Possible gapless helical edge states in hydrogenated graphene.

Electronic band structures in hydrogenated graphene are theoretically investigated by means of first-principle calculations and an effective tight-binding model. It is shown that regularly designed hydrogenation to graphene gives rise to a large band gap about 1 eV. Remarkably, by changing the spatial pattern of the hydrogenation, topologically distinct states can be realized, where the topological nontriviality is detected by C 2 parity indices in bulk and confirmed by the existence of gapless edge/interface states as protected by the mirror and sublattice symmetries. The analysis of the wave functions reveals that the helical edge states in hydrogenated graphene with the appropriate design carry pseudospin currents that are reminiscent of the quantum spin Hall effect. Our work shows the potential of hydrogenated graphene in pseudospin-based device applications.

Topological electronic states in holey graphyne.

We unveil that the holey graphyne (HGY), a two-dimensional carbon allotrope where benzene rings are connected by two -C≡C- bonds fabricated recently in a bottom-up way, exhibits topological electronic states. Using first-principles calculations and Wannier tight-binding modeling, we discover a higher-order topological invariant associated withC2symmetry of the material, and show that the resultant corner modes appear in nanoflakes matching to the structure of precursor reported previously, which are ready for direct experimental observations. In addition, we find that a band inversion between emergentg-like andh-like orbitals gives rise to a nontrivial topology characterized byZ2invariant protected by an energy gap as large as 0.52 eV, manifesting helical edge states mimicking those in the prominent quantum spin Hall effect, which can be accessed experimentally after hydrogenation in HGY. We hope these findings trigger interests towards exploring the topological electronic states in HGY and related future electronics applications.

Topological photonic crystal fiber with honeycomb structure.

We analyze a new type of photonic crystal fiber which consists of the core and cladding that distinct in topology by tuning the position of air holes in each hexagonal unit cell where the C6v symmetry is respected. The p-d band inversion between the core and cladding leads to topological interface modes inside the band gap, which can propagate along the fiber with a nonzero momentum in perpendicular to the corss section of a fiber. The helical topological interface modes possess the pseudospin-momentum locking effect inherited from the corresonding two-dimensional photonic crystal characterized by the Z2 topology. The wave functions for the topological interface modes are analytically studied and compared successfully to the numerical results, enlighting a novel way to use photonic crystal fiber to transfer information.

Topological magnon modes on honeycomb lattice with coupling textures.

Topological magnon modes are expected to be useful for novel applications such as robust information propagation, since they are immune to backscattering and robust against disorder. Although there are several theoretical proposals for topological magnon modes and growing experimental efforts for realizing them by now, it is still desirable to add complementary insights on this important phenomenon. Here, we propose a new scheme to achieve topological magnon where only nearest-neighbour exchange couplings on honeycomb lattice are necessary. In both ferromagnets and antiferromagnets, tuning exchange couplings between and inside hexagonal unit cells induces a topological state accompanied by a band inversion between p-orbital and d-orbital like magnon modes. Topological magnon modes appear at the interface between a topological domain and a trivial domain with magnon currents, which counterpropagate depending on pseudospins originated from orbital angular momenta of magnon modes. This mimics the spin-momentum locking phenomenon in the quantum spin Hall effect.

Many-Body Chern Number without Integration.

The celebrated work of Niu, Thouless, and Wu demonstrated the quantization of Hall conductance in the presence of many-body interactions by revealing the many-body counterpart of the Chern number. The generalized Chern number is formulated in terms of the twisted angles of the boundary condition, instead of the single particle momentum, and involves an integration over all possible twisted angles. However, this formulation is physically unnatural, since topological invariants directly related to observables should be defined for each Hamiltonian under a fixed boundary condition. In this work, we show via numerical calculations that the integration is indeed unnecessary-the integrand itself is effectively quantized and the error decays exponentially with the system size. This implies that the numerical cost in computing the many-body Chern number could, in principle, be significantly reduced as it suffices to compute the Berry connection for a single value of the twisted boundary condition if the system size is sufficiently large.

Topological LC-circuits based on microstrips and observation of electromagnetic modes with orbital angular momentum.

New structures with richer electromagnetic properties are in high demand for developing novel microwave and optic devices aimed at realizing fast light-based information transfer and information processing. Here we show theoretically that a topological photonic state exists in a hexagonal LC circuit with short-range textures in the inductance, which is induced by a band inversion between p- and d-like electromagnetic modes carrying orbital angular momentum, and realize this state experimentally in planar microstrip arrays. Measuring both amplitude and phase of the out-of-plane electric field accurately using microwave near-field techniques, we demonstrate directly that topological interfacial electromagnetic waves launched by a linearly polarized dipole source propagate in opposite directions according to the sign of the orbital angular momentum. The open planar structure adopted in the present approach leaves much room for including other elements useful for advanced information processing, such as electric/mechanical resonators, superconducting Josephson junctions and SQUIDs.

Z_{N} Berry Phases in Symmetry Protected Topological Phases.

We show that the Z_{N} Berry phase (Berry phase quantized into 2π/N) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed through numerics of a relatively small system size. The Z_{N} Berry phase is defined in a N-1-dimensional parameter space of local gauge twists, which we call the "synthetic Brillouin zone," and an appropriate choice of an integration path consistent with the symmetry of the system ensures exact quantization of the Berry phase. We demonstrate the usefulness of the Z_{N} Berry phase by studying two 1D models of bosons, SU(3) and SU(4) Affleck-Kennedy-Lieb-Tasaki models, where topological phase transitions are captured by Z_{3} and Z_{4} Berry phases, respectively. We find that the exact quantization of the Z_{N} Berry phase at the topological transitions arises from a gapless band structure (e.g., Dirac cones or nodal lines) in the synthetic Brillouin zone.

Topological States Characterized by Mirror Winding Numbers in Graphene with Bond Modulation.

Localized electrons appear at the zigzag-shaped edge of graphene due to quantum interference. Here we propose a way for harnessing the edge electronic states to make them mobile, by incorporating a topological view point. The manipulation required is to introduce a pattern of strong-weak bonds between neighboring carbon atoms, and to put side by side two graphene sheets with strong-weak alternation conjugating to each other. The electrons with up and down pseudospins propagate in opposite directions at the interface, similar to the prominent quantum spin Hall effect. The system is characterized by a topological index, the mirror winding number, with its root lying in the Su-Schrieffer-Heeger model for polymer. Taking this point of view, one is rewarded by several ways for decorating graphene edge which result in similar mobile electronic states with topological protection. This work demonstrates that celebrated nanotechnology can be used to derive topological states.

Manipulation of Dirac Cones in Mechanical Graphene.

Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton's law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the "Chern number" occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton's law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases.