Enhanced photonic spin Hall effect with subwavelength topological edge states

Photonic structures offer unique opportunities for controlling light‐matter interaction, including the photonic spin Hall effect associated with the transverse spin‐dependent displacement of a light beam that propagates in specially designed optical media. However, due to small spin‐orbit coupling, the photonic spin Hall effect is usually weak at the nanoscale. Here we suggest theoretically and demonstrate experimentally, in both optics and microwave experiments, the photonic spin Hall effect enhanced by topologically protected edge states in subwavelength arrays of resonant dielectric particles. Based on direct near‐field measurements, we observe the selective excitation of the topological edge states controlled by the handedness of the incident light. Additionally, we reveal the main requirements to the symmetry of photonic structures to achieve the topology‐enhanced spin Hall effect, and also analyse the robustness of the photonic edge states against the long‐range coupling.

     

二维声学系统中的拓扑相变及边界传输

拓扑声学的发现产生了一种可以有效抑制反射的声学边界传输态,不仅让人们重新认识了声传输现象,也扩展了声学新原理功能器件的研究领域。文章将介绍二维系统中拓扑声学的基本概念以及一些拓扑非平庸体系。主要关注利用背景流体构造的声类量子霍尔效应,利用共振耦合环形波导构造Floquet拓扑绝缘体,声类量子自旋霍尔效应以及声谷霍尔效应等。     

Vector valley Hall edge solitons in the photonic lattice with type-II Dirac cones

Topological edge solitons represent a significant research topic in the nonlinear topological photonics. They maintain their profiles during propagation, due to the joint action of lattice potential and nonlinearity, and at the same time are immune to defects or disorders, thanks to the topological protection. In the past few years topological edge solitons were reported in systems composed of helical waveguide arrays, in which the time-reversal symmetry is effectively broken. Very recently, topological valley Hall edge solitons have been demonstrated in straight waveguide arrays with the time-reversal symmetry preserved. However, these were scalar solitary structures. Here, for the first time, we report vector valley Hall edge solitons in straight waveguide arrays arranged according to the photonic lattice with innate type-II Dirac cones, which is different from the traditional photonic lattices with type-I Dirac cones such as honeycomb lattice. This comes about because the valley Hall edge state can possess both negative and positive dispersions, which allows the mixing of two different edge states into a vector soliton. Our results not only provide a novel avenue for manipulating topological edge states in the nonlinear regime, but also enlighten relevant research based on the lattices with type-II Dirac cones.     

空间盘绕型声学超材料的亚波长拓扑谷自旋态

声子晶体的Dirac线性色散关系,使其具有奇特的声拓扑特性,在声波控制领域具有良好的应用前景.目前,声子晶体的拓扑边缘态主要基于Bragg散射所产生的能带结构,难以实现低频声波的受拓扑保护单向边缘传输.本文引入空间盘绕结构,设计了具有C_(3v)对称性的空间盘绕型声学超材料,并研究其布里渊区高对称点(K/K'点)的亚波长Dirac锥形线性色散.接着,通过旋转打破空间盘绕型声学超材料的镜像对称性,使其Dirac简并锥裂开而产生亚波长拓扑相变和亚波长拓扑谷自旋态.最后,采用拓扑相位互逆的声学超材料构造拓扑界面,实现声拓扑谷自旋传输.空间盘绕型声学超材料的亚波长Dirac线性色散与亚波长拓扑谷自旋态突破了声子拓扑绝缘体的几何尺寸限制,为声拓扑稳健传输在低频段的应用提供理论基础.     

Double topological edge states investigation in sonic metamaterials

We investigate the topologically protected sound propagation in sonic metamaterials, analogous to quantum spin hall effect (QSHE). The sonic metamaterials consist of circular rods and meta-molecules arranged in air with a honeycomb-lattice. The on-demand inversion in topological phase can be achieved by two ways of scatterer controls at locally resonant frequency and Bragg frequency. The Helmholtz resonators in the structure are contributed to the formation of subwavelength double Dirac cones which are more likely to appear due to local resonance enhancement with more number of resonators. By combining two sonic metamaterials with different topological invariants, we demonstrate the robust sound propagation and pseudospin-dependent one-way acoustic propagation at the interface. Experimental measurement of the topologically protected acoustic wave transmission matches well with the simulation result.     

Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Symanzik's method applied to fractional quantum Hall edge states

The method of separability, introduced by Symanzik, is applied in order to describe the effect of a boundary for a fractional quantum Hall liquid in the Laughlin series. An Abelian Chern‐Simons theory with plane boundary is considered and the Green functions both in the bulk and on the edge are constructed, following a rigorous, perturbative, quantum field theory treatment. We show that the conserved boundary currents find an explicit interpretation in terms of the continuity equation with the electron density satisfying the Tomonaga‐Luttinger commutation relation.     

Boundary conformal field theory and tunneling of edge quasiparticles in non-Abelian topological states

We explain how (perturbed) boundary conformal field theory allows us to understand the tunneling of edge quasiparticles in non-Abelian topological states. The coupling between a bulk non-Abelian quasiparticle and the edge is due to resonant tunneling to a zero mode on the quasiparticle, which causes the zero mode to hybridize with the edge. This can be reformulated as the flow from one conformally invariant boundary condition to another in an associated critical statistical mechanical model. Tunneling from one edge to another at a point contact can split the system in two, either partially or completely. This can be reformulated in the critical statistical mechanical model as the flow from one type of defect line to another. We illustrate these two phenomena in detail in the context of the ν=5/2 quantum Hall state and the critical Ising model. We briefly discuss the case of Fibonacci anyons and conclude by explaining the general formulation and its physical interpretation.     

Dual-channel tunable near-infrared absorption enhancement with graphene induced by coupled modes of topological interface states

The dual-channel nearly perfect absorption is realized by the coupled modes of topological interface states (TIS) in the near-infrared range. An all-dielectric layered heterostructure composed of photonic crystals (PhC)/graphene/PhC/graphene/PhC on GaAs substrate is proposed to excite the TIS at the interface of adjacent PhC with opposite topological properties. Based on finite element method (FEM) and transfer matrix method (TMM), the dual-channel absorption can be modulated by the periodic number of middle PhC, Fermi level of graphene, and angle of incident light (TE and TM polarizations). Especially, by fine-tuning the Fermi level of graphene around 0.4 eV, the absorption of both channels can be switched rapidly and synchronously. This design is hopefully integrated into silicon-based chips to control light.     

磁性拓扑绝缘体中的量子化反常霍尔效应

文章从平常霍尔效应出发,介绍了反常霍尔效应及其内秉物理机制,并在此基础上介绍了其量子化版本——量子化反常霍尔效应.然后从拓扑有序态的角度,重点讨论了量子化反常霍尔效应与量子霍尔效应、量子自旋霍尔效应、拓扑绝缘体等之间的区别与内在联系.最后介绍了通过在拓扑绝缘体（Bi2Se3, Bi2Te3 和 Sb2Te3）薄膜中掺杂过渡金属元素（Cr 或 Fe）实现量子化反常霍尔效应的方法.     

三聚化非厄密晶格中具有趋肤效应的拓扑边缘态

近年来,探索新的拓扑量子结构、深入分析各种多聚化拓扑晶格中的新奇物理性质已经成为热点.并且,多聚化拓扑模型在量子光学等领域的研究也愈发深入,拥有广阔的发展前景.本文聚焦于研究三聚化非厄密晶格中的新奇拓扑特性.首先,若晶胞内最近邻正反向耦合不相等,三聚化模型中的体态和边缘态出现趋肤效应.其中,随着最近邻耦合正反系数差的增大,拓扑保护的边缘态的宽度和简并度均可被调制,边缘态数量也会减少.其次,当在考虑次近邻耦合的影响时,随着次近邻耦合系数在适当范围内变化,系统本征能谱的上下能隙及其中具有趋肤效应的边缘态也会发生不对称的变化.此外,当适当改变两种耦合系数,三聚化非厄密模型的体态和边缘态的局域程度也会随之发生变化.     

