Fundamental Relation between Electrical and Thermoelectric Transport Coefficients in the Quantum Hall Regime

The two components $S_{\mathrm{xx}}$ and $S_{\mathrm{yx}}$ of the phonon-drag thermoelectric power in two-dimensional electron gases (2DEGs) are found to be related by $S_{\mathrm{yx}}=\alpha B\left({\mathrm{dS}}_{\mathrm{xx}}/\mathrm{dB}\right)$ in the integer and fractional quantum Hall regime. A similar relation exists for electrical resistivity, ${\rho }_{\mathrm{xx}}=\alpha B\left(d{\rho }_{\mathrm{xy}}/\mathrm{dB}\right)$, and we show that experimentally the constant $\alpha$ is the same in both cases indicating the universal character of such relations for transport in 2DEGs. These results link the behavior of $S_{\mathrm{yx}}$, which hitherto has not been understood, to that of $S_{\mathrm{xx}}$ and thus opens a new way of explaining this quantity.