Quantum Hall Effect and Additional Oscillations of Conductivity in Weak Magnetic Fields

Abstract

In the framework of scaling hypothesis for localization of 2D-electrons in a magnetic field B it is shown that at T=0 conductivity σ_xx has maxima at

$$B_n^{(1,2)} = \frac{{mc}}{{e\hbar }}\left\{ {\frac{{E_F }}{{2n + 1}} \pm \left[ {\left( {\frac{{E_F }}{{2n + 1}}} \right)^2 - \left( {\frac{\hbar }{\tau }} \right)^2 } \right]^{\frac{1}{2}} } \right\}$$

((1))

i.e. besides oscillations of the Shubnikov type with maxima of a σ_xx at

$$B_n^{(1)} \simeq \frac{{mc}}{{e\hbar }}\frac{{E_F }}{{n + \frac{1}{2}}}$$

((2))

there is the same number of additional oscillations at

$$B_n^{(2)} = \frac{{mc}}{e}\frac{\hbar }{{E_F \tau ^2 }}\left( {n + \frac{1}{2}} \right).$$

((3))