Thermal Conductance of a Single-Electron Transistor

Abstract

We report on combined measurements of heat and charge transport through a single-electron transistor. The device acts as a heat switch actuated by the voltage applied on the gate. The Wiedemann-Franz law for the ratio of heat and charge conductances is found to be systematically violated away from the charge degeneracy points. The observed deviation agrees well with the theoretical expectation. With large temperature drop between the source and drain, the heat current away from degeneracy deviates from the standard quadratic dependence in the two temperatures. The flow of heat at the microscopic level is a fundamentally important issue, in particular if it can be converted into free energy via thermoelectric effects [1]. The ability of most conductors to sustain heat flow is linked to the electrical conductance σ via the Wiedemann-Franz law: κ/σ = L 0 T , where κ is the heat conductance,3e 2 the Lorenz number and T the temperature. While the understanding of quantum charge transport in nano-electronic devices has reached a great level of maturity, heat transport experiments are lagging far behind [2], for two essential reasons: (i) unlike charge, heat is not conserved and (ii) there is no simple thermal equivalent to the ammeter. Heat transport can nevertheless give insight to phenomena that charge transport is blind to [3,4] and, remarkably, a series of experiments has demonstrated the very universality of the quantization of heat conductance, regardless of the carriers statistics [3][4][5][6][7][8][9][10][11].As device dimensions are reduced, electron interactions gain capital importance, leading to Coulomb blockade in mesoscopic devices in which a small island is connected by tunnel junctions. A metallic island connected to a source and a drain through tunnel junctions exceeding the Klitzing resistance R K = h/e 2 and under the influence of a gate electric field constitutes a Single-Electron Transistor (SET) [12]. The charging energy of the island by a single electron writes E C = e 2 /2C where C is the total capacitance of the island. It defines the temperature and bias thresholds below which single-electron physics appears. In the regime where charge transport is governed by unscreened Coulomb interactions, the question of the associated heat flow has been addressed by several theoretical studies [13][14][15][16][17][18][19][20]. The Wiedemann-Franz law is expected to hold in an SET only at the charge degener- acy points in the limit of small transparency, where the effective transport channel is free from interactions, and is violated otherwise. In this Letter, we report on the measurements of both the heat and charge conduction through a metallic SET, with both quantities displaying a marked gate modulation. A strong deviation from the Wiedemann-Franz law is observed when the transport through the SET is arXiv:1704.02622v1 [cond-mat.mes-hall]

Optimal Thermoelectricity with Quantum Spin Hall Edge States

“…This ideal limit can be realized for transmission functions containing deltafunction like peaks [52]. In this sense, structures with resonant levels like quantum dots are particularly promis- ing [56][57][58][59][60][61][62]. On another hand, electrical power generation out of heat is the aim of thermoelectric heat engines.…”

Nonlinear thermovoltage in a single-electron transistor

“…Introduction.-The use of nano-devices has emerged as one of the key technologies in the quest to establish a sustainable energy system, allowing at the same time the control of heat flow in small circuits [1]. So far, most of the investigations of thermal properties in nanostructures have focused on the thermal conductance [2][3][4][5][6][7][8][9][10][11]. Conversely the thermovoltage, which describes the electrical response to a temperature difference and is directly related to both the power and efficiency of thermal machines [1], is much less studied.…”

“…Fabrication details can be found in Ref. [9] where "sample B" is the device used for this experiment. Figure 1c) shows the absolute value of the current I across the device at 65 mK as a function of the potential bias V b and of the gate-induced charge n g = (C L V L + C R V R + C g V g )/e , where C L , C R and C g are, respectively, the capacitances of the island to L, R and to the gate electrode, and V g is the gate voltage.…”

Mechanically induced thermal breakdown in magnetic shuttle structures

“…We assume that the leads are kept at equal chemical potentials (μ L =μ R ≡μ) but at different temperatures ¹ T T L R , so that a temperature gradient δT=T L −T R is applied to the system. The proposed design of the electrodes (suitable for thermal transport measurements as in [13]) allows one to maintain a temperature difference between the leads, while keeping their chemical potentials equal. To simplify calculations in what follows we will assume that T L =T and T R =0.…”