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Quantum mechanics and Coulomb interaction dictate the behavior of small circuits. The thermal implications cover fundamental topics from quantum control of heat to quantum thermodynamics, with prospects of novel thermal machines and an ineluctably growing influence on nanocircuit engineering. Experimentally, the rare observations thus far include the universal thermal conductance quantum and heat interferometry. However, evidences for many-body thermal effects paving the way to markedly different heat and electrical behaviors in quantum circuits remain wanting. Here we report on the observation of the Coulomb blockade of electronic heat flow from a small metallic circuit node, beyond the widespread Wiedemann-Franz law paradigm. We demonstrate this thermal many-body phenomenon for perfect (ballistic) conduction channels to the node, where it amounts to the universal suppression of precisely one quantum of conductance for the transport of heat, but none for electricity. The inter-channel correlations that give rise to such selective heat current reduction emerge from local charge conservation, in the floating node over the full thermal frequency range ($lesssim$temperature$times k_mathrm{B}/h$). This observation establishes the different nature of the quantum laws for thermal transport in nanocircuits.
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The presence of pronounced electronic correlations in one-dimensional systems strongly enhances Coulomb coupling and is expected to result in distinctive features in the Coulomb drag between them that are absent in the drag between two-dimensional systems. We review recent Fermi and Luttinger liquid theories of Coulomb drag between ballistic one-dimensional electron systems, and give a brief summary of the experimental work reported so far on one-dimensional drag. Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a maximum of the drag resistance R_D when the one-dimensional subbands of the two quantum wires are aligned and the Fermi wave vector k_F is small, and also an exponential decay of R_D with increasing inter-wire separation, both features confirmed by experimental observations. A crucial difference between the two theoretical models emerges in the temperature dependence of the drag effect. Whereas the FL theory predicts a linear temperature dependence, the LL theory promises a rich and varied dependence on temperature depending on the relative magnitudes of the energy and length scales of the systems. At higher temperatures, the drag should show a power-law dependence on temperature, $R_D ~ T^x$, experimentally confirmed in a narrow temperature range, where x is determined by the Luttinger liquid parameters. The spin degree of freedom plays an important role in the LL theory in predicting the features of the drag effect and is crucial for the interpretation of experimental results.
A mesoscopic Coulomb blockade system with two identical transport channels is studied in terms of full counting statistics. It is found that the average current cannot distinguish the quantum constructive interference from the classical non-interference, but the shot noise and skewness are more sensitive to the nature of quantum mechanical interference and can fulfill that task. The interesting super-Poisson shot noise is found and is demonstrated as a consequence of constructive interference, which induces an effective system with fast-and-slow transport channels. Dephasing effects on the counting statistics are carried out to display the continuous transition from quantum interfering to non-interfering transports.
We analyze the heat current flowing across interacting quantum dots within the Coulomb blockade regime. Power can be generated by either voltage or temperature biases. In the former case, we find nonlinear contributions to the Peltier effect that are dominated by conventional Joule heating for sufficiently high voltages. In the latter case, the differential thermal conductance shows maxima or minima depending on the energy level position. Furthermore, we discuss departures from the Kelvin-Onsager reciprocity relation beyond linear response.
We investigate the nonlinear regime of charge and energy transport through Coulomb-blockaded quantum dots. We discuss crossed effects that arise when electrons move in response to thermal gradients (Seebeck effect) or energy flows in reaction to voltage differences (Peltier effect). We find that the differential thermoelectric conductance shows a characteristic Coulomb butterfly structure due to charging effects. Importantly, we show that experimentally observed thermovoltage zeros are caused by the activation of Coulomb resonances at large thermal shifts. Furthermore, the power dissipation asymmetry between the two attached electrodes can be manipulated with the applied voltage, which has implications for the efficient design of nanoscale coolers.
We review the quantum interference effects in a system of interacting electrons confined to a quantum dot. The review starts with a description of an isolated quantum dot. We discuss the status of the Random Matrix theory (RMT) of the one-electron states in the dot, present the universal form of the interaction Hamiltonian compatible with the RMT, and derive the leading corrections to the universal interaction Hamiltonian. Next, we discuss a theoretical description of a dot connected to leads via point contacts. Having established the theoretical framework to describe such an open system, we discuss its transport and thermodynamic properties. We review the evolution of the transport properties with the increase of the contact conductances from small values to values $sim e^2/pihbar$. In the discussion of transport, the emphasis is put on mesoscopic fluctuations and the Kondo effect in the conductance.
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