Model Hamiltonian for the Quantum Anomalous Hall State in Iron-Halogenide

We examine quantum anomalous Hall(QAH) insulators with intrinsic magnetism displaying quantized Hall conductance at zero magnetic fields.The spin-momentum locking of the topological edge stats promises QAH insulators with great potential in device applications in the field of spintronics.Here,we generalize Haldane's model on the honeycomb lattice to a more realistic two-orbital case without the artificial real-space complex hopping.Instead,we introduce an intraorbital coupling,stemming directly from the local spin-orbit coupling(SOC).Our d_(xy)/d_(x~2-y~2) model may be viewed as a generalization of the bismuthene p_x/p_y-model for correlated d-orbitals.It promises a large SOC gap,featuring a high operating temperature.This two-orbital model nicely explains the low-energy excitation and the topology of two-dimensional ferromagnetic iron-halogenides.Furthermore,we find that electronic correlations can drive the QAH states to a c=0 phase,in which every band carries a nonzero Chern number.Our work not only provides a realistic QAH model,but also generalizes the nontrivial band topology to correlated orbitals,which demonstrates an exciting topological phase transition driven by Coulomb repulsions.Both the model and the material candidates provide excellent platforms for future study of the interplay between electronic correlations and nontrivial band topology.     

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.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z_2 Topological Insulator

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator(TI) and topological crystalline insulator(TCI) in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.     

Topological phase in one-dimensional Rashba wire

We study the possible topological phase in a one-dimensional(1D) quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps forming in the bulk energy band and fractional boundary states residing in the gap when the system has an inversion symmetry. These states are topologically nontrivial and can be characterized by a quantized Berry phase ±π or nonzero Chern number through dimensional extension. When the Rashba spin–orbital coupling varies slowly with time, the system can pump out 2 charges in a pumping cycle because of the spin flip effect. This quantized pumping is protected by topology and is robust against moderate disorders as long as the disorder strength does not exceed the opened energy gap.     

The quantum anomalous Hall effect on a star lattice with spin-orbit coupling and an exchange field

We study a star lattice with Rashba spin-orbit coupling and an exchange field and find that there is a quantum anomalous Hall effect in this system, and that there are five energy gaps at Dirac points and quadratic band crossing points. We calculate the Berry curvature distribution and obtain the Hall conductivity (Chern number ν) quantized as integers, and find that ν?=-?1,2,1,1,2 when the Fermi level lies in these five gaps. Our model can be viewed as a general quantum anomalous Hall system and, in limit cases, can give what the honeycomb lattice and kagome lattice give. We also find that there is a nearly flat band with ν?=?1 which may provide an opportunity for realizing the fractional quantum anomalous Hall effect. Finally, the chiral edge states on a zigzag star lattice are given numerically, to confirm the topological property of this system.     

Topological surface States in three-dimensional magnetic insulators

An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these "Hopf insulators" are characterized by a topological invariant as in quantum Hall states and Z2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the three-sphere to the two-sphere. This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model.     

Electronic states with nontrivial topology in Dirac materials

The theoretical studies of phase states with a linear dispersion of the spectrum of low-energy electron excitations have been reviewed. Some main properties and methods of experimental study of these states in socalled Dirac materials have been discussed in detail. The results of modern studies of symmetry-protected electronic states with nontrivial topology have been reported. Combination of approaches based on geometry with homotopic topology methods and results of condensed matter physics makes it possible to clarify new features of topological insulators, as well as Dirac and Weyl semimetals.     

Topological superconductivity in Janus monolayer transition metal dichalcogenides

The Janus monolayer transition metal dichalcogenides (TMDs) $MXY$ ($M={\rm Mo}$, W, $etc$. and $X, Y={\rm S}$, Se, $etc$.) have been successfully synthesized in recent years. The Rashba spin splitting in these compounds arises due to the breaking of out-of-plane mirror symmetry. Here we study the pairing symmetry of superconducting Janus monolayer TMDs within the weak-coupling framework near critical temperature $T_{\rm c}$, of which the Fermi surface (FS) sheets centered around both $ărGamma$ and $K (K')$ points. We find that the strong Rashba splitting produces two kinds of topological superconducting states which differ from that in its parent compounds. More specifically, at relatively high chemical potentials, we obtain a time-reversal invariant $s + f + p$-wave mixed superconducting state, which is fully gapped and topologically nontrivial, $i.e.$, a $\mathbb{Z}_2$ topological state. On the other hand, a time-reversal symmetry breaking $d + p + f$-wave superconducting state appears at lower chemical potentials. This state possess a large Chern number $|C|=6$ at appropriate pairing strength, demonstrating its nontrivial band topology. Our results suggest the Janus monolayer TMDs to be a promising candidate for the intrinsic helical and chiral topological superconductors.     

Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy

Three-dimensional (3D) topological insulators represent a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The unusual surface states of topological insulators rise from the nontrivial topology of their electronic structures as a result of strong spin-orbital coupling. In this review, we will briefly introduce the concept of topological insulators and the experimental method that can directly probe their unique electronic structure: angle resolved photoemission spectroscopy (ARPES). A few examples are then presented to demonstrate the unique band structures of different families of topological insulators and the unusual properties of the topological surface states. Finally, we will briefly discuss the future development of topological quantum materials.     

Multiple coherence resonances by time-periodic coupling strength in scale-free networks of bursting neurons

We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects arise in the case of a sufficiently flat energy band as well as a roughly flat and homogeneous Berry curvature, such that the global Chern number, which is a topological invariant, may be associated with a local non-commutative geometry. This geometry is similar to the more familiar situation of the fractional quantum Hall effect in two-dimensional electron systems in a strong magnetic field.     

