Study on Localized State in Quantum Hall Effect

• Main Authors: Ming-Chiun Wu, 吳銘群
• Other Authors: Yeong-Chuan Kao
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/93594678620562508424

碩士 === 國立臺灣大學 === 物理學研究所 === 90 === The influence of the delta function potential on the Hall resistance of a two-dimensional, degenerate gas is studied using the path integral formalism. The Green function is calculated by the perturbation method and a non-perturbative result for it is obtained after doing the integration of the delta function and the infinite summation. The spectrum of our system is then studied from the pole structure of the Green function. It is found that the renormalization scheme with the real space regularization is needed to get the bound state. And the spectrum is shown to be similar to the impurity-free Landau problem. The original Landau levels are unaltered after the inclusion of the delta function potential. The only effect of the singular potential is the occurrence of the bound state and some s-wave states. The current for each state is then discussed. And the Hall current is shown to be unaffected by the impurity.