Axion insulator is an exotic magnetic topological insulator with zero Chern number but a nonzero quantized Chern-Simons magnetoelectric coupling. A conclusive experimental evidence for axion insulators is still lacking due to the small signal of topological magnetoelectric effect (TME). Here we show that the dynamical magnetoelectric coupling can be induced by the \emph{out-of-plane} surface magnetization dynamics in axion insulator thin films, which further generates a polarization current in the presence of an external magnetic field in the same direction. Such a current is finite in the bulk and increases as the film thickness $d$ decreases, in opposite to TME current which decreases as $d$ decreases. Remarkably, the current in thin films at magnetic resonance is at least ten times larger than that of TME, and thus may serve as a smoking gun signature for axion insulators.
Three-dimensional topological insulators or axion insulators exhibit the topological magnetoelectric effect, which is isotropic with a universal coefficient of proportionality quantized in units of $e^2/2h$. Here we study the finite-size effect of topological magnetoelectric effect, and find the magnetoelectric coefficients are anisotropic, namely $α_{xx}\neqα_{zz}$. Both of them are shown to converge to a quantized value when the thickness of topological insulator film $d$ increases reaching the three-dimensional bulk limit. The nonzero value of $(α_{xx}-α_{zz})\propto1/d$ could be measured b…
Chromia is a magnetoelectric insulator whose bulk magnetoelectric susceptibility contains a non-zero pseudoscalar component, like that present in magnetized topological insulators. We reveal the dynamic axion field of chromia by measuring the temperature dependence of its non-linear magnetoelectric response using a lock-in technique with an AC electric field stimulus. The electric field dependence, magnetic field dependence, and temperature behavior of the second harmonic lock-in signal are all in agreement with theoretical expectations. Our results demonstrate that chromia magnetoelectric res…
Topological insulator (TI) thin films with surface magnetism are expected to exhibit a quantized anomalous Hall effect (QAHE) when the magnetizations on the top and bottom surfaces are parallel, and a quantized topological magnetoelectric (QTME) response when the magnetizations have opposing orientations (axion insulator phase) and the films are sufficiently thick. We present a unified picture of both effects that associates deviations from exact quantization of the QTME caused by finite thickness with non-locality in the side-wall current response function. Using realistic tight-binding model…
More than forty years ago, axion was postulated as an elementary particle with a low mass and weak interaction in particle physics to solve the strong $\mathcal{CP}$ (charge conjugation and parity) puzzle. Axions are also considered as a possible component of dark matter of the universe. However, the existence of axions in nature has not been confirmed. Interestingly, axions arise as pseudoscalar fields derived from the Chern-Simons theory in condensed matter physics. In antiferromagnetic insulators, the axion field can become dynamical induced by spin-wave excitations and exhibits rich exotic…
In this letter, we demonstrate switching of nanomagnets through RKKY interactions in topological insulator-based magnetoelectric devices. The switching speed is dependent on the size of the ferromagnets.
