Electron Temperature Distribution and Hot Spots in Quantum Hall Systems

The spatial variations of the electron temperature in the vicinity of metallic current contacts in a quantum Hall system are calculated based on thermohydrodynamics with an energy gain. It is shown that, at large currents, hot spots with high electron temperatures appear at diagonally opposite corners of a sample. At small currents, however, the electron temperature at one of the corners is lower than the lattice temperature, while that at the other corner is higher than the lattice temperature. As a function of the chemical potential, the electron temperature at each corner shows quantum oscillations.