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Zero modes, Chern number and all that

2010年11月17日 留下评论 Go to comments

零模个数和Chern数的关系
1. 在量子Hall态中Chern数等于边缘激发态的支数。这点可以从Laughlin的flux insertion argument得到。这个关系对一般的时间反演破缺的绝缘体(包括超导体)也成立。

2. 超导体中vortex的零模个数。因为电荷共轭(或者叫粒子-空穴)对称性的关系,vortex的零模个数由Chern数模2给出。类似的是一维超导体两端的零模。可以用dimensional reduction从2维的Z分类得到一维的Z_2分类。见Qi, Hughes, Zhang的文章。

最近的一些文章

Counting Majorana zero modes in superconductors
Luiz Santos, Yusuke Nishida, Claudio Chamon, Christopher Mudry

Topological Majorana and Dirac Zero Modes in Superconducting Vortex Cores
Rahul Roy

Z_2 index theorem for Majorana zero modes in a class D topological superconductor
T. Fukui, T. Fujiwara

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