Topological insulators with a time reversal symmetry breaking perturbation near the surface present a magnetoelectric response that is quantized when the frequency of the probing fields is much smaller than the surface gap induced by the perturbation. In this work we describe the intrinsic finite frequency magnetoelectric response of topological insulators for frequencies of the order and larger than the surface gap, including the experimentally relevant case where the system is metallic. This response affects physical observable quantities and will give rise to new finite frequency phenomena …
Intrinsic magnetic topological insulator ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ is believed to be an axion insulator in its antiferromagnetic ground state. However, direct identification of axion insulators remains experimentally elusive because the observed vanishing Hall resistance, while indicating the onset of the axion field, is inadequate to distinguish the system from a trivial normal insulator. Using numerical Green's functions, we theoretically demonstrate the quantized magnetoelectric current in a tunnel junction of atomically thin ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ sandwiched be…
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $θ$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $θ$ is the same parameter that appears in the "axion electrodynamics" Lagrangian $Δ{\cal L}_{EM} = (θe^2 / 2 πh) {\bf E} \cdot {\bf B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($θ=π$). We compute $θ$ for a simple model that accesses the topological insulator and discu…
A system with a topological insulator slab sandwiched by two one-dimensional photonic crystals as a defect is investigated. A giant topological magnetoelectric effect is proposed which is characterized by two resonant peaks with half-unit transmissions and rich polarization behaviors in the photonic band gap. We also predict a giant optical Hall effect in our system, in which the transverse shift of the transmitted light could be thousand times larger than the wavelength. These effects are purely from the $Θ$-domain walls at the topological insulator interfaces and could be observed easily. Th…
We study the response of topological insulator films to strong magnetic and electric fields beyond the linear response theory. As a model, we use the three-dimensional lattice Wilson-Dirac Hamiltonian where we simultaneously introduce both magnetic field through the Peierls substitution and electric field as a potential energy depending on lattice coordinate. We compute the electron energy spectrum by numerically diagonalizing this Hamiltonian and obtain quantized magnetoelectric polarizability. In addition, we find that the magnetoelectric effect vanishes as the film width decreases due to th…
Topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in units of $e^2/2h$. Here we propose that the topological magnetoelectric effect can be realized in the zero-plateau quantum anomalous Hall state of magnetic topological insulators or ferromagnet-topological insulator heterostructure. The finite-size effect is also studied numerically, where the magnetoelectric coefficient is shown to converge to a quantized value…
The interface between a topological insulator and a ferromagnetic insulator exhibits an interesting interplay of topological Dirac electrons and magnetism. As has been shown recently, the breaking of time-reversal invariance by magnetic order generates a Chern-Simons term in the action, that in turn leads to a Berry phase and a magnetoelectric effect of topological origin. Here, we consider the system in the presence of long-range Coulomb interaction between the Dirac electrons, and find that the magnetoelectric effect of the fluctuating electric field becomes non-local. We derive a Landau-Lif…
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 the surface states. Here, we theoretically propose that the axion insulators with a simple ferromagnetic configuration, such as MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize TME. In a designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical …
We theoretically study the magnetoelectric coupling in a quantum anomalous Hall insulator state induced by interfacing a dynamic magnetization texture to a topological insulator. In particular, we propose that the quantum anomalous Hall insulator with a magnetic configuration of a domain wall, when contacted by electrical reservoirs, acts as a magnetoelectric piston. A moving domain wall pumps charge current between electrical leads in a closed circuit, while applying an electrical bias induces reciprocal domain-wall motion. This piston-like action is enabled by a finite reflection of charge c…
One of the hallmarks of time-reversal-symmetric topological insulators in three dimensions is the topological magnetoelectric effect (TME). So far, a time-reversal breaking variant of this effect has attracted much attention, in the sense that the induced electric charge changes sign when the direction of an externally applied magnetic field is reversed. Theoretically, this effect is described by the so-called axion term. Here, we discuss a time-reversal-symmetric TME, where the electric charge depends only on the magnitude of the magnetic field but is independent of its sign. We obtain this n…
