Hydrodynamic Equations in Quantum Hall Systems at Large Currents

Abstract

Hydrodynamic equations (HDEQs) are derived which describe spatio-temporal evolutions of the electron temperature and the chemical potential of two-dimensional systems in strong magnetic fields in states with large diagonal resistivity appearing at the breakdown of the quantum Hall effect. The derivation is based on microscopic electronic processes consisting of drift motions in a slowly-fluctuating potential and scattering processes due to electron-electron and electron-phonon interactions. In contrast with the usual HDEQs, one of the derived HDEQs has a term with an energy flux perpendicular to the electric field due to the drift motions in the magnetic field. As an illustration, the current distribution is calculated using the derived HDEQs.Comment: 10 pages, 2 Postscript figures, to be published in J. Phys. Soc. Jpn. 71 (2002) No.

Thermohydrodynamics in Quantum Hall Systems

“…A spatial variation of the electron temperature in the Ettingshausen effect in a quantum Hall system has been studied previously in the nonlinear transport regime. 18 Here we make a linear-response calculation and investigate spatial variations and quantum oscillations of the electron temperature.…”

“…The first attempt to construct a general theory for spatio-temporal variations of the electron temperature and the chemical potential in quantum Hall systems was made by one of the present authors. 18 However, this previous theory has been found to employ an inexact formula of the thermal flux density.…”

Spatial distribution of nonequilibrium electrons in quantum Hall devices: Imaging via cyclotron emission

“…This feature might be explained by a theoretically expected nonuniform current distribution caused by an energy flux density that has a component pointing to higher potentials. 21 On the other hand, the situation around the drain contact is different, as clearly seen in Fig. 5͑b͒.…”

“…The characteristic distance L B needed for sufficient cascading is typically more than a few tens of micrometers at an electric field about 10% larger than E c . 20,21 On the side of the source contact, electrons with energies D ϽϽ S Ϫ(ប c )/2 are tunnel injected at corner S L and drift along the junction S L -S H towards corner S H . 5,6 If the longitudinal resistivity is strictly vanishing along the junction region, the polarization fields along this region are strong as well, with the highest amplitude at S L and decreasing amplitudes along the junction towards S H .…”

Observation of the Ettingshausen effect in quantum Hall systems

“…The polarity of the Ettingshausen effect can be explained by Akera's theory. 11,16 Since the direction of the drift motion of electrons is opposite to the Hall current, the y-component q y H of the heat flow density is negative. On the other hand, the dissipative current is carried by excited electrons in the higher Landau level and holes in the lower Landau level (see Fig.…”