量子Hall效应与Berry相因数

QUANTUM HALL EFFECT AND BERRY PHASE FACTOR

本文将绝热过程中的Berry相因数的概念推广到简并系统,并且研究了量子Hall效应与Berry相因数之间的关系,证明了不论是整数还是分数量子Hall电导率都对应于特殊的Berry相因数。

The concept of Berry's phase factor in adiabatic process is generalized to degenerate systems, the relation between the quantum Hall effect and Berry's phase factor is studied. It is shown that the quantum Hall conductance σ_H is really a special Berry's phase factor, and thus has the same geometrical properties.