Theory of the AC breakdown of the quantum Hall effect

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Abstract
The low-frequency ( approximately 1 MHz) breakdown of the integer quantum Hall effect can be understood if semiclassical orbits are present in the sample. These orbits be very long and thus absorb very low-frequency radiation. The diagonal conductivity is not zero, precluding the observation of the resistance plateaux. Using results from percolation theory, one can predict a frequency-dependent conductance sigma xx( omega ) approximately omega -4 rho exp(- omega 0/ omega ), where rho approximately=2/3 and omega 0 can be of the order of 1 MHz or less. This form is universal in the range omega < omega 0. In this range sigma yx( omega ) does not deviate appreciably from its quantised value. For omega >or= omega 0 there is a cross-over to a non-universal regime where sigma xx( omega ) and sigma yx( omega )- sigma yx(0) are of comparable magnitude.