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 discuss its connection to the surface Hall conductivity. The orbital magnetoelectric polarizability can be generalized to the many-particle wavefunction and defines the 3D topological insulator, like the IQHE, in terms of a topological ground-state response function.
We extend a field theoretic approach for the investigation of the electronic charge-current density response of crystalline systems to arbitrary applied electromagnetic fields. The approach leads to the introduction of microscopic polarization and magnetization fields, as well as free charge and current densities, the dynamics of which are described by a lattice gauge theory. The spatial averages of such quantities constitute the fields of macroscopic electrodynamics. We implement this formalism to study the orbital electronic response of a class of insulators to applied uniform dc electric an…
The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the electromagnetic (EM) field in a magnetoelectric (ME) medium is not a trivial problem. The question of whether electromagnetism and magnetoelectricity can coexist without an extension of Maxwell theory arises when we study the effects of EM energy propagation and consider group velocity of the waves in a ME medium. The energy balance equation reveals unusual topolo…
Resonant scattering of electromagnetic (EM) waves by small particles is considered as one of the basic problem in metamaterial science. At present, special subwavelength resonators are considered as structural elements in chiral and bianisotropic metamaterials. There is a general consensus that these small scatterers behave like "artificial atoms", meta-atoms, with strong electrical and magnetic responses and an interconnection between these responses. However, the observed effect of magnetoelectric (ME) coupling in these meta-atoms is not associated with the near-field manipulation properties…
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 explore a model akin to axion electrodynamics in which the axion field $θ(t,\mathbf{x})$ rather than being dynamical is a piecewise constant effective parameter $θ$ encoding the microscopic properties of the medium inasmuch as its permittivity or permeability, defining what we call a $θ$-medium. This model describes a large class of phenomena, among which we highlight the electromagnetic response of materials with topological order, like topological insulators for example. We pursue a Green's function formulation of what amounts to typical boundary-value problems of $θ$-media, when external…
Observation of the universal magnetoelectric effect in a 3D topological insulator
拓扑绝缘体（TI）的电动力学由修改的麦克斯韦方程描述，其包含将电场耦合到介质的磁化和将磁场耦合到介质的极化的附加项，使得耦合系数被量化为每个表面$e^2 / 2 h c $的奇数倍。在这里，我们报告观察到的这种所谓的拓扑磁电（TME）效应。我们使用单色太赫兹（THz）光谱的TI结构配备了半透明的门选择性地解决表面状态。在强外磁场中，当一定频率的线偏振太赫兹辐射通过应变碲化汞三维薄膜的两个表面时，我们观察到一个与精细结构常数$α= e^2 / \hbar c$相等的普遍法拉第旋转角.这些实验提供了对TI的轴子电动力学的深入了解，并可能用于三个基本物理常数的精确定义。
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…
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…
Manifestation of axion electrodynamics through magnetic ordering on edges of topological insulator
基于第一性原理的方法，我们表明，在一个典型的拓扑绝缘体，如Bi $_2$ Se $_3$的相邻表面具有不同的晶面取向之间的功函数的差异产生一个内置的电场刻面边缘周围的单晶。由于晶体中时间反演对称性破缺时的拓扑磁电耦合，电场又迫使有效磁偶极子沿边缘聚集，实现了小面-边缘磁有序。我们表明，预测的磁排序，这只取决于面之间的功函数的差异，实际上是一个体现在真实的固体中的轴子电动力学。
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…
We study the homotopy classification of symmetry representations to describe the bulk topological invariants protected by the combined operation of a two-fold rotation $C_{2z}$ and time-reversal $T$ symmetries. We define topological invariants as obstructions to having smooth Bloch wave functions compatible with a momentum-independent symmetry representation. When the Bloch wave functions are required to be smooth, the information on the band topology is contained in the symmetry representation. This implies that the $d$-dimensional homotopy class of the unitary matrix representation of the sy…
The magnetoelectric coupling of electrons in a three-dimensional solid can be effectively described by axion electrodynamics. Here we report the discovery of the fractional magnetoelectric effect in chiral anomalous semimetals of the three-dimensional massless Wilson fermions, which have linear dispersions at the energy crossing point, and break the chiral symmetry at generic momenta. In the presence of electric and magnetic fields, the time-reversal and parity symmetry breaking give rise to the quarter-quantized topological magnetoelectric effect, which is directly related to the winding numb…
We study the interaction between a topological insulator nanoparticle and a quantum dot subject to an applied electric field. The electromagnetic response of the topological insulator is derived from axion electrodynamics in the quasistatic approximation. Localized modes are quantized in terms of dipolar bosonic modes, which couples dipolarly to the quantum dot. Hence, we treat the hybrid as a two-level system interacting with a single bosonic mode, where the coupling strength encodes the information concerning the nontrivial topology of the nanoparticle. The interaction of the hybrid with the…
Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well-understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. …
Traditional ionic/covalent compound insulators arise from a commensuration between electron count and system volume. On the other hand, conventional topological insulators, outside of quantum hall effect systems, do not typically display such a commensuration. Tnstead, they can undergo a phase transition to a trivial insulator that preserves the electron filling. Nevertheless, in some crystalline insulators, termed filling-enforced quantum band insulators (feQBIs), electron filling can dictate nontrivial topology in the insulating ground state. Currently, little is known about the relation bet…
The intricate interplay between nontrivial topology and magnetism in two-dimensional (2D) materials has led to the emergence of many novel phenomena and functionalities. An outstanding example is the quantum anomalous Hall (QAH) effect, which was realized in magnetically doped topological insulators (TIs) in the absence of magnetic field. Recently, the layered van der Waals compound MnBi2Te4 has been theoretically predicted and experimentally verified to be a TI with interlayer antiferromagnetic (AFM) order. It is a rare stoichiometric material with coexisting topology and magnetism, thus repr…
Axionic tunneling from a topological Kondo insulator
Rutgers University（罗格斯大学）；University of Greifswald（格赖夫斯瓦尔德大学）；Harvard University（哈佛大学）；Sun Yat-sen University（中山大学）；Zhejiang University（浙江大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Pennsylvania（宾夕法尼亚大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
The axion insulator (AXI) has long been recognized as the simplest example of a 3D magnetic topological insulator (TI). The most familiar AXI results from magnetically gapping the surface states of a 3D $\mathbb{Z}_{2}$ TI while preserving the bulk gap. Like the 3D TI, it exhibits a quantized magnetoelectric polarizability of $θ=π$, and can be diagnosed from bulk symmetry eigenvalues when inversion symmetric. However, whereas a 3D TI is characterized by bulk Wilson loop winding, 2D surface states, and the pumping of the 2D $\mathbb{Z}_{2}$ TI index, we show that an AXI with a large number of b…
