In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the genera...In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the general linear Lie algebra gln over the complex field C.展开更多
We study the possible topological phase in a one-dimensional（1D） quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps formi...We study the possible topological phase in a one-dimensional（1D） quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps forming in the bulk energy band and fractional boundary states residing in the gap when the system has an inversion symmetry. These states are topologically nontrivial and can be characterized by a quantized Berry phase ±π or nonzero Chern number through dimensional extension. When the Rashba spin–orbital coupling varies slowly with time, the system can pump out 2 charges in a pumping cycle because of the spin flip effect. This quantized pumping is protected by topology and is robust against moderate disorders as long as the disorder strength does not exceed the opened energy gap.展开更多
The electrocatalysis reactions involving oxygen,such as oxygen evolution reaction(OER)and oxygen reduction reaction(ORR),play a critical role in energy storage/conversion applications,e.g.,fuel cells,metal-air batteri...The electrocatalysis reactions involving oxygen,such as oxygen evolution reaction(OER)and oxygen reduction reaction(ORR),play a critical role in energy storage/conversion applications,e.g.,fuel cells,metal-air batteries,and electrochemical water splitting.The high kinetic energy barrier of the OER/ORR is highly associated with the spin state interconversion between singlet OH^(−)/H_(2)O and triplet O_(2),which is influenced by the spin state and magnetism of catalysts.This Review summarizes recent progress and advances in understanding spin/magnetism-related effects in oxygen electrocatalysis to develop spin theory.It is demonstrated that the spin states(low,intermediate,and high spin)of magnetic transition metal catalysts(TMCs)can directly affect the reaction barriers of OER/ORR by tailoring the bonding of oxygen intermediates with TMCs.Besides,the spin states of TMCs can build a spin-selective channel to filter the electron spins required for the single/triplet interconversion of O species during OER/ORR.In this Review,we introduced many approaches to modulating spin state,for instance,altering the crystal field,oxidation state of active-site ions,and the morphology of TMCs.What’s more,a magnetic field can drive the spin flip of magnetic ions to achieve the spin alignment(↑↑)(i.e.,facilitating spin polarization),which will strengthen the spin selectivity for accelerating the filtration and transfer of the spins with the same direction for the generation and conversion of triplet ↑O=O↑.Importantly,the origin of magnetic field enhancement on OER/ORR are deeply discussed,which provides a great vision for the magnetism-assisted catalysis.Finally,the challenges and perspectives for future development of spin/magnetism catalysis are presented.This Review is expected to highlight the significance of spin/magnetism theory in breaking the bottleneck of electrocatalysis field and promote the development of high-efficientcy electrocatalysts for practical applications.展开更多
The purpose of the paper is to describe the solution to the quantum Yang-Baxter equation associated with the 8-dimensional spin representation Tsp of Uq(so7).The self-duality of Tsp and the symmetry of the correspondi...The purpose of the paper is to describe the solution to the quantum Yang-Baxter equation associated with the 8-dimensional spin representation Tsp of Uq(so7).The self-duality of Tsp and the symmetry of the corresponding braiding matrix are proved.Also,the minimal polynomial of the braiding R-matrix of Tsp is presented explicitly in an ingenious method by taking advantage of nice features of the spin representation Tsp.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11271043)Natural Science Foundation of Beijing(Grant No.1122006)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.201111103110011)
文摘In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the general linear Lie algebra gln over the complex field C.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.115074045 and 11204187)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20131284)
文摘We study the possible topological phase in a one-dimensional（1D） quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps forming in the bulk energy band and fractional boundary states residing in the gap when the system has an inversion symmetry. These states are topologically nontrivial and can be characterized by a quantized Berry phase ±π or nonzero Chern number through dimensional extension. When the Rashba spin–orbital coupling varies slowly with time, the system can pump out 2 charges in a pumping cycle because of the spin flip effect. This quantized pumping is protected by topology and is robust against moderate disorders as long as the disorder strength does not exceed the opened energy gap.
基金financially supported by the National Natural Science Foundation of China(Grants No.52027801,52111530236)the National Postdoctoral Program for Innovative Talents(BX20220002)China Postdoctoral Science Foundation(2022M720204).
文摘The electrocatalysis reactions involving oxygen,such as oxygen evolution reaction(OER)and oxygen reduction reaction(ORR),play a critical role in energy storage/conversion applications,e.g.,fuel cells,metal-air batteries,and electrochemical water splitting.The high kinetic energy barrier of the OER/ORR is highly associated with the spin state interconversion between singlet OH^(−)/H_(2)O and triplet O_(2),which is influenced by the spin state and magnetism of catalysts.This Review summarizes recent progress and advances in understanding spin/magnetism-related effects in oxygen electrocatalysis to develop spin theory.It is demonstrated that the spin states(low,intermediate,and high spin)of magnetic transition metal catalysts(TMCs)can directly affect the reaction barriers of OER/ORR by tailoring the bonding of oxygen intermediates with TMCs.Besides,the spin states of TMCs can build a spin-selective channel to filter the electron spins required for the single/triplet interconversion of O species during OER/ORR.In this Review,we introduced many approaches to modulating spin state,for instance,altering the crystal field,oxidation state of active-site ions,and the morphology of TMCs.What’s more,a magnetic field can drive the spin flip of magnetic ions to achieve the spin alignment(↑↑)(i.e.,facilitating spin polarization),which will strengthen the spin selectivity for accelerating the filtration and transfer of the spins with the same direction for the generation and conversion of triplet ↑O=O↑.Importantly,the origin of magnetic field enhancement on OER/ORR are deeply discussed,which provides a great vision for the magnetism-assisted catalysis.Finally,the challenges and perspectives for future development of spin/magnetism catalysis are presented.This Review is expected to highlight the significance of spin/magnetism theory in breaking the bottleneck of electrocatalysis field and promote the development of high-efficientcy electrocatalysts for practical applications.
基金Supported by the NNSFC(Grant Nos.12171155,12071094,11801394)in part by the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014)。
文摘The purpose of the paper is to describe the solution to the quantum Yang-Baxter equation associated with the 8-dimensional spin representation Tsp of Uq(so7).The self-duality of Tsp and the symmetry of the corresponding braiding matrix are proved.Also,the minimal polynomial of the braiding R-matrix of Tsp is presented explicitly in an ingenious method by taking advantage of nice features of the spin representation Tsp.
