Advances in the fabrication and characterization of nanoscale systems now allow for a deeper understanding of one of the most basic issues in science and technology: the flow of heat at the microscopic level. In this Colloquium we survey recent advances and present understanding of physical mechanisms of energy transport in nanostructures, focusing mainly on molecular junctions and atomic wires. We examine basic issues such as thermal conductivity, thermoelectricity, local temperature and heating, and the relation between heat current density and temperature gradient -known as Fourier's law. We critically report on both theoretical and experimental progress in each of these issues, and discuss future research opportunities in the field.

The interplay of superconductivity and disorder has intrigued scientists for several decades. Disorder is expected to enhance the electrical resistance of a system, whereas superconductivity is associated with a zero-resistance state. Although, superconductivity Superconductivity-the occurrence of the zero-resistance state-has been a central issue in solid-state physics for nearly a hundred years. About half a century after its discovery Bardeen, Cooper and Schreiffer 13 (BCS) explained its microscopic foundation. BCS theory

Despite its intrinsic non-equilibrium origin, thermoelectricity in nanoscale systems is usually described within a static scattering approach which disregards the dynamical interaction with the thermal baths that maintain energy flow. Using the theory of open quantum systems we show instead that unexpected properties, such as a resonant structure and large sign sensitivity, emerge if the non-equilibrium nature of this problem is considered. Our approach also allows us to define and study a local temperature, which shows hot spots and oscillations along the system according to the coupling of the latter to the electrodes. This demonstrates that Fourier's law -a paradigm of statistical mechanics -is generally violated in nanoscale junctions. PACS numbers: 72.15.Jf,73.63.Rt,65.80.+n Non-equilibrium (NE) processes at the nanoscale are receiving a great deal of attention due in large part to the advancements in fabrication and manipulation of these systems.[1] An especially interesting class of NE phenomena pertain to energy transport and the conversion of thermal to electrical energy. When a thermal gradient ∆T is applied to a finite system, electrons respond by departing from their ground state to partially accumulate at one end of the system, thus creating a measurable voltage difference ∆V . The ratio S = − ∆V ∆T is called thermopower [2], and has been measured in a variety of nano-scale systems such as quantum point contacts [3], atomic-size metallic wires [4], quantum dots [5], Si nanowires [6] and recently in molecular junctions [7]. In a bulk material, when S < 0 the transient current is carried by electrons; when S > 0 it is carried by holes.In nanoscale systems this NE problem has recently received a lot of attention [3,[8][9][10][11][12][13]. In these theories the single-particle scattering formalism [14] is used to relate the thermopower to single-particle transmission probabilities. This approach, however, does not take into account the dynamical formation of the thermopower and neglects the fact that even at steady state, when the charge current is zero an energy current is still present, like, e.g., in insulators [15]. Another effect neglected by such theories, which is now within reach of experimental verification [16], is the formation of local temperature variations along the structure. In order to study all these effects one needs to describe a nanoscale system interacting with an environment that maintains the thermal gradient, namely one needs to resort to a theory of NE open quantum systems.In this letter we introduce such a theory, based on a generalization of quantum master equations, and use it to study the dynamical formation of thermo-electric effects in nanojunctions. We show that the thermopower is a highly non-linear function of the thermal gradient and it is very sensitive to the junction geometry, even in the simplest case of non-interacting electrons. This precludes an easy interpretation of its sign in terms of electrons or holes as it has been argued in some literature [3,[8][9][...

Understanding the interplay between illumination and the electron distribution in metallic nanostructures is a crucial step towards developing applications such as plasmonic photocatalysis for green fuels, nanoscale photodetection and more. Elucidating this interplay is challenging, as it requires taking into account all channels of energy flow in the electronic system. Here, we develop such a theory, which is based on a coupled Boltzmann-heat equations and requires only energy conservation and basic thermodynamics, where the electron distribution, and the electron and phonon (lattice) temperatures are determined uniquely. Applying this theory to realistic illuminated nanoparticle systems, we find that the electron and phonon temperatures are similar, thus justifying the (classical) single-temperature models. We show that while the fraction of high-energy “hot” carriers compared to thermalized carriers grows substantially with illumination intensity, it remains extremely small (on the order of 10−8). Importantly, most of the absorbed illumination power goes into heating rather than generating hot carriers, thus rendering plasmonic hot carrier generation extremely inefficient. Our formulation allows for the first time a unique quantitative comparison of theory and measurements of steady-state electron distributions in metallic nanostructures.

Recent experiments claimed that the enhancement of catalytic reaction rates occurs via the reduction of activation barriers driven by non-equilibrium ("hot") electrons in plasmonic metal nanoparticles. These experiments place plasmonic photo-catalysis as a promising path for enhancing the efficiency of various chemical reactions. Here, we argue that what appears to be photo-catalysis is in fact thermo-catalysis, driven by the well-known plasmon-enhanced ability of illuminated metallic nanoparticles to serve as heat sources. Specifically, we point to some of the most important papers in the field, and show that a simple theory of illumination-induced heating can explain the extracted experimental data to remarkable agreement, with minimal to no fit parameters. We further show that any small temperature difference between the photocatalysis experiment and a control experiment performed under uniform external heating is effectively amplified by the exponential sensitivity of the reaction, and very likely to be interpreted incorrectly as "hot" electron effects.