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.     

Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

We investigate novel features of three-dimensional non-Hermitian Weyl semimetals,paying special attention to the unconventional bulk-boundary correspondence.We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram,which is also confirmed by the energy spectra from our numerical results.It is shown that,in sharp contrast to Hermitian systems,the conventional(Bloch)bulk-boundary correspondence breaks down in non-Hermitian topological semimetals,which is caused by the non-Hermitian skin effect.We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals:the topological edge modes are determined by the non-Bloch Chern number of the bulk bands.Moreover,these topological edge modes can manifest as the unidirectional edge motion,and their signatures are consistent with the non-Bloch bulk-boundary correspondence.Our work establishes the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.     

Topologically protected edge gap solitons of interacting Bosons in one-dimensional superlattices

We comprehensively investigate the nontrivial states of an interacting Bose system in a cosine potential under the open boundary condition. Our results show that there exists a kind of stable localized state: edge gap solitons. We argue that the states originate from the eigenstates of independent edge parabolas. In particular, the edge gap solitons exhibit a nonzero topological-invariant behavior. The topological nature is due to the connection of the present model to the quantized adiabatic particle transport problem. In addition, the composition relations between the gap solitons and the extended states are also discussed.     

Bloch oscillations in GaAs/AlGaAs superlattices after excitation well above the bandgap

Bloch oscillations of wave packets in semiconductor superlattices are observed by THz-emission spectroscopy after pulsed photo-excitation well above the fundamental band-gap. We show that Bloch oscillations are induced by excitation of states in both the first and the second electron miniband.     

Effect of disorders on topological phases in one-dimensional optical superlattices

In a recent paper, Lang et al. proposed that edge states and topological phases can be observed in one-dimensional optical superlattices. They showed that the topological phases can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions. However, disorders are not considered in their model. To study the effect of disorders on the topological phases, we introduce random potentials to the model for optical superlattcies.Our calculations show that edge states are robust against the disorders. We find the edge states are very sensitive to the number of the sites in the optical superlattice and we propose a simple rule to describe the relationship between the edge states and the number of sites. The density plateaus are also robust against weak disorders provided that the average density is calculated over a long interval. The widths of the plateaus are proportional to the widths of the bulk energy gaps when there are disorders. The disorders can diminish the bulk energy gaps. So the widths of the plateaus decrease with the increase of disorders and the density plateaus disappear when disorders are too strong. The results in our paper can be used to guide the experimental detection of topological phases in one-dimensional systems.     

The appearance of gap solitons in a nonlinear Schrödinger lattice

We study the appearance of discrete gap solitons in a nonlinear Schrödinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase (q=π/2) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this “nonlinear gap boundary” are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose-Einstein condensates in periodic potentials. For lattices whose gap edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.     

THz-field induced nonlinear transport and dc voltage generation in a semiconductor superlattice due to Bloch oscillations

We report on a theoretical analysis of terahertz (THz-) field induced nonlinear dynamics of electrons in a semiconductor superlattice that are capable to perform Bloch oscillations. Our results suggest that for a strong THz-field a dc voltage should be generated. We have analyzed the real-time dynamics using a balance equation approach to describe the electron transport in a superlattice miniband. Taking account of both Bloch oscillations of electrons in a superlattice miniband and dissipation, we studied the influence of a strong THz-field on currently available superlattices at room temperature. We found that a THz-field can lead to a negative conductance resulting in turn in a THz-field induced dc voltage, and that the voltage per superlattice period should show, for varying amplitue of the THz-field, a form of wisted plateaus with the middle points being with high precision equal to the photon energy divided by the electron charge. We show voltage to the finite voltage state, and that in the finite voltage state dynamic localization of the electrons in a miniband occurs.     

Topology of a parity-time symmetric non-Hermitian rhombic lattice

We investigate the topological properties of a trimerized parity–time(PT)symmetric non-Hermitian rhombic lattice.Although the system is PT-symmetric,the topology is not inherited from the Hermitian lattice;in contrast,the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices.The bulk–boundary correspondence is valid and the Bloch bulk captures the band topology.Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach.In addition,the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice.Our findings reveal the topological properties of the??PT-symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases.     

Topological insulator: Spintronics and quantum computations

Topological insulators are emergent states of quantum matter that are gapped in the bulk with timereversal symmetry-preserved gapless edge/surface states, adiabatically distinct from conventional materials. By proximity to various magnets and superconductors, topological insulators show novel physics at the interfaces, which give rise to two new areas named topological spintronics and topological quantum computation. Effects in the former such as the spin torques, spin-charge conversion, topological antiferromagnetic spintronics, and skyrmions realized in topological systems will be addressed. In the latter, a superconducting pairing gap leads to a state that supports Majorana fermions states, which may provide a new path for realizing topological quantum computation. Various signatures of Majorana zero modes/edge mode in topological superconductors will be discussed. The review ends by outlooks and potential applications of topological insulators. Topological superconductors that are fabricated using topological insulators with superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.     