Quantum anomalous Hall effect and related topological electronic states

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

声子晶体中的声谷态输运

如同自旋电子学中的自旋,固体中的能谷自由度可视为新的信息载体,从而用于未来的电子器件设计。最近,作者将谷态的概念引入到声子晶体中,揭示其涡旋属性并建立激发选择定则。有趣的是,声谷态可由外部声场直接激发,并通过探测声子晶体内外的声场分布展示其极化特性。这种涡旋手性锁定的谷输运将为人们提供全新的声波操控方式。考虑到声和物质的相互作用,也可预期谷涡旋态的其它新奇应用,如旋转操纵微颗粒等。进一步研究发现,存在两类拓扑非平庸的声谷霍尔相,它们之间的界面可以支持拓扑保护的边缘态。研究表明,该边缘态具备各种新颖的性质,如谷选择性激发、边界拐弯抗反射等。     

Floquet bands and photon-induced topological edge states of graphene nanoribbons

Floquet theorem is widely used in the light-driven systems. But many 2 D-materials models under the radiation are investigated with the high-frequency approximation, which may not be suitable for the practical experiment. In this work,we employ the non-perturbative Floquet method to strictly investigate the photo-induced topological phase transitions and edge states properties of graphene nanoribbons under the light irradiation of different frequencies(including both low and high frequencies). By analyzing the Floquet energy bands of ribbon and bulk graphene, we find the cause of the phase transitions and its relation with edge states. Besides, we also find the size effect of the graphene nanoribbon on the band gap and edge states in the presence of the light.     

Valley Hall effect and Nernst effect in strain engineered graphene

We theoretically predict the existence of tunneling valley Hall effect and Nernst effect in the normal/strain/normal graphene junctions, where a strained graphene is sandwiched by two normal graphene electrodes. By applying an electric bias a pure transverse valley Hall current with longitudinal charge current is generated. If the system is driven by a temperature bias, a valley Nernst effect is observed, where a pure transverse valley current without charge current propagates. Furthermore, the transverse valley current can be modulated by the Fermi energy and crystallographic orientation. When the magnetic field is further considered, we obtain a fully valley-polarized current. It is expected these features may be helpful in the design of the controllable valleytronic devices.     

Gauge potential formulations of the spin Hall effect in graphene

Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit interaction is expressed in terms of kinematic momenta by introducing a gauge potential. A formulation of the spin Hall conductivity is established by requiring that the time evolution of this kinematic momentum vector vanishes. We then calculated the conductivity employing the Berry gauge fields. We show that both of the gauge fields can be deduced from the pure gauge field arising from the Foldy-Wouthuysen transformations.     

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.     

Transverse electric field-induced quantum valley Hall effects in zigzag-edge graphene nanoribbons

We have investigated gapless edge states in zigzag-edge graphene nanoribbons under a transverse electric field across the opposite edges by using a tight-binding model and the density functional theory calculations. The tight-binding model predicted that a quantum valley Hall effect occurs at the vacuum-nanoribbon interface under a transverse electric field and, in the presence of edge potentials with opposite signs on opposite edges, an additional quantum valley Hall effect occurs under a much lower field. Dangling bonds inevitable at the edges of real nanoribbons, functional groups terminating the edge dangling bonds, and spin polarizations at the edges result in the edge potentials. The density functional theory calculations confirmed that asymmetric edge terminations, such as one having hydrogen at an edge and fluorine at the other edge, lead to the quantum valley Hall effect even in the absence of a transverse electric field. The electric field-induced half-metallicity in the antiferromagnetic phase, which has been intensively investigated in the last decade, was revealed to originate from a half-metallic quantum valley Hall effect.     

从分数量子霍尔效应到拓扑量子计算

分数量子霍尔效应系统是奇异的量子液体,其中的准粒子激发可以带分数电荷,甚至具有非阿贝尔的统计性质。理论研究表明,这些准粒子可以用来实现在硬件上可容错的量子计算,即拓扑量子计算。文章在介绍分数量子霍尔效应及其在拓扑量子计算中的潜在应用基础上,重点回顾了近五年来对填充因子为5/2的分数量子霍尔态中非阿贝尔准粒子的实验探测和部分相关理论诠释。