The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the ...The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.展开更多
The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite...The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.展开更多
基金supported by the National Basic Research Program of China (Grant Nos. 2009CB929504,2011CB922103,and 2010CB923400)the National Natural Science Foundation of China (Grant Nos. 11225420,11074110,11174125,11074109,and 91021003)+1 种基金the Priority Academic Program Development of Jiangsu Higher Education Institutions,China,the US NSF (Grant Nos. DMR-0906816 and DMR-1205734)Princeton MRSEC (Grant No. DMR-0819860)
文摘The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.
基金Project supported by the National Basic Research Program of China(Grant Nos.2009CB929504,2011CB922103,and 2010CB923400)the National Natural Science Foundation of China(Grant Nos.11225420,11074110,11174125,11074109,11074111,and 91021003)+3 种基金the Priority Academic Program Development of Jiangsu Higher Education Institutions,Chinathe Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010364)the US NSF(Grant Nos.DMR-0906816 and DMR-1205734)he Princeton MRSEC(Grant No.DMR-0819860)
文摘The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.
