topological phases, and provide a platform for exploring exotic transport phenomena, such as the quantum anomalous Hall effect and the quantum spin Hall effect. Recently, magnetic topological materials have attracted considerable interests due to the possibility to study the interplay between topological and magnetic orders. In particular, the quantum anomalous Hall and axion insulator phases can be realized in topological insulators with magnetic order. MnBi2Te4, as the first intrinsic antiferromagnetic topological insulator discovered, allows the examination of existing theoretical predictions; it has been extensively studied, and many new discoveries have been made. Here we review the progress made on MnBi2Te4 from both experimental and theoretical aspects. The bulk crystal and magnetic structures are surveyed first, followed by a review of theoretical calculations and experimental probes on the band structure and surface states, and a discussion of various exotic phases that can be realized in MnBi2Te4. The properties of MnBi2Te4 thin films and the corresponding transport studies are then reviewed, with an emphasis on the edge state transport. Possible future research directions in this field are also discussed.

Topological magnetoelectric response in ferromagnetic axion insulators

The topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to the demanding magnetic configuration required to gap all surface states. Here, we theoretically propose that axion insulators with a simple ferromagnetic configuration, such as the MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize the TME. In the designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical electric field, the surface Hall currents give rise to a nearly half-quantized orbital moment, accompanied by a gapless chiral hinge mode circulating in parallel. Thus, the orbital magnetization from the two topological origins can be easily distinguished by reversing the electric field. Our work paves the way for direct observation of the TME in realistic axion-insulator materials.

Axion insulator state in hundred-nanometer-thick magnetic topological insulator sandwich heterostructures

An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number layer. All these samples have a thickness of ~ 10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~ 106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~ 3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase.

Chern-Insulator Phase in Antiferromagnets

The long-sought Chern insulators that manifest a quantum anomalous Hall effect are typically considered to occur in ferromagnets. Here, we theoretically predict the realizabilities of Chern insulators in antiferromagnets, in which the magnetic sublattices are connected by symmetry operators enforcing zero net magnetic moment. Our symmetry analysis provides comprehensive magnetic layer point groups that allow antiferromagnetic (AFM) Chern insulators, revealing that an in-plane magnetic configuration is required. Followed by first-principles calculations, such design principles naturally lead to two categories of material candidates, exemplified by monolayer RbCr4S8 and bilayer Mn3Sn with collinear and noncollinear AFM orders, respectively. We further show that the Chern number could be tuned by slight ferromagnetic canting as an effective pivot. Our work elucidates the nature of the Chern-insulator phase in AFM systems, paving a new avenue for designing quantum anomalous Hall insulators with the integration of nondissipative transport and the promising advantages of the AFM order.

Half-quantized helical hinge currents in axion insulators

Fractional quantization can emerge in noncorrelated systems due to the parity anomaly, while its condensed matter realization is a challenging problem. We propose that in axion insulators (AIs), parity anomaly manifests a unique fractional boundary excitation: the half-quantized helical hinge currents. These helical hinge currents microscopically originate from the lateral Goos-Hänchen (GH) shift of massless side-surface Dirac electrons that are totally reflected from the hinges. Meanwhile, due to the presence of the massive top and bottom surfaces of the AI, the helical current induced by the GH shift is half-quantized. The semiclassical wave packet analysis uncovers that the hinge current has a topological origin and its half quantization is robust to parameter variations. Lastly, we propose an experimentally feasible six-terminal device to identify the half-quantized hinge channels by measuring the nonreciprocal conductances. Our results advance the realization of the half-quantization and topological magnetoelectric responses in AIs.

Giant nonlocal edge conduction in the axion insulator state of MnBi2Te4

The recently discovered antiferromagnetic (AFM) topological insulator (TI) MnBi₂Te₄ represents a versatile material platform for exploring exotic topological quantum phenomena in nanoscale devices. It has been proposed that even-septuple-layer (even-SL) MnBi₂Te₄ can host helical hinge currents with unique nonlocal behavior, but experimental confirmation is still lacking. In this work, we report transport studies of exfoliated MnBi₂Te₄ flakes with varied thicknesses down to the few-nanometer regime. We observe giant nonlocal transport signals in even-SL devices when the system is in the axion insulator state but vanishingly small nonlocal signal in the odd-SL devices at the same magnetic field range. In conjunction with theoretical calculations, we demonstrate that the nonlocal transport is via the helical edge currents mainly distributed at the hinges between the side and top/bottom surfaces. The helical edge currents in the axion insulator state may find unique applications in topological quantum devices.