The kinetic magnetoelectric effect is an orbital analogue of the Edelstein effect and offers an additional degree of freedom to control magnetisation via the charge current. Here we theoretically propose a gigantic kinetic magnetoelectric effect in topological insulators and interpret the results in terms of topological surface currents. We construct a theory of the kinetic magnetoelectric effect for a surface Hamiltonian of a topological insulator, and show that it well describes the results by direct numerical calculation. This kinetic magnetoelectric effect depends on the details of the sur…
A quantized version of the magnetoelectric effect, known as the topological magnetoelectric effect, can exist in a time-reversal invariant topological insulator with all its surface states gapped out by magnetism. This topological phase, called the axion insulator phase, has been theoretically proposed but is still lack of conclusive experimental evidence due to the small signal of topological magnetoelectric effect. In this work, we propose that the dynamical in-plane magnetization in an axion insulator can generate a "pseudo-electric field", which acts on the surface state of topological ins…
Lecture-notes: introducing and discussing basics on axion electrodynamics with application in the calculation of the images generated by an electric (or a magnetic) charge located close to an interface ordinary insulator-topological insulator
Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of "topological insulators" in which those symmetries are unbroken. Previous work has shown how to compute spin and lattice contributions to the magnetoelectric tensor. Here we solve the problem of orbital contributions by computing the frozen-lattice electronic polarization induced by a magnetic field. One part of this response (the "Chern-Simons term") can appear even in time-reversal-symmetric materials and has been previously sho…
We theoretically study magnetoelectric effects in a heterostructure of a generic band insulator and a ferromagnet. In contrast to the kinetic magnetoelectric effect in metals, referred to as the Edelstein effect or the inverse spin galvanic effect, our mechanism relies on virtual interband transitions between the valence and conduction bands and therefore immune to disorder or impurity scattering. By calculating electric field-induced magnetization by the linear response theory, we reveal that the magnetoelectric effect shows up without specific parameter choices. The magnetoelectric effect qu…
It has been proposed that topological insulators can be best characterized not as surface conductors, but as bulk magnetoelectrics that -- under the right conditions-- have a universal quantized magnetoelectric response coefficient $e^2/2h$. However, it is not clear to what extent these conditions are achievable in real materials that can have disorder, finite chemical potential, residual dissipation, and even inversion symmetry. This has led to some confusion and misconceptions. The primary goal of this work is to illustrate exactly under what real life scenarios and in what context topologic…
Recently, the search for an axion insulator state in the ferromagnet-3D topological insulator (TI) heterostructure and $\mathrm{MnBi_2Te_4}$ has attracted intensive interest. However, its detection remains difficult in experiments. We systematically investigate the disorder-induced phase transition of the axion insulator state in a 3D TI with antiparallel magnetization alignment surfaces. It is found that there exists a 2D disorder-induced phase transition which shares the same universality class with the quantum Hall plateau to plateau transition. Then, we provide a phenomenological theory wh…
Three-dimensional topological insulator films in contact with magnetic layers exhibit intriguing magneto-optical and magnetoelectric phenomena, but little is known beyond the linear response regime. We demonstrate that the presence of two electric fields parallel to the surface of the film induces a perpendicular AC polarization, whereas a static polarization can be induced by applying a single circularly polarized electromagnetic wave. These phenomena are determined by the second-order susceptibility, which also controls the manner in which the anomalous Hall current is modulated by a perpend…
Topological states of quantum matter have attracted great attention in condensed matter physics and materials science. The study of time-reversal-invariant (TRI) topological states in quantum materials has made tremendous progress in both theories and experiments. As a great success, thousands of TRI topological materials are predicted through sweeping search. Richer exotic phenomena are expected to appear in magnetic topological materials because of varied magnetic configurations, but this study falls much behind due to the complex magnetic structures and transitions. Here, we predict the tet…
The surface of a 3D topological insulator is a new type of two dimensional electron gas (2DEG). The exactly quantized magneto-optical or axionic response of a 3D topological insulator is a direct result of the Berry's phase protected spin-momentum locked states on its surface. (PRL Viewpoint http://physics.aps.org/node/3810).
