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
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.
