Topological insulators have unconventional gapless edge states where disorder-induced back-scattering is suppressed. In photonics, such edge states lead to unidirectional waveguides which are useful for integrated photonic circuitry. Cavity modes, another type of fundamental component in photonic chips, however, are not protected by band topology because of their lower dimensions. Here we demonstrate that concurrent wavevector space and real-space topology, dubbed as dual-topology, can lead to light-trapping in lower dimensions. The resultant photonic-bound state emerges as a Jackiw–Rebbi soliton mode localized on a dislocation in a two-dimensional photonic crystal, as proposed theoretically and discovered experimentally. Such a strongly confined cavity mode is found to be robust against perturbations. Our study unveils a mechanism for topological light-trapping in lower dimensions, which is invaluable for fundamental physics and various applications in photonics.
In this work, the Graph Coloring Problem and its generalizations -the Bandwidth Coloring Problem, the Multicoloring Problem and the Bandwidth Multicoloring Problem -are studied. A Squeaky Wheel Optimization with Tabu Search heuristic is developed and experiments using benchmark geometric test cases show that the algorithm performs well for these problems and achieves results for the Bandwidth Multicoloring Problem which improve on results obtained by other researchers.
A VO2(B) ultrathin vertical nanosheet array was prepared
by the hydrothermal method. The influence of the concentration of
oxalic acid on the crystal structure and room-temperature NO2 sensing performance was studied. The morphology and crystal structure
of the nanosheets were characterized by scanning electron microscopy,
transmission electron microscopy, and X-ray diffraction. Room-temperature
gas sensing measurements of this structure to NO2 with
a concentration span from 0.5 to 5 ppm were carried out. The experimental
results showed that the thickness of the vertical VO2(B)
nanosheet was lower than 20 nm and close to the 2 times Debye length
of VO2(B). The response of the sensor based on this structure
to 5 ppm NO2 was up to 2.03, and the detection limit was
20 ppb. Its high response performance was due to the fact that the
target gas could completely control the entire conductive path by
forming depletion layers on the surface of VO2(B) nanosheets.
Density functional theory was used to analyze the adsorption of NO2 on the VO2(B) surface. It is found that the band
gap of VO2(B) becomes narrower and the Fermi level moves
to the valence band after NO2 adsorption, and the density
of states near the Fermi level increases significantly. This ultrathin
vertical nanosheet array structure can make VO2(B) detect
NO2 with high sensitivity at room temperature and therefore
has potential applications in the field of low-power-consumption gas
sensors.
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