Phase-controlled topological plasmons in 1D graphene nanoribbon array

In this Letter, we report on the phase-controlled topological plasmons in 1D graphene nanoribbons (GNRs) based on a Su−Schrieffer−Heeger (SSH) model variant. By considering the dipole–dipole mode interactions, we first study the normal SSH model by an effective Hamiltonian and calculate the Zak phase as a topological invariant, finding that it is nontrivial (trivial) when the coupling distance is bigger (smaller) than half the period. Then, we reveal that the edge modes with fields highly localized at only one side exist in the model with nontrivial topology and shows the robustness of strong field confinement and extreme frequency stability against in-plane and out-of-plane disorders. Finally, we introduce the offset SSH model variant by vertically offsetting one of the GNR in SSH unit, which allows us to greatly engineer both the width of topological gap and the number of topological windows. The underlying physics are uncovered by defining a parameter called phase difference, which reveals that the topological edge modes appear (disappear) generally near the positions where the inter-unit coupling strength is bigger (smaller) than the intra-unit coupling strength, and, more notably, the phase difference is around even (odd) multiple numbers of π, which is much different from the normal SSH model where the topological phase is simply affected by the resonator distance. In addition to opening up a possibility to explore the fundamental physics of topologically protected graphene plasmons, this work also offers potential applications of these concepts to design graphene-based plasmon devices with immunity to structural imperfections.

[1]  S. Wen,et al.  Topological plasmons in stacked graphene nanoribbons. , 2023, Optics letters.

[2]  Si-Yuan Yu,et al.  Tunable Topological Fano Resonances in Graphene-Based Nanomechanical Lattices , 2022, Physical Review Applied.

[3]  S. Wen,et al.  Plasmonically induced transparency in phase-coupled graphene nanoribbons , 2022, Physical Review B.

[4]  Yueke Wang,et al.  Graphene-based dual-band near-perfect absorption in Rabi splitting between topological edge and Fabry–Perot cavity modes , 2021, Journal of Optics.

[5]  N. Peres,et al.  Topological Graphene Plasmons in a Plasmonic Realization of the Su–Schrieffer–Heeger Model , 2021, ACS Photonics.

[6]  Jiangfeng Du,et al.  Dynamic Observation of Topological Soliton States in a Programmable Nanomechanical Lattice. , 2021, Nano letters.

[7]  W. Hsueh,et al.  Tunable light absorption of graphene using topological interface states. , 2020, Optics letters.

[8]  M. Soljačić,et al.  Observation of topologically enabled unidirectional guided resonances , 2020, Nature.

[9]  R. Ma,et al.  A high-performance topological bulk laser based on band-inversion-induced reflection , 2019, Nature Nanotechnology.

[10]  C. Y. Zhao,et al.  Terahertz topological plasmon polaritons for robust temperature sensing , 2019, Physical Review Materials.

[11]  C. Y. Zhao,et al.  Wideband tunable infrared topological plasmon polaritons in dimerized chains of doped-silicon nanoparticles , 2019, Journal of Applied Physics.

[12]  S. Haas,et al.  Localized plasmons in topological insulators , 2019, Physical Review B.

[13]  Jeffery W. Allen,et al.  Electrically defined topological interface states of graphene surface plasmons based on a gate-tunable quantum Bragg grating , 2019, Nanophotonics.

[14]  R. El-Ganainy,et al.  Experimental Realization of Multiple Topological Edge States in a 1D Photonic Lattice , 2019, Laser & Photonics Reviews.

[15]  Lei Wang,et al.  Nonlinear light generation in topological nanostructures , 2018, Nature Nanotechnology.

[16]  Changying Zhao,et al.  Topological phonon polaritons in one-dimensional non-Hermitian silicon carbide nanoparticle chains , 2018, Physical Review B.

[17]  S. Wen,et al.  Plasmonically induced transparency in double-layered graphene nanoribbons , 2018, Photonics Research.

[18]  A. Sihvola,et al.  Resonances in small scatterers with impedance boundary , 2018, Physical Review B.

[19]  C. Y. Zhao,et al.  Topological photonic states in one-dimensional dimerized ultracold atomic chains , 2018, 1804.00157.

[20]  M. Bandres,et al.  Topological insulator laser: Experiments , 2018, Science.

[21]  F. A. Pinheiro,et al.  Edge modes of scattering chains with aperiodic order. , 2018, Optics letters.

[22]  Gennady Shvets,et al.  Two-dimensional topological photonics , 2017, Nature Photonics.

[23]  Simon R. Pocock,et al.  The effects of retardation on the topological plasmonic chain: plasmonic edge states beyond the quasistatic limit , 2017, 1710.09782.

[24]  Xiang Zhang,et al.  Infrared Topological Plasmons in Graphene. , 2017, Physical review letters.

[25]  Deng Pan,et al.  Topologically protected Dirac plasmons in a graphene superlattice , 2017, Nature Communications.

[26]  Weijia Wen,et al.  Topological edge modes in multilayer graphene systems. , 2015, Optics express.

[27]  F. G. D. Abajo,et al.  Plasmon wave function of graphene nanoribbons , 2015 .

[28]  A. Jauho,et al.  Localized plasmons in graphene-coated nanospheres , 2014, 1412.7042.

[29]  M. Soljačić,et al.  Topological photonics , 2014, Nature Photonics.

[30]  F. D. Abajo,et al.  Graphene Plasmonics: Challenges and Opportunities , 2014, 1402.1969.

[31]  Yuri S. Kivshar,et al.  Topological Majorana States in Zigzag Chains of Plasmonic Nanoparticles , 2014 .

[32]  Z. Q. Zhang,et al.  Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems , 2014, 1401.1309.

[33]  C. T. Chan,et al.  Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide , 2014, Nature Communications.

[34]  A Goetschy,et al.  Non-Hermitian Euclidean random matrix theory. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Zheng Wang,et al.  Observation of unidirectional backscattering-immune topological electromagnetic states , 2009, Nature.

[36]  Zak,et al.  Berry's phase for energy bands in solids. , 1989, Physical review letters.