Nonlinear dynamical stability of gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice

We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice. Honeycomb lattices possess a unique band structure, the first and second bands intersect at a set of so-called Dirac points. Deformation can result in the merging and disappearance of the Dirac points, and support the gap solitons. We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures being in-phase or out-of-phase. We also investigate the linear stabilities and nonlinear stabilities of these gap solitons. These results have applications of the localized structures in nonlinear optics, and may helpful for exploiting topological properties of a deformed lattice.     

基于复合蜂窝结构的宽带周期与非周期声拓扑绝缘体

具有良好可重构性、良好缺陷兼容性及紧凑型的声学拓扑结构可能成为声学发展中一个有前景的方向.本文设计了一种可调谐、应用于空气声的二维宽带复合蜂窝形晶格结构,其元胞拥有两个变量:一个是中心圆的缩放参数s,另一个是"花瓣"图案围绕其质心的旋转角度q.研究发现当s为1.2, q为±33°时,在结构的布里渊区中心点出现四重简并态.在±33°两侧,能带会发生反转,体系经历拓扑相变;同时,结构的相对带隙宽带逐渐增加,其中q为0°和60°时,相对带宽分别为0.39和0.33.本研究还计算了由这两种转角的声子晶体组成的拼合结构的投影能带,发现在其体带隙中存在着边界态并验证了此拓扑边界的缺陷免疫特性.最后通过变化s,构建了一种非周期性双狄拉克锥型的声拓扑绝缘体并验证了其缺陷免疫性.本研究的体系相对带宽显著超过已知体系,将为利用声拓扑边界的声波器件微型化打下良好的基础.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

Strongly nonlinear topological phases of cascaded topoelectrical circuits

Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and transitions in one-dimensional electrical circuits composed of nonlinear capacitors. Nonlinear topological interface modes arise on domain walls of the circuit lattices, whose topological phases are controlled by the amplitudes of nonlinear voltage waves. Experimentally measured topological transition amplitudes are in good agreement with those derived from nonlinear topological band theory. Our prototype paves the way towards flexible metamaterials with amplitude-controlled rich topological phases and is readily extendable to two and three-dimensional systems that allow novel applications.     

Impurity Effects at Surfaces of a Photon-Dressed Bi_2Se_3 Thin Film

We investigate the impurity effects on surfaces of a thin film topological insulator, applied by an off-resonant circular polarized light. It is found that the off-resonant driving induces a quantized total Hall conductivity, when the driving strength is larger than a critical value and the Fermi level lies in the band gap, indicating that our system is converted into the topological phase. We also find that with the increasing disorder strength, the Dirac masses of top and bottom surfaces are renormalized and then fixed to half of their initial values, respectively,which will shrink the widths of the half-integer plateau of anomalous Hall conductivities.     

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.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom--field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index $k$ is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom--field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

Interface-induced topological phase and doping-modulated bandgap of two-dimensioanl graphene-like networks

Biphenylene is a new topological material that has attracted much attention recently. By amplifying its size of unit cell, we construct a series of planar structures as homogeneous carbon allotropes in the form of polyphenylene networks. We first use the low-energy effective model to prove the topological three periodicity for these allotropes. Then, through first-principles calculations, we show that the topological phase has the Dirac point. As the size of per unit cell increases, the influence of the quaternary rings decreases, leading to a reduction in the anisotropy of the system, and the Dirac cone undergoes a transition from type II to type I. We confirm that there are two kinds of non-trivial topological phases with gapless and gapped bulk dispersion. Furthermore, we add a built-in electric field to the gapless system by doping with B and N atoms, which opens a gap for the bulk dispersion. Finally, by manipulating the built-in electric field, the dispersion relations of the edge modes will be transformed into a linear type. These findings provide a hopeful approach for designing the topological carbon-based materials with controllable properties of edge states.     

Nature of the intrinsic relation between Bloch-band tunneling and modulational instability

In an example of Bose-Einstein condensates embedded in two-dimensional optical lattices, we show that in nonlinear periodic systems modulational instability and interband tunneling are intrinsically related phenomena. By direct numerical simulations we find that tunneling results in attenuation or enhancement of instability. On the other hand, instability results in asymmetric nonlinear tunneling. The effect strongly depends on the band gap structure and it is especially significant in the case of the resonant tunneling. The symmetry of the coherent structures emerging from the instability reflects the symmetry of both the stable and the unstable states between which the tunneling occurs. Our results provide evidence of the profound effect of the band structure on the superfluid-insulator transition.     

Bloch-Zener oscillations across a merging transition of Dirac points

Bloch oscillations are a powerful tool to investigate spectra with Dirac points. By varying band parameters, Dirac points can be manipulated and merged at a topological transition toward a gapped phase. Under a constant force, a Fermi sea initially in the lower band performs Bloch oscillations and may Zener tunnel to the upper band mostly at the location of the Dirac points. The tunneling probability is computed from the low-energy universal Hamiltonian describing the vicinity of the merging. The agreement with a recent experiment on cold atoms in an optical lattice is very good.     

