This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.
Twisted trilayer graphene(TLG)may be the simplest realistic system so far,which has flat bands with nontrivial topology.Here,we give a comprehensive calculation about its band structures and the band topology,i.e.,val...Twisted trilayer graphene(TLG)may be the simplest realistic system so far,which has flat bands with nontrivial topology.Here,we give a comprehensive calculation about its band structures and the band topology,i.e.,valley Chern number of the nearly flat bands,with the continuum model.With realistic parameters,the magic angle of twisted TLG is about 1.12°,at which two nearly flat bands appears.Unlike the twisted bilayer graphene,a small twist angle can induce a tiny gap at all the Dirac points,which can be enlarged further by a perpendicular electric field.The valley Chern numbers of the two nearly flat bands in the twisted TLG depends on the twist angleθand the perpendicular electric field E⊥.Considering its topological flat bands,the twisted TLG should be an ideal experimental platform to study the strongly correlated physics in topologically nontrivial flat band systems.And,due to its reduced symmetry,the correlated states in twisted TLG should be quite different from that in twisted bilayer graphene and twisted double bilayer graphene.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10171003, No.10231040) the Doctoral Education Program Foundation of China.
文摘This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.
基金the National Natural Science Foundation of China(11534001,11874160,11274129,11874026,and 61405067)the National Key Research and Development Program of China(2017YFA0403501)+1 种基金the Fundamental Research Funds for the Central Universities(HUST:2017KFYXJJ027)the National Basic Research Program of China(2015CB921102).
文摘Twisted trilayer graphene(TLG)may be the simplest realistic system so far,which has flat bands with nontrivial topology.Here,we give a comprehensive calculation about its band structures and the band topology,i.e.,valley Chern number of the nearly flat bands,with the continuum model.With realistic parameters,the magic angle of twisted TLG is about 1.12°,at which two nearly flat bands appears.Unlike the twisted bilayer graphene,a small twist angle can induce a tiny gap at all the Dirac points,which can be enlarged further by a perpendicular electric field.The valley Chern numbers of the two nearly flat bands in the twisted TLG depends on the twist angleθand the perpendicular electric field E⊥.Considering its topological flat bands,the twisted TLG should be an ideal experimental platform to study the strongly correlated physics in topologically nontrivial flat band systems.And,due to its reduced symmetry,the correlated states in twisted TLG should be quite different from that in twisted bilayer graphene and twisted double bilayer graphene.
