INELASTIC-SCATTERING, MULTIFRACTALITY, AND SCALING IN THE INTEGER QUANTUM HALL-EFFECT

We calculate inelastic scattering rates near the center of the Landau band of integer quantum Hall effect (IQHE) systems. It is shown that the generalized fractal dimension D-2 of the multifractal wave functions enters into the temperature dependence of the energy loss rate for hot electrons via a universal exponent eta = 2 - D-2 characterizing the eigenfunction correlations. The same is the case for the inelastic scattering time due to electron-phonon scattering. Thus, measurements of both quantities open, in principle, the possibility of experimentally checking the theoretical models of multifractality in the IQHE. On the other hand, the temperature dependence of the scattering time tau(ee) due to electron-electron interactions remains unchanged compared to two-dimensional metallic systems.