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Recently, topological chains have attracted extensive attention because of their simple structure, rich physics and important applications. In this work, we theoretically and experimentally uncover that the abundant topological phases of periodic trimer chain composed of one kind of meta-atom, namely split-ring resonators (SRRs), can be flexibly controlled by tunning the rotation angle of SRRs. On the one hand, we study the rotation controlled phase transition between two topological distinguished trimer chains with inversion symmetry. The generation of symmetric edge states can be easily controlled in this phase transition. On the other hand, the topological phases of the trimer chain broken inversion symmetry is demonstrated. Especially, the rotation controlled asymmetric edge states are observed in this process. So, rotation provides a new degree of freedom to manipulate edge states in the trimer chain composed of SRRs. The results in this work not only provide a flexible way to observe controlled edge states, but also provide a good research platform for designing other topological models with complex coupling distributions. [ABSTRACT FROM AUTHOR]

In this paper, plasmonic responses of phosphorene in the presence of strain and doping have been systematically investigated. Based on density functional theory, permittivities include both the intraband and interband transitions of electrons have been calculated. Due to the modification of the band structure, significantly higher Drude plasma frequency has been observed along the zigzag direction, other than the armchair direction as in the usual case. The resulting unusual plasmonic responses change their anisotropy, both in the elliptic as well as the hyperbolic regimes. Based on our calculations, positive strain as large as 5% along the zigzag direction can even lead to so-called reversed hyperbolic plasmonic responses. The k -surfaces of the plasmonic modes in extended monolayer have been analytically solved, and it is found that actively switching the topology (between elliptic and hyperbolic regimes) of the plasmonic responses by changing the Fermi level is possible in phosphorene at certain frequencies. In the end, a simple model has been proposed to describe such plasmonic responses in the infrared and the parameters of the model have been listed in tables which can be used directly in calculating the permittivities. Our studies may extend the scope of existing investigations of phosphorene plasmons and lead to band engineering as a way to control plasmons in two-dimensional materials.

In this study, a Dirac cone is yielded at the corner of the Brillouin zone of a two-dimensional solid phononic crystal, which consists of a triangular array of hexagonal steel with a trilobal hole drilled in the center. With the rotation of the trilobal hole, the Dirac degeneracy switches between the deterministic form and accidental form. Every Dirac point is the critical state of a topological phase transition process, which occurs six times within an angular period of $120^\circ .$ This structure offers a flexible way to achieve topological transitions and provides multiple routes to construct an interface that supports valley-dependent edge states between two topologically distinct PCs. The associated backscattering suppressed wave propagation along the multiple curved interface channels is also demonstrated. In addition, our design shows the robust propagation of topological interface states against the perturbation of the structure. This study could potentially be significant in the design of acoustic devices for practical applications, such as acoustic signal lossless transport and tunable multi-channel sound transmission.

Stanene, as a counterpart of graphene, but with much larger spin–orbit coupling (SOC) strength, has recently been synthesized experimentally. Based on first principle calculations and an effective model, we systematically study the electronic and topological properties of bulk stanene under vertical electric field and biaxial strain, which can be naturally introduced by substrates. We find that a topological nontrivial–trivial transition occurs under a critical vertical electric field and an insulator–metal transition happens under critical biaxial strains. We also systematically study the edge state of zigzag nanoribbons. We find that the topological edge state has strong nonlinear dispersion that is different from the previous oversimplified tight-binding (TB) model. A much more practical TB model is built, which captures the strongly nonlinear dispersion of the edge states very well. We investigate four magnetic configurations of the zigzag ribbon edge states in detail and find that the emergence of magnetism for the edge atoms and the magnetization direction have a remarkable impact on the spin-current-carrying edge channels. Furthermore, a half-metallic state can be induced in stanene nanoribbons by applying a transverse electric field, and opposite spin channels can be chosen by reversing the electric field direction. Our results are instructive for future research and applications on stanene and other related buckled systems.