Van der Waals Engineering of Ultrafast Carrier Dynamics in Magnetic Heterostructures

Heterostructures composed of the intrinsic magnetic topological insulator MnBi₂Te₄ and its nonmagnetic counterpart Bi₂Te₃ host distinct surface electronic band structures depending on the stacking order and exposed termination. Here, we probe the ultrafast dynamical response of MnBi₂Te₄ and MnBi₄Te₇ following near-infrared optical excitation using time- and angle-resolved photoemission spectroscopy and disentangle surface from bulk dynamics based on density functional theory slab calculations of the surface-projected electronic structure. We gain access to the out-of-equilibrium charge carrier populations of both MnBi₂Te₄ and Bi₂Te₃ surface terminations of MnBi₄Te₇, revealing an instantaneous occupation of states associated with the Bi₂Te₃ surface layer followed by carrier extraction into the adjacent MnBi₂Te₄ layers with a laser fluence-tunable delay of up to 350 fs. The ensuing thermal relaxation processes are driven by phonon scattering with significantly slower relaxation times in the magnetic MnBi₂Te₄ septuple layers. The observed competition between interlayer charge transfer and intralayer phonon scattering demonstrates a method to control ultrafast charge transfer processes in MnBi₂Te₄-based van der Waals compounds.

Direct visualization of edge state in even-layer MnBi2Te4 at zero magnetic field

Being the first intrinsic antiferromagnetic (AFM) topological insulator (TI), MnBi2Te4 is argued to be a topological axion state in its even-layer form due to the antiparallel magnetization between the top and bottom layers. Here we combine both transport and scanning microwave impedance microscopy (sMIM) to investigate such axion state in atomically thin MnBi2Te4 with even-layer thickness at zero magnetic field. While transport measurements show a zero Hall plateau signaturing the axion state, sMIM uncovers an unexpected edge state raising questions regarding the nature of the "axion state". Based on our model calculation, we propose that the edge state of even-layer MnBi2Te4 at zero field is derived from gapped helical edge states of the quantum spin Hall effect with time-reversal-symmetry breaking, when a crossover from a three-dimensional TI MnBi2Te4 to a two-dimensional TI occurs. Our finding thus signifies the richness of topological phases in MnB2Te4 that has yet to be fully explored.

Helical Luttinger Liquid on the Edge of a Two-Dimensional Topological Antiferromagnet

A boundary helical Luttinger liquid (HLL) with broken bulk time-reversal symmetry belongs to a unique topological class that may occur in antiferromagnets (AFM). Here, we search for signatures of HLL on the edge of a recently discovered topological AFM, MnBi₂Te₄ even-layer. Using a scanning superconducting quantum interference device, we directly image helical edge current in the AFM ground state appearing at its charge neutral point. Such a helical edge state accompanies an insulating bulk which is topologically distinct from the ferromagnetic Chern insulator phase, as revealed in a magnetic field driven quantum phase transition. The edge conductance of the AFM order follows a power law as a function of temperature and source-drain bias which serves as strong evidence for HLL. Such HLL scaling is robust at finite fields below the quantum critical point. The observed HLL in a layered AFM semiconductor represents a highly tunable topological matter compatible with future spintronics and quantum computation.

Observation of Magnetism-Induced Topological Edge State in Antiferromagnetic Topological Insulator MnBi4Te7

Breaking time reversal symmetry in a topological insulator may lead to quantum anomalous Hall effect and axion insulator phase. MnBi₄Te₇ is a recently discovered antiferromagnetic topological insulator with T_N ∼ 12.5 K, which is composed of an alternatively stacked magnetic layer (MnBi₂Te₄) and nonmagnetic layer (Bi₂Te₃). By means of scanning tunneling spectroscopy, we clearly observe the electronic state present at a step edge of a magnetic MnBi₂Te₄ layer but absent at nonmagnetic Bi₂Te₃ layers at 4.5 K. Furthermore, we find that as the temperature rises above T_N the edge state vanishes, while the point defect induced state persists upon an increase in temperature. These results confirm the observation of magnetism-induced edge states. Our analysis based on an axion insulator theory reveals that the nontrivial topological nature of the observed edge state.

Topological spintronics and magnetoelectronics

Topological electronic materials, such as topological insulators, are distinct from trivial materials in the topology of their electronic band structures that lead to robust, unconventional topological states, which could bring revolutionary developments in electronics. This Perspective summarizes developments of topological insulators in various electronic applications including spintronics and magnetoelectronics. We group and analyse several important phenomena in spintronics using topological insulators, including spin-orbit torque, the magnetic proximity effect, interplay between antiferromagnetism and topology, and the formation of topological spin textures. We also outline recent developments in magnetoelectronics such as the axion insulator and the topological magnetoelectric effect observed using different topological insulators.