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.

4 pages, 1 Postscript figure, corrected equations, to be published in J. Phys. Soc. Jpn. 70 (2001) No.6

References in corpus (1)

• Electronic Processes at the Breakdown of the Quantum Hall Effect

Cited by in corpus (5)

• Self-consistent local-equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields
• Realistic modelling of quantum point contacts subject to high magnetic fields and with current bias at out of linear response regime
• Hydrodynamic Equations in Quantum Hall Systems at Large Currents
• Thermohydrodynamics in Quantum Hall Systems
• Theoretical Investigation of Local Electron Temperature in Quantum Hall Systems