Spatial distribution of thermoelectric voltages in a Hall-bar shaped two-dimensional electron system under a magnetic field

Abstract

We have investigated the spatial distribution of the electron temperature generated in a two-dimensional electron system (2DES) subjected to a perpendicular magnetic field. We measure thermoelectric voltages between Ohmic contacts located at the end of the voltage-probe arms of a Hall bar fabricated from a GaAs/AlGaAs 2DES wafer, immersed in the mixing chamber of a dilution refrigerator held at 20 mK. Magneto-oscillations due to the Landau quantization are examined for the thermoelectric voltages between the contact pairs straddling the main bar (arrangement to measure the transverse component Vyx), and between the pairs located along the same side of the main bar (arrangement for the longitudinal component Vxx). For the former arrangement, the oscillation amplitude diminishes with the distance from the heater. For the latter arrangement, the pair on one side exhibits much larger amplitude than the pair on the opposite side, and the relation becomes reversed by inverting the magnetic field. The behaviours of the oscillation amplitude are qualitatively explained by the spatial distribution of the electron temperature numerically calculated taking into consideration the thermal diffusion into the voltage contacts and the electron-phonon interaction. For both arrangements, the oscillations are shown to derive predominantly from the transverse (Nernst) component, Syx, of the thermopower tensor. The calculation also reveals that the voltage probes, introducing only minor disturbance at zero magnetic field, substantially reduce the temperature once a magnetic field is applied, and the thermoelectric voltages generated at the voltage arms account for a significant part of the measured voltages.