Observation of multivortex solitons in photonic lattices

We report on the first observation of topologically stable spatially localized multivortex solitons generated in optically induced hexagonal photonic lattices. We demonstrate that topological stabilization of such nonlinear localized states can be achieved through self-trapping of truncated two-dimensional Bloch waves and confirm our experimental results by numerical simulations of the beam propagation in weakly deformed lattice potentials in anisotropic photorefractive media.     

Exact confined eigenstates in one-dimensional finite periodic systems with arbitrary symmetric basis

A set of eigenenergy equations for complete confinement of N periodic one-dimensional system with arbitrary symmetric potential in each cell is presented. Exact eigenenergies and their eigenfunctions are solved analytically. We find different solutions on the band edge states comparing early results solved by conventional methods. Our results show that higher band edge state of each bandgap is dependent on the confined length, but lower band edge state is independent of the length. Moreover, wavefunctions for lower band edge states are Bloch waves but those for other eigenstates, including higher band edge states, do not obey Bloch waves.     

Tamm oscillations in semi-infinite nonlinear waveguide arrays

We demonstrate the existence of nonlinear Tamm oscillations at the interface between a substrate and a one-dimensional waveguide array with either cubic or saturable, self-focusing or self-defocusing nonlinearity. Light is trapped in the vicinity of the array boundary due to the interplay between the repulsive edge potential and Bragg reflection inside the array. In the special case when this potential is linear these oscillations reduce themselves to surface Bloch oscillations.     

Linear and nonlinear vibrations and waves in optical or acoustic superlattices (photonic or phonon crystals)

A model of a dielectric or an elastic superlattice is proposed which describes quite simply the frequency spectrum of electromagnetic or acoustic waves. The frequency band spectrum of a one-dimensional lattice consists of minibands, which narrow down with increasing frequency (so that the forbidden bands in the spectrum broaden with increasing frequency). An elementary analysis of the spectrum of a one-dimensional lattice reveals the presence of many forbidden frequency bands in this case as well. It is shown that dynamic equations for superlattices can be generalized to the nonlinear case, leading to equations of the type of the nonlinear Schrödinger equation for the lattice. Soliton excitations are described and the particle-like dynamics of solitons is demonstrated. Local vibrations near point defects of different complexity in superlattices are studied and graphically illustrated. The existence of Bloch oscillations of a wave packet in a superlattice in a homogeneous external field is discussed.     

Band structures of bilayer graphene superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of "topological" edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.     

On the topological explanation of the integer quantum hall effect

We investigate the static and dynamic Kubo Hall conductivity of a non-interacting electron system in a random potential on a torus. Considering the universal covering space of the torus the Bloch theorem is applied for rational values of the filling factor. The localisation is simulated by the assumption of bound states. The Hall conductivity at zero temperatur is shown to be topologically quantized, if the Fermi energy lies in a spectral gap or in a localisation regime. The relation to previous formulations of the topological approach to the integer quantum Hall effect (QHE) is discussed.     

Topological horseshoe in nonlinear Bloch system

This paper demonstrates rigorous chaotic dynamics in nonlinear Bloch system by virtue of topological horseshoe and numerical method. It considers a properly chosen cross section and the corresponding Poincar'e map, and shows the existence of horseshoe in the Poincar'e map. In this way, a rigorous verification of chaos in the nonlinear Bloch system is presented.     

Pseudo topological insulators

We predict pseudo topological insulators that have been previously overlooked. We determine some conditions under which robust pseudo topological edge states appear and illustrate our idea on the Su–Schrieffer–Heeger (SSH) model with extra chiral symmetry breaking potentials. We discuss that pseudo topological insulating phase transition occurs without band gap closing.     

时间反演对称性破缺系统中的拓扑零能模

Su-Schreiffer-Heeger模型预测了在一维周期晶格的边缘处可能出现零维的拓扑零能模,其能量本征值总是出现在能隙的正中间.本文以半导体微腔阵列中光子和激子在强耦合情况下形成的准粒子为例,通过准粒子的自旋轨道耦合与Zeeman效应,研究了时间反演对称性破缺对拓扑零能模的影响.发现拓扑零能模的能量本征值可以随着自旋轨道耦合强度的变化在整个带隙内移动,自旋相反的模式移动方向相反;在二维微腔阵列中发现了沿着晶格边缘移动的拓扑零能模,提出了一维零能模的概念.由于时间反演对称性的破缺,这种一维拓扑零能模解除了在相反传输方向上的能级的简并,从而在传输过程中出现极强的绕过障碍物的能力.     

Photogalvanic effects in topological insulators

We discuss optical absorption in topological insulators and study possible photoelectric effects theoretically. We found that absorption of circularly polarized electromagnetic waves in two-dimensional topological insulators results in electric current in the conducting 1D edge channels, the direction of the current being determined by the light polarization. We suggest two ways of inducing such a current: due to magnetic dipole electron transitions stimulated by irradiation of frequency below the bulk energy gap, and due to electric dipole transitions in the bulk at frequencies larger than the energy gap with subsequent capture of the photogenerated carriers on conducting edge states.