We report transport studies on (Bi,Sb)2Te3 topological insulator thin films with tunable electronic band structure. We find a doping and temperature regime in which the Hall coefficient is negative indicative of electron-type carriers, whereas the Seebeck coefficient is positive indicative of hole-type carriers. This sign anomaly is due to the distinct transport behaviors of the bulk and surface states: the surface Dirac fermions dominate magnetoelectric transport while the thermoelectric effect is mainly determined by the bulk states. These findings may inspire new ideas for designing topolog…
The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase…
Topological insulators (TIs) exhibit a quantized magnetoelectric response when time-reversal symmetry is broken on its surface. This unusual electromagnetic (EM) response is a unique macroscopic manifestation of the quantum Hall effect on the TI surface and it is described by a quantized Chern-Simons theory. In this paper, we construct the Green's function (GF) describing the EM response of two topological media separated by a cylindrical interface. This GF, in the appropriate limits, describes the magnetoelectric effect of both i) a cylindrical TI surrounded by a dielectric fluid, and ii) a T…
One of the intriguing properties characteristic to three-dimensional topological materials is the topological magnetoelectric phenomena arising from a topological term called the $θ$ term. Such magnetoelectric phenomena are often termed the axion electrodynamics, since the $θ$ term has exactly the same form as the action describing the coupling between a hypothetical elementary particle, axion, and a photon. The axion was proposed about forty years ago to solve the so-called strong CP problem in quantum chromodynamics, and is now considered as a candidate for dark matter. In this tutorial, we …
We study the magnetization dynamics in ferromagnet$\mid$insulator$\mid$ferromagnet and ferromagnet$\mid$insulator$\mid$normal metal ultra-small tunnel junctions, and the associated voltage drop in the presence of an electromagnetic environment assisting the tunneling processes. We show that the environment strongly affects the resulting voltage, which becomes a highly non-linear function of the precession cone angle $θ$. We find that voltages comparable to the driving frequency $ω$ can be reached even for small precession cone angles $θ$, in stark contrast to the case where the environment is …
Magnetic skyrmions are topologically protected spin-whirl quasiparticles currently considered as promising components for ultra-dense memory devices. In the bulk they form lattices that are stable over just a few Kelvin below the ordering temperature. This narrow stability range presents a key challenge for applications, and finding ways to tune the SkL stability over a wider phase space is a pressing issue. Here we show experimentally that the skyrmion phase in the magnetoelectric insulator ${\text{Cu}_2 \text{O} \text{Se} \text{O}_3}$ can either expand or shrink substantially depending on th…
We study the generalization of the three-dimensional two-band Hopf insulator to the case of many bands, where all the bands are separated from each other by band gaps. The obtained $\mathbb{Z}$ classification of such a $N$-band Hopf insulator is related to the quantized isotropic magnetoelectric coefficient of its bulk. The boundary of a $N$-band Hopf insulator can be fully gapped, and we find that there is no unique way of dividing a finite system into bulk and boundary. Despite this non-uniqueness, we find that the magnetoelectric coefficient of the bulk and the anomalous Hall conductivity o…
The dynamical axion field is a new state of quantum matter where the magnetoelectric response couples strongly to its low-energy magnetic fluctuations. It is fundamentally different from an axion insulator with a static quantized magnetoelectric response. The dynamical axion field exhibits many exotic phenomena such as axionic polariton and axion instability. However, these effects have not been experimentally confirmed due to the lack of proper topological magnetic materials. Here by combining analytic models and first-principles calculations, we predict a series of van der Waal layered Mn$_2…
We extend the recently-developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing to calculate th…
Based on a first-principles approach, we show that in a single crystal of a prototypical topological insulator such as Bi$_2$Se$_3$ the difference in the work function between adjacent surfaces with different crystal-face orientations generates a built-in electric field around facet edges. Owing to the topological magnetoelectric coupling for a given broken time-reversal symmetry in the crystal, the electric field, in turn, forces effective magnetic dipoles to accumulate along the edges, realizing the facet-edge magnetic ordering. We demonstrate that the predicted magnetic ordering which depen…
When time-reversal symmetry is broken on its surface, topological insulators exhibit a magnetoelectric response which is described by axion electrodynamics. A direct consequence of this theory is the appearance of a magnetic field that resembles the one produced by a magnetic image monopole when a point-like electric charge is located near the surface of the material. In this paper we investigate the more realistic problem when the point-like charge is replaced by a finite size sphere at constant potential. We calculate the electromagnetic fields using the potential formulation in a particular…
The optical properties of a spherical topological insulator embedded concentrically in a single-electron system consisting of a core-shell GaAs quantum dot are analyzed, when the system is under a uniform external magnetic field. The topological insulator's magnetoelectric response is computed in the effective framework of $θ$-electrodynamics, which allows analytical calculations for the induced electric and magnetic potentials by Green's Function method. The GaAs Hamiltonian is constructed in the effective-mass approximation, and its corresponding Schrödinger equation is numerically solved th…
Axion is a hypothetical elementary particle which was initially postulated to solve the charge conjugation-parity problem in particle physics. Interestingly, the axion state has emerged in effective theory of topological insulators and has attracted extensive attention in condensed matter physics. Time-reversal or inversion symmetry constrains the axion field $θ$ to be quantized. When both the time-reversal and inversion symmetries are broken by, say, an antiferromagnetic order, the axion field $θ$ could become unquantized and dynamical along with magnetic fluctuations, which is termed the dyn…
We investigate the instability due to dynamical axion field near the topological phase transition of insulators. We first point out that the amplitude of dynamical axion field is bounded for magnetic insulators in general, which suppresses the axion instability. Near the topological phase transition, however, the axion field may have a large fluctuation, which decreases the critical electric field for the instability and increases the axion induced magnetic flux density. Using two different model Hamiltonians, we report the electromagnetic response of the axion field in details.
