Measurement of diffusion thermopower in the quantum Hall systems

We have measured diffusion thermopower in a two-dimensional electron gas at low temperature ($T$=40 mK) in the field range 0 $<B<$ 3.4 T, by employing the current heating technique. A Hall bar device is designed for this purpose, which contains two crossing Hall bars, one for the measurement and the other used as a heater, and is equipped with a metallic front gate to control the resistivity of the areas to be heated. In the low magnetic field regime ($B\leq$ 1 T), we obtain the transverse thermopower $S_{yx}$ that quantitatively agrees with the $S_{yx}$ calculated from resistivities using the generalized Mott formula. In the quantum Hall regime ($B\geq$ 1T), we find that $S_{yx}$ signal appears only when both the measured and the heater area are in the resistive (inter-quantum Hall transition) region. Anomalous gate-voltage dependence is observed above $\sim$1.8 T, where spin-splitting in the measured area becomes apparent.