Aspects of Floquet bands and topological phase transitions in a continuously driven superlattice

The recent creation of novel topological states of matter via periodic driving fields has attracted much attention. To contribute to the growing knowledge on this subject, we study the well-known Harper-Aubry-André model modified by a continuous time-periodic modulation and report on its topological properties along with several other interesting features. The Floquet bands are found to have non-zero Chern numbers which are generally different from those in the original static model. Topological phase transitions (discontinuous change of Chern numbers) take place as we tune the amplitude or period of the driving field. We demonstrate that the non-trivial Floquet band topology manifests via the quantized transport of Wannier states in the lattice space. For certain parameter choices, very flat yet topologically non-trivial Floquet bands emerge, a feature potentially useful for simulating the physics of strongly correlated systems. In some cases with an even number of Floquet bands, the spectrum features linearly dispersing Dirac cones which hold potential for the simulation of high energy physics or Klein tunnelling. Taking open boundary conditions, we observe anomalous counter-propagating chiral edge modes and degenerate zero modes. We end by discussing how these theoretical predictions may be verified experimentally.     

Topological transport in Dirac electronic systems:A concise review

Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters protected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase and Berry curvature, which provide precise definitions of the topological phases. In this topical review, transport properties of topological insulator(Bi2Se3), topological Dirac semimetal(Cd3As2), and topological insulator-graphene heterojunction are presented and discussed. Perspectives about transport properties of two-dimensional topological nontrivial systems,including topological edge transport, topological valley transport, and topological Weyl semimetals, are provided.     

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one and two dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the pseudo-quantum electrodynamics (PQED). The well-known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well-known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.     

Topological Anderson insulator in two-dimensional non-Hermitian systems

We study the disorder-induced phase transition in two-dimensional non-Hermitian systems. First, the applicability of the noncommutative geometric method(NGM) in non-Hermitian systems is examined. By calculating the Chern number of two different systems(a square sample and a cylindrical one), the numerical results calculated by NGM are compared with the analytical one, and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction. Then, we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect. For the square sample, the stability of the non-Hermitian Chern insulator under disorder is confirmed. Significantly,we obtain a nontrivial topological phase induced by disorder. This phase is understood as the topological Anderson insulator in non-Hermitian systems. Finally, the disordered phase transition in the cylindrical sample is also investigated. The clean non-Hermitian cylindrical sample has three phases, and such samples show more phase transitions by varying the disorder strength:(1) the normal insulator phase to the gapless phase,(2) the normal insulator phase to the topological Anderson insulator phase, and(3) the gapless phase to the topological Anderson insulator phase.     

Higher-Order Topological Spin Hall Effect of Sound

We theoretically propose a reconfigurable two-dimensional(2 D) hexagonal sonic crystal with higher-order topology protected by the six-fold,C_6,rotation symmetry.The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit cell.In the nontrivial phase,the sonic crystal realizes the topological spin Hall effect in a higher-order fashion:(i) the edge states emerging in the bulk band gap exhibit partial spin-momentum correlation and are gapped due to the reduced spatial symmetry at the edges.(ii) The gapped edge states,on the other hand,stabilize the topological corner states emerging in the edge band gap.The partial spin-momentum correlation is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta,where the pseudospin is emulated by the acoustic orbital angular momentum.We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.     

Topological nature of the phonon Hall effect

We provide a topological understanding of the phonon Hall effect in dielectrics with Raman spin-phonon coupling. A general expression for phonon Hall conductivity is obtained in terms of the Berry curvature of band structures. We find a nonmonotonic behavior of phonon Hall conductivity as a function of the magnetic field. Moreover, we observe a phase transition in the phonon Hall effect, which corresponds to the sudden change of band topology, characterized by the altering of integer Chern numbers. This can be explained by touching and splitting of phonon bands.     

High Chern number phase in topological insulator multilayer structures: A Dirac cone model study

We employ the Dirac cone model to explore the high Chern number (C) phases that are realized in the magnetic-doped topological insulator (TI) multilayer structures by Zhao et al. [Nature 588 419 (2020)]. The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters, then the Chern number phase diagrams of the TI multilayer structures are obtained. The high-C behavior is attributed to the band inversion of the renormalized Dirac cones, along with which the spin polarization at the $\varGamma$ point will get increased. Moreover, another two TI multilayer structures as well as the TI superlattice structures are studied.     

二维三角格点系统中的拓扑陈数

利用紧束缚模型对二维三角周期格点中各能带的陈数分布进行研究.通过严格对角化方法得到体系能量本征值和对应的本征态，再利用Kubo公式计算出量子化的霍尔电导、态密度及各扩展态对应的陈数.在傅里叶变换下将哈密顿量转换到k空间从而得到体系的能谱分布.研究表明：次近邻格点之间的跳跃积分t'的不同取值影响体系各能带对应的陈数分布，计算得到当t'=1/2时体系三个能带从低到高对应的陈数分布为{-4，5，-1}，t'=-1/2时其对应陈数分布变化为{2，-4，2}，而t'=±1/4时对应的陈数分布都为{2，-1，-1}.同时发现：能谱帯隙的宽度和对应霍尔平台的宽度一致，并且k空间的能带越平坦，其对应的在霍尔电导跳跃处的态密度峰就越高越尖锐，而该处霍尔电导跳跃就越陡峭.