The effect of disorder on local electron temperature in quantum Hall systems

Abstract

The local electron temperature distribution is calculated considering a two dimensional electron system in the integer quantum Hall regime in presence of disorder and uniform perpendicular magnetic fields. We solve thermo-hydrodynamic equations to obtain the spatial distribution of the local electron temperature in the linear-response regime. It is observed that, the variations of electron temperature exhibit an antisymmetry regarding the center of the sample in accordance with the location of incompressible strips. To understand the effect of sample mobility on the local electron temperature we impose a disorder potential calculated within the screening theory. Here, long range potential fluctuations are assumed to simulate cumulative disorder potential depending on the impurity atoms. We observe that the local electron temperature strongly depends on the number of impurities in narrow samples. The electron temperature $$T_e$$ versus position calculated for different values of the modulation potential $$V_0$$ . The calculations are done at $$T_\mathrm{L} = 0.04 \,E_F^0/k_B$$ lattice temperature considering impurity $$N_l = 6600$$ and repeated for three different values of magnetic field $$\hbar \omega _c/E_F^0 = 0.80$$ , 0.85 and 0.90. The insets show the enlarged region for the left side.