We study theoretically a three-dimensional correlated and spin-orbit coupled system, the half-filled extended Fu-Kane-Mele-Hubbard model on a diamond lattice, focusing on the topological magnetoelectric response of the antiferromagnetic insulator phase. In the antiferromagnetic insulator phase, the Dirac-like low-energy effective Hamiltonian is obtained. Then the theta term, which results in the magnetoelectric response, is derived as a consequence of the chiral anomaly. The realization of the dynamical axion field in our model is discussed. The relation with a symmetry broken phase induced by…
We propose to use ferromagnetic insulator MnBi2Se4/Bi2Se3/antiferromagnetic insulator Mn2Bi2Se5 heterostructures for the realization of the axion insulator state. Importantly, the axion insulator state in such heterostructures only depends on the magnetization of the ferromagnetic insulator and hence can be observed in a wide range of external magnetic field. Using density functional calculations and model Hamiltonian simulations, we find that the top and bottom surfaces have opposite half-quantum Hall conductance, with a sizable global spin gap of 5.1 meV opened for the topological surface st…
We investigate the interaction between a topological insulator nanoparticle and a quantum dot in an impulse magnetic field. Since topological insulators are nonmagnetic, after the impulse has ended only the localised topological surface modes, which are quantised in terms of dipolar bosonic modes, thus coupling dipolarly to the quantum dot. Hence, the hybrid system can be treated as a single bosonic mode interacting with a two-level system, where the coupling strength is quantised in terms of the magnetoelectric polarizability. We implement the interaction of the hybrid with the environment th…
We propose that the dynamical axion field can be realized in a magnetic topological insulator superlattice or a topological paramagnetic insulator. The magnetic fluctuations of these systems produce a pseudoscalar field which has an axionic coupling to the electromagnetic field, and thus it gives a condensed-matter realization of the axion electrodynamics. Compared to the previously proposed dynamical axion materials where a long range antiferromagnetic order is required, the systems proposed here have the advantage that only a uniform magnetization or a paramagnetic state is needed for the dy…
Magnetoelectric effect in multiferroic metals via a direct spin-charge interaction
Key Lab of advanced optoelectronic quantum architecture and measurement (MOE), and School of Interdisciplinary Science, Beijing Institute of Technology（北京理工大学光电量子架构与测量教育部重点实验室，交叉科学研究院）
The axion is a hypothetical but experimentally undetected particle. Recently, the antiferromagnetic topological insulator MnBi$_2$Te$_4$ has been predicted to host the axion insulator, but the experimental evidence remains elusive. Specifically, the axion insulator is believed to carry "half-quantized" chiral currents running antiparallel on its top and bottom surfaces. However, it is challenging to measure precisely the half-quantization. Here, we propose a nonlocal surface transport device, in which the axion insulator can be distinguished from normal insulators without a precise measurement…
