144 research outputs found
Unconventional Flatband Line States in Photonic Lieb Lattices
Flatband systems typically host "compact localized states"(CLS) due to
destructive interference and macroscopic degeneracy of Bloch wave functions
associated with a dispersionless energy band. Using a photonic Lieb
lattice(LL), we show that conventional localized flatband states are inherently
incomplete, with the missing modes manifested as extended line states which
form non-contractible loops winding around the entire lattice. Experimentally,
we develop a continuous-wave laser writing technique to establish a
finite-sized photonic LL with specially-tailored boundaries, thereby directly
observe the unusually extended flatband line states.Such unconventional line
states cannot be expressed as a linear combination of the previously observed
CLS but rather arise from the nontrivial real-space topology.The robustness of
the line states to imperfect excitation conditions is discussed, and their
potential applications are illustrated
Photonic realization of a generic type of graphene edge states exhibiting topological flat band
Cutting a honeycomb lattice (HCL) can end up with three types of edges
(zigzag, bearded and armchair), as is well known in the study of graphene edge
states. Here we theoretically investigate and experimentally demonstrate a
class of graphene edges, namely, the twig-shaped edges, using a photonic
platform, thereby observing edge states distinctive from those observed before.
Our main findings are: (i) the twig edge is a generic type of HCL edges
complementary to the armchair edge, formed by choosing the right primitive cell
rather than simple lattice cutting or Klein edge modification; (ii) the twig
edge states form a complete flat band across the Brillouin zone with
zero-energy degeneracy, characterized by nontrivial topological winding of the
lattice Hamiltonian; (iii) the twig edge states can be elongated or compactly
localized along the boundary, manifesting both flat band and topological
features. Such new edge states are realized in a laser-written photonic
graphene and well corroborated by numerical simulations. Our results may
broaden the understanding of graphene edge states, bringing about new
possibilities for wave localization in artificial Dirac-like materials.Comment: 13 pages, 4 figure
Persistent homology analysis of a generalized Aubry-Andr\'{e}-Harper model
Observing critical phases in lattice models is challenging due to the need to
analyze the finite time or size scaling of observables. We study how the
computational topology technique of persistent homology can be used to
characterize phases of a generalized Aubry-Andr\'{e}-Harper model. The
persistent entropy and mean squared lifetime of features obtained using
persistent homology behave similarly to conventional measures (Shannon entropy
and inverse participation ratio) and can distinguish localized, extended, and
crticial phases. However, we find that the persistent entropy also clearly
distinguishes ordered from disordered regimes of the model. The persistent
homology approach can be applied to both the energy eigenstates and the
wavepacket propagation dynamics.Comment: Published version. 8 pages, 9 figure
Flatband Line States in Photonic Super-Honeycomb Lattices
We establish experimentally a photonic super-honeycomb lattice (sHCL) by use
of a cw-laser writing technique, and thereby demonstrate two distinct flatband
line states that manifest as noncontractible-loop-states in an infinite
flatband lattice. These localized states (straight and zigzag lines) observed
in the sHCL with tailored boundaries cannot be obtained by superposition of
conventional compact localized states because they represent a new topological
entity in flatband systems. In fact, the zigzag-line states, unique to the
sHCL, are in contradistinction with those previously observed in the Kagome and
Lieb lattices. Their momentum-space spectrum emerges in the high-order
Brillouin zone where the flat band touches the dispersive bands, revealing the
characteristic of topologically protected bandcrossing. Our experimental
results are corroborated by numerical simulations based on the coupled mode
theory. This work may provide insight to Dirac like 2D materials beyond
graphene
Quantitative Analysis of Porous Silicon Nanoparticles Functionaliza-tion by 1H NMR
Porous silicon (PSi) nanoparticles have been applied in various fields, such as catalysis, imaging, and biomedical applications, because of their large specific surface area, easily modifiable surface chemistry, biocompatibility, and biodegradability. For biomedical applications, it is important to precisely control the surface modification of PSi-based materials and quantify the functionalization density, which determines the nanoparticle’s behavior in the biological system. Therefore, we propose here an optimized solution to quantify the functionalization groups on PSi, based on the nuclear magnetic resonance (NMR) method by combining the hydrolysis with standard 1H NMR experiments. We optimized the hydrolysis conditions to degrade the PSi, providing mobility to the molecules for NMR detection. The NMR parameters were also optimized by relaxation delay and the number of scans to provide reliable NMR spectra. With an internal standard, we quantitatively analyzed the surficial amine groups and their sequential modification of polyethylene glycol. Our investigation provides a reliable, fast, and straightforward method in quantitative analysis of the surficial modification characterization of PSi requiring a small amount of sample.Peer reviewe
Universal momentum-to-real-space mapping of topological singularities
Topological properties of materials, as manifested in the intriguing
phenomena of quantum Hall effect and topological insulators, have attracted
overwhelming transdisciplinary interest in recent years. Topological edge
states, for instance, have been realized in versatile systems including
electromagnetic-waves. Typically, topological properties are revealed in
momentum space, using concepts such as Chern number and Berry phase. Here, we
demonstrate a universal mapping of the topology of Dirac-like cones from
momentum space to real space. We evince the mapping by exciting the cones in
photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with
vortex beams of topological charge l, optimally aligned for a chosen pseudospin
state s, leading to direct observation of topological charge conversion that
follows the rule of l to l+2s. The mapping is theoretically accounted for all
initial excitation conditions with the pseudospin-orbit interaction and
nontrivial Berry phases. Surprisingly, such a mapping exists even in a deformed
lattice where the total angular momentum is not conserved, unveiling its
topological origin. The universality of the mapping extends beyond the photonic
platform and 2D lattices: equivalent topological conversion occurs for 3D
Dirac-Weyl synthetic magnetic monopoles, which could be realized in ultracold
atomic gases and responsible for mechanism behind the vortex creation in
electron beams traversing a magnetic monopole field
Realization of robust boundary modes and non-contractible loop states in photonic Kagome lattices
Corbino-geometry has well-known applications in physics, as in the design of
graphene heterostructures for detecting fractional quantum Hall states or
superconducting waveguides for illustrating circuit quantum electrodynamics.
Here, we propose and demonstrate a photonic Kagome lattice in the
Corbino-geometry that leads to direct observation of non-contractible loop
states protected by real-space topology. Such states represent the "missing"
flat-band eigenmodes, manifested as one-dimensional loops winding around a
torus, or lines infinitely extending to the entire flat-band lattice. In finite
(truncated) Kagome lattices, however, line states cannot preserve as they are
no longer the eigenmodes, in sharp contrast to the case of Lieb lattices. Using
a continuous-wave laser writing technique, we experimentally establish finite
Kagome lattices with desired cutting edges, as well as in the Corbino-geometry
to eliminate edge effects. We thereby observe, for the first time to our
knowledge, the robust boundary modes exhibiting self-healing properties, and
the localized modes along toroidal direction as a direct manifestation of the
non-contractible loop states
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