Non-Hermitian topological Anderson insulators

Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger model.We show that the non-Hermiticity can enhance the topological phase against disorders by increasing bulk gaps.Moreover,we uncover a topological phase which emerges under both moderate non-Hermiticity and disorders,and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes.Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators.We reveal that the system has unique non-monotonous localization behavior and the topological transition is accompanied by an Anderson transition.These properties are general in other non-Hermitian models.     

Electrostatic field effects on three-dimensional topological insulators

Three-dimensional topological insulators are a new class of quantum matter which has interesting connections to nearly all main branches of condensed matter physics. In this article, we briefly review the advances in the field effect control of chemical potential in three-dimensional topological insulators. It is essential to the observation of many exotic quantum phenomena predicted to emerge from the topological insulators and their hybrid structures with other materials. We also describe various methods for probing the surface state transport. Some challenges in experimental study of electron transport in topological insulators will also be briefly discussed.     

Topological hierarchy matters — topological matters with superlattices of defects

Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states.In this paper,we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters.We find that both topological defects(quantized vortices) and non topological defects(vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects.These topological mid-gap states have nontrivial topological properties,including the nonzero Chern number and the gapless edge states.Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters.     

Unidirectional transport in amorphous topological photonic crystals

Many works on topological insulators have focused on periodic lattice systems,where short-and long-range order is considered.Here we construct a two-dimensional amorphous photonic crystal with short-range order and a controllable level of long-range order and experimentally investigate the transport of topological edge states in this amorphous system.We demonstrate that topology properties remain constant with unidirectional edge state propagation,immune to specific disorder strength.The partiti...     

Topological states in quasicrystals

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.     

Probe Knots and Hopf Insulators with Ultracold Atoms

Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing.     

Proximity effects in topological insulator heterostructures

Topological insulators （Tls） are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to TI-based heterostructures, in which con- ventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent studies on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insu- lator or other topologically trivial systems. Using first-principles approaches, we have realized the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topo- logical helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath, These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI- based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications.     

Correlation Renormalized and Induced Spin-Orbit Coupling

Interplay of spin-orbit coupling(SOC) and electron correlation generates a bunch of emergent quantum phases and transitions, especially topological insulators and topological transitions. We find that electron correlation will induce extra large SOC in multi-orbital systems under atomic SOC and change ground state topological properties. Using the Hartree–Fock mean field theory, phase diagrams of px/py orbital ionic Hubbard model on honeycomb lattice are well studied. In general, correction of s...     

Electronic Structure of the Weak Topological Insulator Candidate Zintl Ba3Cd2Sb4

One of the greatest triumph of condensed matter physics in the past ten years is the classification of materials by the principle of topology.The existence of topological protected dissipationless surface state makes topological insulators great potential for applications and hotly studied.However,compared with the prosperity of strong topological insulators,theoretical predicted candidate materials and experimental confirmation of weak topological insulators(WTIs) are both extremely rare.By com...     

Machine-learning-driven on-demand design of phononic beams

The development of phononic crystals, especially their interaction with topological insulators, allows exploration of the anomalous properties of acoustic/elastic waves for various applications. However, rapidly and inversely exploring the geometry of specific targets remains a major challenge. In this work, we show how machine learning can address this challenge by studying phononic crystal beams using two different inverse design schemes. We first develop the theory of phononic beams using the transfer matrix method. Then, we use the reinforcement learning algorithm to effectively and inversely design the structural parameters to maximize the bandgap width. Furthermore, we employ the tandem-architecture neural network to solve the training-difficulty problem caused by inconsistent data and complete the task of inverse structure design with the targeted topological properties. The two inverse-design schemes have different adaptabilities, and both are characterized by high efficiency and stability. This work provides deep insights into the combination of machine learning, topological property,and phononic crystals and offers a reliable platform for rapidly and inversely designing complex material and structure properties.     

Topological crystalline insulators

The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces. These topological crystalline insulators are the counterpart of topological insulators in materials without spin-orbit coupling. Their band structures are characterized by new topological invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.     

Topological photonic states in artificial microstructures[Invited]

Topological photonics provides a new opportunity for the examination of novel topological properties of matter, in which the energy band theory and ideas in topology are utilized to manipulate the propagation of photons. Since the discovery of topological insulators in condensed matter, researchers have studied similar topological effects in photonics.Topological photonics can lead to materials that support the robust unidirectional propagation of light without back reflections. This ideal transport property is unprecedented in traditional optics and may lead to radical changes in integrated optical devices. In this review, we present the exciting developments of topological photonics and focus on several prominent milestones of topological phases in photonics, such as topological insulators, topological semimetals, and higher-order topological phases. We conclude with the prospect of novel topological effects and their applications in topological photonics.     

