Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between ...Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the randomgate-voltage induced Φ_(0)/2-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the Φ_(0)/2-period Al'tshuler–Aronov–Spivak oscillation proportional to sin^(2)(2πΦ/Φ_(0)) by quenching the Φ_(0)-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced π Berry phase is key to such weak antilocalization behavior with zero return probability at Φ = 0. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at Φ = 0. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.展开更多
Optical cavities play crucial roles in enhanced light-matter interaction,light control,and optical communications,but their dimensions are limited by the material property and operating wavelength.Ultrathin planar cav...Optical cavities play crucial roles in enhanced light-matter interaction,light control,and optical communications,but their dimensions are limited by the material property and operating wavelength.Ultrathin planar cavities are urgently in demand for large-area and integrated optical devices.However,extremely reducing the planar cavity dimension is a critical challenge,especially at telecommunication wavelengths.Herein,we demonstrate a type of ultrathin cavities based on large-area grown Bi_(2)Te_(3)topological insulator(TI)nanofilms,which present distinct optical resonance in the near-infrared region.The result shows that the Bi_(2)Te_(3)TI material presents ultrahigh refractive indices of>6 at telecommunication wavelengths.The cavity thickness can approach 1/20 of the resonance wavelength,superior to those of planar cavities based on conventional Si and Ge high refractive index materials.Moreover,we observed an analog of the electromagnetically induced transparency(EIT)effect at telecommunication wavelengths by depositing the cavity on a photonic crystal.The EIT-like behavior is derived from the destructive interference coupling between the nanocavity resonance and Tamm plasmons.The spectral response depends on the nanocavity thickness,whose adjustment enables the generation of obvious Fano resonance.The experiments agree well with the simulations.This work will open a new door for ultrathin cavities and applications of TI materials in light control and devices.展开更多
Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively ...Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively generalized and strengthened.Moreover,we can describe the complete distributivity of lattices with them as well.In this paper,we give the mutually descrip- tive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices, and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces, weakly induced spaces and induced spaces(they are called S-spaces).Furthermore,we will investi- gate the structure of the co-topology of S-space,solve a series of interesting problems on product, N-compactness and metrization of S-spaces.展开更多
In this paper, we prove that （L^X,5） is T0,T1, T2, regular （T3）, normal （T4） and completely regular spaces if and only if （R（L）^X, ω（δ）） is T0, T1, T2, regular （T3）, normal （T4） and completely regula...In this paper, we prove that （L^X,5） is T0,T1, T2, regular （T3）, normal （T4） and completely regular spaces if and only if （R（L）^X, ω（δ）） is T0, T1, T2, regular （T3）, normal （T4） and completely regular spaces, respectively, and （L^X,δ） is N-compact if and only if （R（L）^X, ω（δ）） is N-compact.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 12074172, 11674160, and 11974168)the Startup Grant at Nanjing University+1 种基金the State Key Program for Basic Researches of China (Grant No. 2017YFA0303203)the Excellent Programme at Nanjing University。
文摘Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the randomgate-voltage induced Φ_(0)/2-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the Φ_(0)/2-period Al'tshuler–Aronov–Spivak oscillation proportional to sin^(2)(2πΦ/Φ_(0)) by quenching the Φ_(0)-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced π Berry phase is key to such weak antilocalization behavior with zero return probability at Φ = 0. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at Φ = 0. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1404800)the National Natural Science Foundation of China(Grant Nos.11974283,61705186,and 11774290)+2 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2020JM-13)the“Double First-Class”Construction Fund Project(Grant No.0206022GH0202)the Fundamental Research Funds for the Central Universities(Grant No.D5000220175)
文摘Optical cavities play crucial roles in enhanced light-matter interaction,light control,and optical communications,but their dimensions are limited by the material property and operating wavelength.Ultrathin planar cavities are urgently in demand for large-area and integrated optical devices.However,extremely reducing the planar cavity dimension is a critical challenge,especially at telecommunication wavelengths.Herein,we demonstrate a type of ultrathin cavities based on large-area grown Bi_(2)Te_(3)topological insulator(TI)nanofilms,which present distinct optical resonance in the near-infrared region.The result shows that the Bi_(2)Te_(3)TI material presents ultrahigh refractive indices of>6 at telecommunication wavelengths.The cavity thickness can approach 1/20 of the resonance wavelength,superior to those of planar cavities based on conventional Si and Ge high refractive index materials.Moreover,we observed an analog of the electromagnetically induced transparency(EIT)effect at telecommunication wavelengths by depositing the cavity on a photonic crystal.The EIT-like behavior is derived from the destructive interference coupling between the nanocavity resonance and Tamm plasmons.The spectral response depends on the nanocavity thickness,whose adjustment enables the generation of obvious Fano resonance.The experiments agree well with the simulations.This work will open a new door for ultrathin cavities and applications of TI materials in light control and devices.
基金The Project Supported by National Natural Science Foundation of China.
文摘Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively generalized and strengthened.Moreover,we can describe the complete distributivity of lattices with them as well.In this paper,we give the mutually descrip- tive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices, and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces, weakly induced spaces and induced spaces(they are called S-spaces).Furthermore,we will investi- gate the structure of the co-topology of S-space,solve a series of interesting problems on product, N-compactness and metrization of S-spaces.
基金Foundation item： the National Natural Science Foundation of China （No. 10471083） the Natural Science Foundation of Zhejiang Education Committee （No. 20060500）.
文摘In this paper, we prove that （L^X,5） is T0,T1, T2, regular （T3）, normal （T4） and completely regular spaces if and only if （R（L）^X, ω（δ）） is T0, T1, T2, regular （T3）, normal （T4） and completely regular spaces, respectively, and （L^X,δ） is N-compact if and only if （R（L）^X, ω（δ）） is N-compact.