Photoinduced anisotropic edge states and signatures of nonequilibrium spin polarization in silicene nanoribbons

Most topological phase transitions are accompanied by the emergence of surface/edge states with spin dependence. Usually, the quantized Hall conductivity cannot characterize the anisotropic transports and spin dependence of topological states. Here, we study the intricate topological phase transition and the anisotropic behavior of edge states in silicene nanoribbon submitted to an electric field or/and a light irradiation. It is interesting to find that a circularly polarized light can induce a type-II quantum anomaly Hall phase, which is manifested as the high Chern number and the strong anisotropic edge states. Besides the measurement of the quantized Hall conductivity, we further propose to probe these topological phase transitions and the anisotropy of edge states by measuring the current-induced nonequilibrium spin polarization. It is found that the spin polarization exhibits more signatures about the behavior of surface/edge states, beyond the quantized Hall conductivity, especially for spin-dependent transports with different velocities.     

采用振幅耦合方法研究多旋转中心混沌振子的相同步

为了找到具有多个旋转中心的混沌系统的相同步与其动力学拓朴变化之间的对应关系，采用线性振幅线性耦合方法，研究了Lorenz系统和Duffing系统的相同步，首先对Lorenz系统和Duffing系统分别进行极坐标变换，在线性振幅耦合基础上计算了两个系统的平均旋转数和Lyapunov指数，发现，随耦合强度的增大，系统相同步与系统的Lyapunov指数跃变存在一一对应的关系，这表明具有多个旋转中心的混沌系统的相同步与系统动力学拓朴变化也存在着对应关系. 关键词： Lyapunov指数 振幅耦合 相同步     

Tailoring edge and interface states in topological metastructures exhibiting the acoustic valley Hall effect

In this study, we investigate the acoustic topological insulator or topological metastructure, where an acoustic wave can exist only in an edge or interface state instead of propagating in bulk. Breaking the structural symmetry enables the opening of the Dirac cone in the band structure and the generation of a new band gap, wherein a topological edge or interface state emerges.Further, we systematically analyze two types of topological states that stem from the acoustic valley Hall effect mechanism;one type is confined to the boundary, whereas the other type can be observed at the interface between two topologically different structures. Results denote that the selection of different boundaries along with appropriately designed interfaces provides the acoustic waves in the band gap range with abilities of one-way propagation, dual-channel propagation, immunity from backscattering at sharp corners, and/or transition between propagation at interfaces and boundaries. Furthermore, we show that the acoustic wave propagation paths can be tailored in diverse and arbitrary ways by combing the two aforementioned types of topological states.     

Zone folding induced tunable topological interface states in one-dimensional phononic crystal plates

In previous literature, the realization of topological interface state in one-dimensional periodic system is strongly relied on the tedious parameter adjustment to search for the Dirac cone. In this paper, based on a strategy of zone folding, multiple topological interface modes for the shear horizontal guided waves in one dimensional phononic crystal plate are investigated by using finite element method and eigenmode matching theory, in which the Dirac points are formed by simply making the unit cell double. Significantly, by simply contracting or expanding the stubs can bring the topological phase transition. Furthermore, the topological phase transition is further achieved by varying the height of the stubs. The proposed designs will be more convenient to be applied in real engineering.     

一维颗粒声子晶体的拓扑相变及可调界面态

基于Su-Schrieffer-Heeger模型,构造了一种一维非线性声子晶体,通过调控外加在声子晶体上的预紧力,可调控声子晶体的拓扑态,从而实现拓扑相变.利用这一效应,把该非线性声子晶体与另一线性声子晶体形成异质结构,可以实现一种新型声学开关:通过调节预紧力即调控非线性声子晶体的拓扑相,可以实现异质结构中界面态从无到有的转变,从而实现了开关效应.利用该效应可望开发新型声学器件,如可调谐振器、可调滤波器、可调隔振器等.     

基于手性声子晶体的谷拓扑声输运

研究手性风车形散射体构建的谷拓扑声波导。具有右手与左手手性风车形散射体的声子晶体具有截然不同的声谷拓扑特性。当两种手性风车形散射体从-60°旋转到60°时,其所构建的声子晶体均出现2次偶然简并的狄拉克点与谷霍尔相变。基于两种具有相反谷霍尔相的手性声子晶体构建的谷拓扑声波导,在其重叠体带隙内存在一对局域在波导分界面处的谷态边缘态。实验研究表明,该边缘态可以很好的支持谷拓扑声输运,且对弯曲与无序两种缺陷具有一定的鲁棒性.      

Coupling-matrix approach to the Chern number calculation in disordered systems

The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.     

Topological phase transition in cavity optomechanical system with periodical modulation

We investigate the topological phase transition and the enhanced topological effect in a cavity optomechanical system with periodical modulation. By calculating the steady-state equations of the system, the steady-state conditions of cavity fields and the restricted conditions of effective optomechanical couplings are demonstrated. It is found that the cavity optomechanical system can be modulated to different topological Su-Schrieffer-Heeger (SSH) phases via designing the optomechanical couplings legitimately. Meanwhile, combining the effective optomechanical couplings and the probability distributions of gap states, we reveal the topological phase transition between trivial SSH phase and nontrivial SSH phase via adjusting the decay rates of cavity fields. Moreover, we find that the enhanced topological effect of gap states can be achieved by enlarging the size of system and adjusting the decay rates of cavity fields.     

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.