Observation of Topological Links Associated with Hopf Insulators in a Solid-State Quantum Simulator

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties,including nontrivial topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.     

Topological phases and phase transitions on the honeycomb lattice

We investigate possible phase transitions among the different topological insulators in a honeycomb lattice under the combined influence of spin-orbit couplings and staggered magnetic flux. We observe a series of topological phase transitions when tuning the flux amplitude, and find topologically nontrivial phases with high Chern number or spin-Chern number. Through tuning the exchange field, we also find a new quantum state which exhibits the electronic properties of both the quantum spin Hall state and quantum anomalous Hall state. The topological characterization based on the Chern number and the spin-Chern number are in good agreement with the edge-state picture of various topological phases.     

Topological insulators in three dimensions

We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel "topological metal" surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.     

Observation of topological valley transport of elastic waves in bilayer phononic crystal slabs

In this Letter, we propose a unique bilayer design of phononic crystal slabs that are constructed by two layers of snowflake phononic crystal plates connected by a honeycomb array of cylinders. By tuning orientations of snowflake-shaped holes in both layers, we achieve two kinds of valley-projected topological elastic insulators distinguished by conventional and layer-polarized topological valley Hall phases. Then, between different conventional and layer-polarized topological valley Hall phases, two kinds of edge modes, layer-mixed and layer-polarized edge modes, are obtained and explored. In finite-size samples, the interesting topological transport properties, which the elastic wave can propagate alternatively between both layers and only in a single layer, are realized by exciting layer-mixed and layer-polarized edge states. In addition, we design an interlayer converter to realize conversion of the elastic wave propagation between both layers. Our research promotes the development of topological elastic insulators and provides a route for various practical applications.     

Identifying Two-Dimensional <Emphasis Type="Italic">Z</Emphasis><Subscript>2</Subscript> Antiferromagnetic Topological Insulators

We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate Néel antiferromagnet, where staggered magnetization breaks the symmetry with respect to both elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called Z₂ topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of topological invariants has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram, using a recently proposed criterion for centrosymmetric systems [13]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular examples treated in this work, and admit straightforward generalization. We illustrate this by two examples of non-centrosymmetric systems, where no simple criteria have been known to identify topological phases. We also present, for some cases, an explicit construction of edge states in an antiferromagnetic topological insulator.     

具有全局对称性的强关联拓扑物态的规范场论

在有对称性保护的条件下,拓扑能带绝缘体等自由费米子体系的拓扑不变量可以在能带结构计算中得到.但是,为了得到强关联拓扑物质态的拓扑不变量,我们需要全新的理论思路.最典型的例子就是分数量子霍尔效应:其低能有效物理一般可以用Chern-Simons拓扑规范场论来计算得到;霍尔电导的量子化平台蕴含着十分丰富的强关联物理.本文将讨论存在于玻色和自旋模型中的三大类强关联拓扑物质态:本征拓扑序、对称保护拓扑态和对称富化拓扑态.第一类无需考虑对称性,后两者需要考虑对称性.理论上,规范场论是一种非常有效的研究方法.本文将简要回顾用规范场论来研究强关联拓扑物质态的一些研究进展.具体内容集中在"投影构造理论"、"低能有效理论"、"拓扑响应理论"三个方面.     

Magnetic and topological transitions in three-dimensional topological Kondo insulator

Using an extended slave-boson method,we draw a global phase diagram summarizing both magnetic phases and paramagnetic(PM) topological insulators(TIs) in a three-dimensional topological Kondo insulator(TKI). By including electron hopping(EH) up to the third neighbors, we identify four strong TI(STI) phases and two weak TI(WTI) phases. Then, the PM phase diagrams characterizing topological transitions between these TIs are depicted as functions of EH,f-electron energy level,and hybridization constant. We also find an insulator-metal transition from an STI phase that has surface Fermi rings and spin textures in qualitative agreement with the TKI candidate SmBs. In the weak hybridization regime, antiferromagnetic(AF) order naturally arises in the phase diagrams. Depending on how the magnetic boundary crosses the PM topological transition lines,AF phases are classified into the AF topological insulator(AFTI) and the non-topological AF insulator, according to their Z_2 indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTIs showing distinguishable surface dispersions around their Dirac points.