Topological phonon polaritons in one-dimensional non-Hermitian silicon carbide nanoparticle chains

Abstract

Topological phonon polaritons (TPhPs) are highly protected and localized edge modes that are capable of achieving a strong confinement of electromagnetic waves and immune to impurities and disorder. Here we realize TPhPs by constructing one-dimensional dimerized silicon carbide nanoparticle chains, which mimic the topological property of the well-known Su-Schrieffer-Heeger (SSH) model. We analytically calculate the complex band structure of such chains by taking all nearfield and far-field dipole-dipole interactions into account. For longitudinal modes, we demonstrate that, despite the non-Hermiticity and breaking of the chiral symmetry, the band topology can be still characterized by the complex Zak phase, which is quantized and indicates a topological phase transition when the dimerization parameter β changes from less than 0.5 to larger than 0.5, like the conventional Hermitian SSH model. By calculating the eigenmodes of a finite chain, we find such a dimerized chain with β > 0.5 supports nontrivial topological eigenmodes localized over both of its edges, indicating the validity of the bulk-boundary correspondence. On the other hand, for transverse modes, we discover a topological phase transition by increasing the lattice constant, which is due to the presence of strong long-range far-field dipole-dipole interactions decaying with the distance r as 1/r for an infinitely long chain. However, we surprisingly find the emergence of non-Hermitian skin effect in a finite chain, which leads to the breakdown of the bulk-boundary correspondence. Furthermore, by incorporating the effect of localized bulk eigenmodes and proposing a modified complex Zak phase for a finite lattice, we still recover the topological behavior of the conventional SSH model. Our comprehensive study provides profound implications to the fields of non-Hermitian topological physics and quantum mechanical models with long-range interactions. In addition to the theoretical analysis, we demonstrate the excitation of the topological phonon polaritons and show their enhancement to the photonic LDOS. These TPhPs offer an efficient tool for enhancing light-matter interaction in the mid-infrared. arXiv:1807.08276v3 [cond-mat.mes-hall]

Wideband tunable infrared topological plasmon polaritons in dimerized chains of doped-silicon nanoparticles

“…which is related to the difference of the winding of the off-diagonal elements of the effective Hamiltonian around the origin. It is shown that although the present system is non-Hermitian and exhibits a breaking of chiral symmetry, the complex Zak phase is still quantized (only two values, 0 and π, are allowed) in a similar way as in a chirally symmetric system due to the fact that the eigenvectors are independent of the diagonal elements of the effective Hamiltonian [17,35,36]. According to Eq.…”

“…To see the localization behavior more clearly, here N = 2000 is used for the chain. We can find that for higher doping concentrations, the localization length of the topological edge modes become longer, which is a result of smaller interparticle dipole-dipole interactions [36]. To be more specific, with higher concentrations, the frequency of the topological modes becomes higher, leading to a shorter resonance wavelength.…”

“…Then we describe the electric dipole approximation and the coupled-dipole model. On this basis, the analytical calculation of the Bloch band structure for an infinitely long chain and the eigenmode distribution for a finite lattice are given [36].…”

“…In our system, the dipole moments of the NPs in the longitudinal eigenmodes are polarized along the x-axis, while those in the transverse eigenmodes are polarized perpendicular to the x-axis. In this paper, we are mainly concerned with the longitudinal eigenmodes because transverse ones are more strongly coupled to the free-space radiation and the band gap of transverse eigenmodes is much narrower, which makes it difficult to observe these topological eigenmodes experimentally [35,36].…”

“…Here z + = exp (i(k + k x )d) and z − = exp (i(k − k x )d), and Li s (z) is polylogrithm (or Jonquiére's function) Li s (z) = ∞ n=1 z n /n s sum series [54]. The off-diagonal elements are [36]…”