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 twodimensional 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 V yx ), and between the pairs located along the same side of the main bar (arrangement for the longitudinal component V xx ). 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, S yx , 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.

Joule heating and the thermal conductivity of a two-dimensional electron gas at cryogenic temperatures studied by modified 3$ω$ method

“…( 9), we assumed that K xx is independent of T e , which is a good approximation for 2DEGs at low temperatures (T e 1 K). 28 We have also shown that I(δ, α) ≃ α for α 0.5 in a moderate-to-high magnetic field where δ approaches π/2 in a high-mobility 2DEG, and thus J Q (T s , T d ) becomes independent of α:…”

“…The heat deposited to this area by the Joule heating, ρ xx j 2 bW , is lost by diffusion through the voltage arms into the electric contact (J Q ) or by being imparted to the lattice via the electron-phonon interaction (P e-ph ). 27 In a recent publication, 28 the present authors have shown that the thermal flux from the high-temperature end (T s ) to the low-temperature end (T d ) along the length of the rectangular 2DEG area (length L and width W ), when placed in a magnetic field, is given by…”

“…We have deduced the highest (T H ) and the lowest (T L ) temperatures of the oscillating T e for various values of the heating current. Employing the temperature response to the Joule heating thus acquired, we have further drawn out the thermal conductivity κ xx of the 2DEG, with the aid of the simple formula we have deduced in a recent publication 28 modelling the thermal flux through the voltage arms, and the well known formulas for the power per area transferred from the 2DEG to the lattice system. 15,28,29 The resulting κ xx is found to be roughly in agreement with the thermal conductivity estimated from the electrical conductivity via the Wiedemann-Franz law.…”

“…( 12). The power per area transferred from the 2DEG at the temperature T e to the phonons at the temperature T p is written as 15,28,29 P e-ph (T e , T p ) = P df l (T e , T p ) + P pz l (T e , T p ) + 2P pz t (T e , T p ), ( 13) with…”

“…On the other hand, we assume that the temperature of the electrical contact is the same as the bath temperature, T d = T bath , since the contact pad made of a thin metallic (AuGeNi) film has a granular surface (see the inset to Fig. 4) and therefore expected to be in good thermal contact with the surrounding helium liquid, 28 in marked contrast with the thin slab buried in the GaAs substrate. Taking the average temperature T ave as resulting from the root mean square value of the Joule heating, we substitute T e = T ave and ρ xx j 2 = R bg,ave I 2 0 /(ab) into Eq.…”