Topologically-protected Edge States Research Articles

Observation of Topological Transmission in Terahertz Domino Waveguide Array

In this paper, we propose on-chip terahertz domino waveguide array structures which can enable the topological effect and enhance the robustness of terahertz transmission. Terahertz topological effect (include topologically-protected edge states and binding states) is excited by constructing kink and antikink structures in designed domino waveguide arrays. Furthermore, the robustness of topological waveguide arrays is successfully demonstrated. The topological transmission effects have been experimentally demonstrated using scanning near-field terahertz microscopy. Our study provides a new approach to study the topological photonic transport of waveguide arrays in the terahertz regime and has potential application in terahertz integrated circuit.

Analytic expressions for topologically protected edge states in Su–Schrieffer–Heeger model

The Su–Schrieffer–Heeger (SSH) model can demonstrate the topological phase transition of spinless fermions in a two-dimensional square lattice. In this work, we investigate the topologically protected edge states (TESs) in 1D SSH ribbons by using the wave mechanics approach. A concise analytic equation is derived to determine the localization length of TESs. Based on the resulted localization length, the explicit analytic expressions are given for the energy dispersions and wave functions of TESs in 1D SSH ribbons. The effect of the size of the 1D SSH ribbon on the topological phase transition and the critical exponent of the localization length of TESs are further demonstrated. It also shows that the degeneracy of TESs is lifted due to the coupling of the two-side TESs. Our results can elucidate the TESs appearing in nontrivial phase, and can also be employed to optimize the structure of the nanoribbon devices.

All-optical logic gates based on anomalous Floquet photonic topological insulator structures

Topological photonics is an incipient research area where the well-developed theory and applications of so-called topological insulators is applied to photonic systems. In that vein, specially-designed ring waveguides, arranged in a periodic structure and evanescently coupled, have shown the ability to propagate edge states that are robust against defects in the lattice. Here, we propose the application of photonic topologically-protected edge states (TPES) in the anomalous Floquet photonic topological insulator structures to develop a device that is able to behave as OR, AND, and XOR logic gates, depending on the characteristics of the excitation field. Materials and dimensions of the device are amenable to conventional fabrication methods, opening the possibility for implementation in on-chip photonic communication technology. We conclude by applying our results to the implementation of an all-optical two bit calculator based on TPES, a potential building block for future computational technology.

Topological protection in non-Hermitian Haldane honeycomb lattices

Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically-protected edge states in non-Hermitian lattices has sparked an intensive search for systems where this kind of states are sustained. Here, we present the first study on the emergence of topological edge states in two-dimensional Haldane lattices exhibiting balanced gain and loss. In line with recent studies on other Chern insulator models, we show that edge states can be observed in the so-called broken $\mathcal{P}\mathcal{T}$-symmetric phase, that is, when the spectrum of the gain-loss-balanced system's Hamiltonian is not entirely real. More importantly, we find that such topologically protected edge states emerge irrespective of the lattice boundaries, namely zigzag, bearded or armchair.

A bipartite Kronig–Penney model with Dirac-delta potential scatterers

Here we present a simple extension to the age-old Kronig–Penney model, which is made to be bipartite by varying either the scatterer separations or the potential heights. In doing so, chiral (sublattice) symmetry can be introduced. When such a symmetry is present, topological chiral symmetry protected edge states are seen to exist in correspondence with the standard quantised Zak phase bulk invariant. This quantisation behaviour may also be observed within a ‘gauge’-invariant on-diagonal matrix element of a unit eigenvalue equation. The solution proceeds through the conventional scattering formalism used to study the Kronig–Penney model, which does not require further tight-binding approximations or mapping into a Su–Schrieffer–Heeger model. The cases in which chiral symmetry is absent are then seen to not host topologically protected edge states, as verified by zero bulk invariants.

Reconfigurable topological insulator for elastic waves.

Inspired by the quantum valley Hall effect, a mechanical topological insulator (TI) purposely built for reconfigurability is proposed and experimentally demonstrated. An aluminum plate serves as the host medium with periodically arranged voids and fixed inclusions used to break mirror symmetry. Reconfigurability is derived from the ability to easily alter the imperfection type (void or fixed inclusion) in any unit cell. The corresponding band structure of the proposed hexagonal unit cell is obtained using numerical means, which documents double-folded Dirac cones at the K-points. The breaking of mirror symmetry results in a topologically protected bandgap. Furthermore, topologically protected edge states (TPES) at the interface of two structures with opposite Chern numbers have been demonstrated numerically, and verified experimentally, for different desired trajectories. These TPES are robust against backscattering at defect locations and sharp bends. The proposed reconfigurable TI can be a stepping-stone platform toward building mechanical logic and circuits, which have advantages over electronic equivalents in harsh operating conditions, or to replace wireless systems near dead-zones of metallic and carbon fiber structures.

Topological pumping of edge states via adiabatic passage

Topological pumping of edge states in finite crystals or quasicrystals with non-trivial topological phases provides a powerful means for robust excitation transfer. In most schemes of topological pumping, the edge states become delocalized and immersed into the continuum during the adiabatic cycle, requiring extremely slow evolution to avoid nonadiabatic effects. Here a scheme of topological pumping based on adiabatic passage of edge and interface states is proposed, which is more robust against nonadiabatic effects and avoids delocalization of the state over the entire adiabatic cycle. The scheme is illustrated by considering adiabatic passage in a system sustaining two topologically-protected edge states and one interface state, realized by interfacing two dimerized Su-Schrieffer-Heeger chains with different topological order

Interaction quench and thermalization in a one-dimensional topological Kondo insulator

We study the nonequilibrium dynamics of a one-dimensional topological Kondo insulator, modelled by a $p$-wave Anderson lattice model, following a quantum quench of the on-site interaction strength. Our goal is to examine how the quench influences the topological properties of the system, therefore our main focus is the time evolution of the string order parameter, entanglement spectrum and the topologically-protected edge states. We point out that postquench local observables can be well captured by a thermal ensemble up to a certain interaction strength. Our results demonstrate that the topological properties after the interaction quench are preserved. Though the absolute value of the string order parameter decays in time, the analysis of the entanglement spectrum, Loschmidt echo and the edge states indicates the robustness of the topological properties in the time-evolved state. These predictions could be directly tested in state-of-the-art cold-atom experiments.

Novel conductance step in carbon nanotube with wing-like zigzag graphene nanoribbons**Project supported by the National Natural Science Foundation of China (Grant No. 10947004) and the Government Scholarship for Overseas Studies of Jiangsu Province, China.

Connecting one armchair carbon nanotube (CNT) to several zigzag graphene nanoribbons (ZGNRs) we find that the topologically-protected edge states of ZGNRs and the massless Dirac particle inherited from CNT still hold from the analysis of the band structure and the edge state. Furthermore, the lowest conductance step at the valley bottom increases proportionally with increasing the number of ZGNR wings. A novel conductance step of a peak occurs in the valley, which is two steps higher than the lowest step at the valley bottom. In addition, with increasing the number of ZGNR wings the width of the novel conductance step becomes narrow.

Non-Hermitian bidirectional robust transport

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-enviroment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996)], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically-protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the Hatano- Nelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

Controlled Coupling of Spin-Resolved Quantum Hall Edge States

We introduce and experimentally demonstrate a new method that allows us to controllably couple copropagating spin-resolved edge states of a two-dimensional electron gas (2DEG) in the integer quantum Hall regime. The scheme exploits a spatially periodic in-plane magnetic field that is created by an array of Cobalt nanomagnets placed at the boundary of the 2DEG. A maximum charge or spin transfer of 28±1% is achieved at 250 mK.