Current-Induced Cooling Phenomenon in a Two-Dimensional Electron Gas Under a Magnetic Field

Abstract

We investigate the spatial distribution of temperature induced by a dc current in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential φ and the temperature T in a 2DEG enclosed in a square area surrounded by insulatedadiabatic (top and bottom) and isopotential-isothermal (left and right) boundaries (with φ left < φ right and T left = T right ), using a pair of nonlinear Poisson equations (for φ and T ) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the vicinity of the left-bottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.

Finite shot noise and electron heating at quantized conductance in high-mobility quantum point contacts

“…On the other hand, at finite magnetic field, the electron motion and thus the heat conduction has chirality because of the Lorentz force. The dissipated energy or the "hot spot" is carried away from the QPC efficiently by this chirality 37 . This topic is nothing but the thermal Hall effect.…”

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

“…It is difficult, however, to quantitatively assess the decrement mainly owing to the difficulty in determining the area of the interface between the helium and the granular metallic film. Note, however, that the temperature difference between voltage contacts, if present, allows for the longitudinal component, S xx , to contribute to the thermoelectric voltages by resuming the first term in equation (30). As pointed out earlier, the footprint of S xx is barely discernible in the lineshape of the experimentally observed oscillations shown in figures 2 and 3, suggesting the absence of appreciable temperature difference between the measured contact pairs.…”

“…By further defining t y  º -, we can see that solving equation (3) with these boundary conditions is mathematically equivalent to the process obtaining the electric field, reported by Rendell and Girvin [3], if we replace the electric field, the current density and the potential by t , j Q /L 0 and ψ, respectively. We can thus make use of the analytic solution presented in the paper [3] (we follow the coordinate system used in [30]) to have t t J = -g ( ) e a cos , 6…”

“…The thermoelectric voltage f i, j between the contacts i and j, to be compared with the experimentally measured value, is obtained by integrating −E along the path  C j i connecting the contacts, In our boundary conditions, we assumed that the temperatures of all the voltage contacts are the same as the temperature of the mixing chamber T L =T bath , and thus the first term in equation (30) vanishes for all the combinations of i and j. This indicates that under the present boundary conditions and the assumptions of the temperature-independent isotropic ŝ , primarily resulting from our experimental conditions that the sample is immersed in the low-temperature 3 He/ 4 He mixture, both V xx and V yx probe only the off-diagonal (Nernst) component S yx of the thermopower tensor and are insensitive to the diagonal (Seebeck) component S xx .…”

“…First, we simply assumed that the higher-temperature end of the main Hall bar (x = L and −W/2<y<W/2) has a constant temperature T H inferred from the SdH amplitude measured with the voltage probes located on the other side of the secondary (heater) Hall bar (see figure 1). We have neglected the spatial variation of the temperature within the heater section, which can be especially pronounced when the magnetic field is applied and a hot spot is generated [30]. Second, we set all the Ohmic contacts at the temperature T L =T bath of the mixing chamber in which the sample is immersed.…”