Spatial Distributions of Electron Temperature in Quantum Hall Systems with Compressible and Incompressible Strips

Spatial distributions of the electron temperature perpendicular to the applied current are obtained in quantum Hall systems with compressible and incompressible strips at low lattice temperatures by solving equations of electron number conservation and energy conservation as well as Poisson's equation self-consistently. In the linear-response regime, variations of the electron temperature concentrate in the incompressible strips as the lattice temperature decreases. The electron temperature indicates an antisymmetric distribution: it becomes lower than the lattice temperature in the side of a sample with a higher electrochemical potential, and higher in the opposite side. Around the breakdown of the quantum Hall effects, the electron temperature becomes much higher than the lattice temperature as the applied current increases. Reflecting the anti-symmetric distribution in the linear-response regime, the rise of the electron temperature is suppressed in the higher potential side with increasing current. In the same side, the current density becomes large and the current-induced potential shows a steep variation. At even larger currents, accompanying disappearance of the compressible and incompressible strips, the electron temperature becomes uniform.