Quantum hall effect

Restricted Access.Quantization of dc Hall conductance a t low temperatures of .a .two-dimensional generate electron obtaining in the.inversion layer of a Metal-Oxid~ Semiconductor~ Field-Effect- Transistor(M, OSFET) discovered recently by Von-Klidzing et al is a surprise of experimental and theoretical solid state physics. The high precision, to wit to 1 par t in l0 , of the quantization a t integral multiplies of e / 2 n k provides on the one hand an "atomic" metrological standard 6f resistance, while on the other a value of the . Sommerfeld fine-structure constant of unprecedented accuracy. Hence, its importance. In. this talk I will attempt a .plausible theoretical understanding of this remarkable phenomenon. I will be . Concerned with the single most important aspect of it, namely, that of the insensitiveness of quantization (i.e. robustness) t o potential disorder which is. not only always present but without which QHE may not be observed ;at all. Along the line I will discuss corrections, if at all, due t o . finite sample size, non: zero electric-field and finite magnetic field..:Fractional quantum Hall effect which is. essentially a many-body effect associated with-certain rational fractional filling of the lowest Landau level a t higher. magnetic. fields, will not be discussed