〈ノート〉多体問題とグリーン関数との関係の研究--グリーン関数と多体問題(20)量子統計力学(12)

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[Synopsis] In this paper, we discuss the quantization of the Hall conductivity of two-dimensional metals which has been observed by Klitzing, Dorda, and Pepper in Phys. Rev. Letter 45 494 (1980). Such a system can be made by injecting electrons into the interface of an alloy sandwich of a thin film about 500A thick by application of the transition technology. In the Hall experiment, the direct resistivities p_<xx> and the Hall resisitivities p_<xy>, have been measured at very low temperature. The Hall resisitivities p_<xy>, is the ratio of the electric field in the y direction to the Hall current density in the x direction. The Landau level filling factor v is defined by v＝N/g＝<hn>/<(-e)B>. Here, n is the density of electrond. The Hall resistivities exhibits plateau at v＝1, 2/3, 1/3 with values equal to 1/v in unit of h/<(-e)^2>. And at the same time, the direct resistivity p_<xx> drops to very low values. The value at v ＝1 is called the integer quantized Hall effect. The values at v＝2/3, 1/3 are called the fractional quantized Hall effect. The integer quantized Hall effect is explained in simple method and also in the method of metallic loop with quantum mechanics. But it dose not explain the plateau in the data. The plateau is explained the presence of impurities.