Theoretical investigation of local electron temperature in quantum Hall systems

In this work we solve thermo-hydrodynamical equations considering a two dimensional electron system in the integer quantum Hall regime, to calculate the spatial distribution of the local electron temperature. We start from the self-consistently calculated electrostatic and electrochemical potentials in equilibrium. Next, by imposing an external current, we investigate the variations of the electron temperature in the linear-response regime. Here a local relation between the electron density and conductivity tensor elements is assumed. Following the Ohm's law we obtain local current densities and by implementing the results of the thermo-hydrodynamical theory, calculate the local electron temperature. We observe that the local electron temperature strongly depends on the formation of compressible and incompressible strips.

Calculated the local electron temperature deviation versus position, for different values of the magnetic field. It strongly depends on the compressible and incompressible strips.Figure optionsDownload as PowerPoint slideHighlights
► We calculate the electron temperature in the linear-response regime.
► We impose realistic boundary conditions so define experimental systems accurately.
► The current carried by the incompressible strips heats the electron system locally.
► One side of the sample heats up, whereas the opposing edge is cooled down.
► The variation of the local electron temperature strongly depends on magnetic field.