An official website of the United States government
Abstract Modern technological advances allow for the study of systems with additional synthetic dimensions. Higher-order topological insulators in topological states of matters have been pursued in lower physical dimensions by exploiting synthetic dimensions with phase transitions. While synthetic dimensions can be rendered in the photonics and cold atomic gases, little to no work has been succeeded in acoustics because acoustic wave-guides cannot be weakly coupled in a continuous fashion. Here, we formulate the theoretical principles and manufacture acoustic crystals composed of arrays of acoustic cavities strongly coupled through modulated channels to evidence one-dimensional (1D) and two-dimensional (2D) dynamic topological pumpings. In particular, the higher-order topological edge-bulk-edge and corner-bulk-corner transport are physically illustrated in finite-sized acoustic structures. We delineate the generated 2D and four-dimensional (4D) quantum Hall effects by calculating first and second Chern numbers and physically demonstrate robustness against the geometrical imperfections. Synthetic dimensions could provide a powerful way for acoustic topological wave steering and open up a platform to explore any continuous orbit in higher-order topological matter in dimensions four and higher.
more »
« less
Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries
The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA—the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.
more »
« less
- Award ID(s):
- 1809915
- PAR ID:
- 10347557
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 34
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Higher‐order topological insulators (HOTIs) represent a new type of topological system, supporting boundary states localized over boundaries, two or more dimensions lower than the dimensionality of the system itself. Interestingly, photonic HOTIs can possess a richer physics than their original condensed matter counterpart, supporting conventional HOTI states based on tight‐binding coupling, and a new type of topological HOTI states enabled by long‐range interactions. Here, a new mechanism to establish all‐dielectric infrared HOTI metasurfaces exhibiting both types of HOTI states is proposed, supported by a topological transition accompanied by the emergence of topological Wannier‐type polarization. Two kinds of near‐field experimental studies are performed: i) the solid immersion spectroscopy and ii) near‐field imaging using scattering scanning near‐field optical microscopy to directly observe the topological transition and the emergence of HOTI states of two types. It is shown that the near‐field profiles indicate the displacement of the Wannier center across the topological transition leading to the topological dipole polarization and emergence of the topological boundary states. The proposed all‐dielectric HOTI metasurface offers a new approach to confine the optical field in micro‐ and nano‐scale topological cavities and thus paves the way to achieve a novel nanophotonic technology.more » « less
-
Classical wave systems have constituted an excellent platform for emulating complex quantum phenomena, such as demonstrating topological phenomena in photonics and acoustics. Recently, a new class of topological states localized in more than one dimension of a D -dimensional system, referred to as higher-order topological (HOT) states, has been reported, offering an even more versatile platform to confine and control classical radiation and mechanical motion. Here, we design and experimentally study a 3D topological acoustic metamaterial supporting third-order (0D) topological corner states along with second-order (1D) edge states and first-order (2D) surface states within the same topological bandgap, thus establishing a full hierarchy of nontrivial bulk polarization–induced states in three dimensions. The assembled 3D topological metamaterial represents the acoustic analog of a pyrochlore lattice made of interconnected molecules, and is shown to exhibit topological bulk polarization, leading to the emergence of boundary states.more » « less
-
Abstract The emergence of a fractal energy spectrum is the quintessence of the interplay between two periodic parameters with incommensurate length scales. crystals can emulate such interplay and also exhibit a topological bulk-boundary correspondence, enabled by their nontrivial topology in virtual dimensions. Here we propose, fabricate and experimentally test a reconfigurable one-dimensional (1D) acoustic array, in which the resonant frequencies of each element can be independently fine-tuned by a piston. We map experimentally the full Hofstadter butterfly spectrum by measuring the acoustic density of states distributed over frequency while varying the long-range order of the array. Furthermore, by adiabatically changing the phason of the array, we map topologically protected fractal boundary states, which are shown to be pumped from one edge to the other. This reconfigurable crystal serves as a model for future extensions to electronics, photonics and mechanics, as well as to quasi-crystalline systems in higher dimensions.more » « less
-
Topological photonics allows for the deterministic creation of electromagnetic modes of any dimensionality lesser than that of the system. In the context of two-dimensional systems such as metasurfaces, topological photonics enables trapping of light in 0D cavities defined by boundaries of higher-order topological insulators and topological defects, as well as guiding of optical fields along 1D boundaries between topologically distinct domains. More importantly, it allows engineering interactions of topological modes with radiative continuum, which opens new opportunities to control light-matter interactions, scattering, generation, and emission of light. This review article aims at highlighting recent work in the field focusing on the control of radiation and generation of light in topological metasurfaces.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2100691118
