The Theory of Von Klitzing’s Constant and Phases

Abstract

Abstract-TheHall resistivity is found to become a function of spin. For positive spin, one value is found but for negative sign in the spin, another value occurs. In this way, there is never only one value of the resistivity but there is doubling of values. The value of the von Klitzing's constant is a special case of more general dependence of resistivity on the spin. We investigate the effect of Landau levels. For extreme quantum limit, n=0, the effective charge of the electron becomes (1/2)ge. The fractional charge arises for finite value of the angular momentum. There is a formation of spin clusters. As the field increases, there is a phase transition from spin ½ to spin 3/2 so that g value becomes 4 and various values of n in Landau levels, g(n+1/2), form plateaus in the Hall resistivity.

Electron Spin in Quantum Hall Effect in Al_xGa_1-xas: D. C. Tsui's Data

“…(iii) Shrivastava's theory [ 8,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In this theory spin is used with both signs so that the g value is (2j+1)/(2l+1) with j = l ± s and hence the flux quantization becomes spin dependent and the charge of the electron becomes e*=(1/2)ge.…”