In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete bounda...In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete boundary unit cells(i.e.,boundary defects)even though the bulk polarization is zero,which challenges the conventional understanding of HOTIs.Here,based on a Kekul´e-distorted honeycomb lattice with incomplete unit cells,we reveal that incomplete unit cells exhibit fractional charges through the analysis of Wannier centers by developing a compensation method and creating the concept of Wannier center domain(WCD)which is the smallest region that one Wannier center occupies.This method compensates for the missing parts of these boundary incomplete unit cells with additional WCDs to make them complete.The compensated WCDs automatically carry the corresponding charge,and this charge together with that of the incomplete unit cell constitutes the total charge of the complete unit cell after compensation.We conclude that the emergence of corner states is attributed to the filling anomaly,which is a fundamental mechanism.Our results refresh the understanding of HOTIs,especially those with structural discontinuities,and provide a novel design for topological states which have application value in producing optical functional devices.展开更多
地点:中国旅行社驻外分社营业部Setting:China Travel Service,Overseas Branch人物:杰克·乔治、黄先生Characters:Jack George and Mr.Huang 会话 Dialogue黄先生:乔治先生,您决定了没有?Mr.Huang:Have you made up your mind,Mr....地点:中国旅行社驻外分社营业部Setting:China Travel Service,Overseas Branch人物:杰克·乔治、黄先生Characters:Jack George and Mr.Huang 会话 Dialogue黄先生:乔治先生,您决定了没有?Mr.Huang:Have you made up your mind,Mr.George?乔治:你叫我杰克好了。我决定从上海入境。展开更多
基金supported by the Natural Science Basic Research Program of Shaanxi Province (Grant Nos.2024JC-JCQN-06 and2025JC-QYCX-006)the National Natural Science Foundation of China (Grant No.12474337)Chinese Academy of Sciences Project (Grant Nos.E4BA270100,E4Z127010F,E4Z6270100,and E53327020D)。
文摘In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete boundary unit cells(i.e.,boundary defects)even though the bulk polarization is zero,which challenges the conventional understanding of HOTIs.Here,based on a Kekul´e-distorted honeycomb lattice with incomplete unit cells,we reveal that incomplete unit cells exhibit fractional charges through the analysis of Wannier centers by developing a compensation method and creating the concept of Wannier center domain(WCD)which is the smallest region that one Wannier center occupies.This method compensates for the missing parts of these boundary incomplete unit cells with additional WCDs to make them complete.The compensated WCDs automatically carry the corresponding charge,and this charge together with that of the incomplete unit cell constitutes the total charge of the complete unit cell after compensation.We conclude that the emergence of corner states is attributed to the filling anomaly,which is a fundamental mechanism.Our results refresh the understanding of HOTIs,especially those with structural discontinuities,and provide a novel design for topological states which have application value in producing optical functional devices.
文摘地点:中国旅行社驻外分社营业部Setting:China Travel Service,Overseas Branch人物:杰克·乔治、黄先生Characters:Jack George and Mr.Huang 会话 Dialogue黄先生:乔治先生,您决定了没有?Mr.Huang:Have you made up your mind,Mr.George?乔治:你叫我杰克好了。我决定从上海入境。
