Hydrodynamic Equation for the Breakdown of the Quantum Hall Effect in a Uniform Current
Abstract
The hydrodynamic equation for the spatial and temporal evolution of the electron temperature T_e in the breakdown of the quantum Hall effect at even-integer filling factors in a uniform current density j is derived from the Boltzmann-type equation, which takes into account electron-electron and electron-phonon scatterings. The derived equation has a drift term, which is proportional to j and to the first spatial derivative of T_e. Applied to the spatial evolution of T_e in a sample with an abrupt change of the width along the current direction, the equation gives a distinct dependence on the current direction as well as a critical relaxation, in agreement with the recent experiments.
Keywords
Cite
@article{arxiv.cond-mat/0010212,
title = {Hydrodynamic Equation for the Breakdown of the Quantum Hall Effect in a Uniform Current},
author = {Hiroshi Akera},
journal= {arXiv preprint arXiv:cond-mat/0010212},
year = {2009}
}
Comments
4 pages, 1 Postscript figure, corrected equations, to be published in J. Phys. Soc. Jpn. 70 (2001) No.6