The feasibility of realizing a photonic Floquet topological insulator (PFTI) in an atomic ensemble is demonstrated by Yiqi Zhang et al. (pp. 331–338) . The interference of three coupling fields will split energy levels periodically, to form a periodic refractive index structure with honeycomb profile that can be adjusted by different frequency detunings and intensities of the coupling fields. This in turn will affect the appearance of Dirac cones in momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, gaps open at Dirac points, and one obtains a PFTI in an atomic vapor. An obliquely incident beam will be able to move along the zigzag edge of the lattice without scattering energy into the PFTI, due to the confinement of edge states. The appearance of Dirac cones and the formation of a photonic Floquet topological insulator can be shut down by the third‐order nonlinear susceptibility and opened up by the fifth‐order one. 相似文献
Topological aspects of the electronic properties of graphene,
including edge effects, with the tight-binding model
on a honeycomb lattice and its extensions
to show the following:
(i) Presence of the pair of massless Dirac dispersions, which is the
origin of anomalous properties including a peculiar quantum Hall
effect (QHE), is not accidental to honeycomb, but is
generic for a class of two-dimensional lattices that interpolate
between square and π-flux lattices. Topological stability
guarantees persistence of the peculiar QHE.
(ii) While we have the massless Dirac dispersion only around E=0,
the anomalous QHE associated with the Dirac cone
unexpectedly persists for a wide range of the chemical potential.
The range is bounded by van Hove singularities, at which we predict
a transition to the ordinary fermion behaviour accompanied by
huge jumps in the QHE with a sign change.
(iii) We establish a coincidence between the quantum Hall effect
in the bulk and the quantum Hall effect for the edge states,
which is another topological effect. We have also explicitly
shown that the E=0 edge states in honeycomb in zero
magnetic field persist in magnetic field.
(iv) We have also identified a topological origin of the
fermion doubling in terms of the chiral symmetry. 相似文献
We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects. 相似文献
The feasibility of realizing a photonic Floquet topological insulator (PFTI) in an atomic ensemble is demonstrated. The interference of three coupling fields will split energy levels periodically, to form a periodic refractive index structure with honeycomb profile that can be adjusted by different frequency detunings and intensities of the coupling fields. This in turn will affect the appearance of Dirac cones in momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, gaps open at Dirac points, and one obtains a PFTI in an atomic vapor. An obliquely incident beam will be able to move along the zigzag edge of the lattice without scattering energy into the PFTI, due to the confinement of edge states. The appearance of Dirac cones and the formation of a photonic Floquet topological insulator can be shut down by the third‐order nonlinear susceptibility and opened up by the fifth‐order one.
Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson–hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points. 相似文献
The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieblattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) anduniform exchange field. The Lieb lattice has a simple cubic symmetry, which ischaracterized by the single Dirac-cone per Brillouin zone and the middle flat band in theband structure. The intrinsic SOC is essentially needed to open the full energy gap in thebulk. The QSH effect could survive even in the presence of the exchange field. In terms ofthe first Chern number and the spin Chern number, we study the topological nature and thetopological phase transition from the time-reversal symmetry broken QSH effect to the QAHeffect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributionsare obtained numerically, where the helical edge states and the chiral edge states revealthe non-trivial topological QSH and QAH properties, respectively. 相似文献
In this paper, we find that topological insulators with time-reversal symmetryand inversion symmetry featuring two-dimensional quantum spin Hall (QSH) state can be divided into 16 classes, which are characterized by four Z2topological variables ζk=0,1 at four points with high symmetry in the Brillouin zone. We obtain the corresponding edge states for each one of these sixteen classes of QSHs. In addition, it is predicted that massless fermionic excitations appear at the quantum phase transition between different QSH states. In the end, we also briefly discuss the three-dimensional case. 相似文献
Topological quantum states have attracted great attention both theoretically and experimentally.Here,we show that the momentum-space lattice allows us to couple two Su-Schrieffer-Heeger(SSH)chains with opposite dimerizations and staggered interleg hoppings.The coupled SSH chain is a four-band model which has sublattice symmetry similar to the SSH4.Interestingly,the topological edge states occupy two sublattices at the same time,which can be regarded as a one-dimension analogue of the type-II corner state.The analytical expressions of the edge states are also obtained by solving the eigenequations.Finally,we provide a possible experimental scheme to detect the topological winding number and corresponding edge states. 相似文献
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics. 相似文献
We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice and also describe novel coherent states where the populations of clockwise and anticlockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems, including optically induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices. 相似文献
It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triplepoint semimetal phases, can emerge in antiferromagnetic(AFM) half-Heusler compounds. However, how to determine the AFM structure and to distinguish different topological phases from transport behaviors remains unknown. We show that, due to the presence of combined time-reversal and fractional translation symmetry, the recently proposed second-order nonlinear Hall effect can be used to characterize different topological phases with various AFM configurations. Guided by the symmetry analysis, we obtain expressions of the Berry curvature dipole for different AFM configurations. Based on the effective model, we explicitly calculate the Berry curvature dipole, which is found to be vanishingly small for the triple-point semimetal phase, and large in the Weyl semimetal phase. Our results not only put forward an effective method for the identification of magnetic orders and topological phases in AFM half-Heusler materials, but also suggest these materials as a versatile platform for engineering the nonlinear Hall effect. 相似文献
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. 相似文献
The quantum spin Hall (QSH) effect is considered to be unstable to perturbations violating the time-reversal (TR) symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced. 相似文献