Temperature dependence of the quantum Hall resistance

We report high-precision measurements of the temperature dependence of the quantum Hall resistance for two GaAs heterostructures. The Hall resistivity ${\rho }_{\mathrm{xy}}\mathrm{}\left(T\right)\mathrm{}$ is found to vary linearly with the minimum resistivity along the device ${\rho }_{\mathrm{xx}}^{min}\mathrm{}\left(T\right)\mathrm{}$ and to depend upon the sample, Hall probe set, and magnetic field direction, but to approach a sample-independent value as $T\to 0$. The temperature-dependent shift of ${\rho }_{\mathrm{xy}}\mathrm{}\left(T\right)\mathrm{}$ from ${\rho }_{\mathrm{xy}}\mathrm{}\left(0\right)\mathrm{}$ can be significant even for very flat Hall steps and is inconsistent with standard mechanisms.