#### Date of Degree

5-2019

#### Document Type

Dissertation

#### Degree Name

Ph.D.

#### Program

Physics

#### Advisor

Alexander B. Khanikaev

#### Committee Members

Azriel Z. Genack

Andrea Alu

Vinod Menon

Pouyan Ghaemi

#### Subject Categories

Condensed Matter Physics | Engineering Physics | Optics | Other Physics | Quantum Physics

#### Keywords

photonic Klein tunneling, far field probing, non-Hermitian topology, PT phase transition, generalized chiral symmetry, acoustic crystalline insulator

#### Abstract

Recent surge of interest in topological insulators, insulating in their interior but conducting at the surfaces or interfaces of different domains, has led to the discovery of a variety of new topological states, and their topological invariants are characterized by numerous approaches in the category of topological band theory. The common features shared by topological insulators include, the topological phase transition occurs if the bulk bandgap is formed due to the symmetries reduction, the topological invariants exist characterizing the global properties of the material and inherently robust to disorder and continuous perturbations irrespective of the local details. Most importantly, these topological systems might support dissipation-free boundary transport of electrons or zero dimensional localization of solid states.

Topological insulators have not only attracted tremendous attentions from the communities of condensed matter, but also inspired various explorations in classical systems by their unique properties such as robustness against many forms of perturbations, as well as the ability to emulate exotic quantum states of matter. A variety of topological systems, including the bulk polarized crystalline insulator, quantum Hall effect edge state and quantum spin-Hall effect in 2D and 3D, Floquet topological insulator as well as topological crystalline insulators, have been emulated with great success in electromagnetic material, mechanical and acoustic crystal, encouraging the use of their exotic characteristics in practical applications.

Based on these motivations, to study topological phenomena in classical systems, several projects have been investigated in this thesis. In Chapter 3, the one-way Dirac-like conical dispersion is achieved in the bi-anisotropic photonic crystal at the crossover of valley Hall effect and analog quantum spin Hall effect in photonics. In our design, the inversion symmetry of the triangular photonic lattice is reduced by triangularizing the rods, leading to the topological valley Hall effect. In addition, the pseudo spin-orbit interaction created by bi-anisotropic couplings of the electromagnetic waves transits the system from the normal insulating regime into the quantum spin Hall regime. It is shown that such effective response of energy dispersion has dramatic implications on photon transport. First of all, pseudo spin and valley dependent one-way Klein tunneling is observed in the photonic platform. In addition, the one-way propagating edge states coexist with the bulk continuum which has opposite pseudo spin polarization compared to the states of edge. These exotic phenomena offer new ways for the future application of one-way broadcast by selective excitation on the multiple degrees of freedom of the photons.

In chapter 4, we show the topological states of an open photonic system can be explored via far field measurement. To observe the topological transition of the bulk modes, we design and fabricate a photonic crystal slab made of silicon pillars and operated at the near-infrared spectral range. Since the Dirac-like cones of interest are above the light cone of the air, the pseudo spin modes of Dirac-like cones can couple to the continuum of the environment through radiation. Besides, dipolar polarized modes have larger coupling to the external excitation than the quadrupolar polarized modes because of symmetries matching of modes and source. Using these facts, we measure the angle resolved far field transmittance/reflectance spectra, which reveal inversion between the bulk dispersions of topological lattice and trivial lattice via observing the switching of dark and bright spectra. Additionally, the topological invariant is extracted by fitting the experimental spectra with the coupled modes equations. What’s more, the topological edge states located at the stitched domain walls are also probed by the far field extinction, thus further confirm the topological properties of the system.

In chapter 5, we demonstrate that the parity-time (PT) symmetric interfaces formed between non-Hermitian amplifying (“gainy”) and lossy topological crystals exhibit PT phase transitions separating phases of lossless and decaying/amplifying topological edge transport. *Exceptional points *(EPs) are found in these complex-valued interface spectra separating* *(i)* *PT symmetric real-valued regime with evenly distributed wavefunction in both gainy and lossy domains and (ii) PT broken complex-valued regime, in which edge states predominantly localize in one of the domains. Despite its complex-valued character, the edge spectrum remains gapless in the imaginary direction and interconnects complex-valued bulk bands through the EPs. We find that the regimes exist when the real edge spectrum is embedded into the bulk continuum without mixing. The proposed systems are experimentally feasible in photonics, which is evidenced by our rigorous full-wave simulations of PT-symmetric all dielectric photonic graphene. Besides valley topological states, Chern topological phases are also investigated in the non-Hermitian Haldane model. Interestingly, despite the complex bulk spectrum of the Chern insulator, the bulk-interface correspondence principle still holds, as long as the topological gap remains open. PT symmetric-interfaced Haldane model also support the PT phase transition of the edge states.

In chapter 6, we introduce a new class of topological crystals characterized by nontrivial bulk polarization. In addition to edge conduction, these systems have been shown to host Wannier type higher-order topological states, the corner states at a specific geometry. We introduce and measure topological bulk polarization in 3D printed two-dimensional acoustic meta-structures, and observe topological transitions as the design parameters are tuned. We also demonstrate that the topological meta-structure hosts both 1D edge and Wannier-type second-order corner states through acoustic density of states measurement. We observe the second order topological states protected by the generalized chiral symmetry of the meta-structure, which are localized at the corners and are pinned to ‘zero energy’. The generalized chiral symmetry of the three-atom sublattice also enables the corner states spectral overlap with the continuum of bulk states without leakage at some parameter range. The confinement and inherent robustness of the corner states is theoretically analyzed and experimentally confirmed by deliberately introducing disorder. Furthermore, the edge states have the angular momentum that reverses for opposite propagation direction, thus supporting directional excitation.

#### Recommended Citation

Ni, Xiang, "Topological Insulating States in Photonics and Acoustics" (2019). *CUNY Academic Works.*

https://academicworks.cuny.edu/gc_etds/3146

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#### Included in

Condensed Matter Physics Commons, Engineering Physics Commons, Optics Commons, Other Physics Commons, Quantum Physics Commons