Dynamical critical behavior in the integer quantum Hall effect
Abstract
We investigate dynamical scaling properties in the integer quantum Hall effect for noninteracting electrons at zero temperature, by means of the frequencyinduced peak broadening of the dissipative longitudinal conductivity $\sigma_{xx}(\omega)$. This quantity is calculated numerically in the lowest Landau level for various values of the Fermi energy $E$, of the frequency $\omega$, and of the system size $L$. Data for the width $W(\omega,L)$ of the peak are analyzed by means of the dynamical finitesize scaling law $W(\omega,L)\approx L^{1/\nu}f\bigl(\omega L^z\bigr)$, where $\nu$ is the static critical exponent of the localization length, and $z$ is the dynamical exponent. A fit of the data, assuming $\nu=2.33$ is known, yields $z=1.19\pm 0.13$. This result indicates that the dynamical exponent in the integer quantum Hall effect may be different from the pertinent space dimension ($d=2$), even in the absence of interactions between electrons.
 Publication:

arXiv eprints
 Pub Date:
 September 1996
 arXiv:
 arXiv:condmat/9609265
 Bibcode:
 1996cond.mat..9265A
 Keywords:

 Condensed Matter
 EPrint:
 REVTeX, 11 pages, 5 figures