Energy flow, thermoelectricity and Fourier's law at the nanoscale
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 energy at the microscopic level. This knowledge is also likely to impact our ability to build more efficient devices for energy generation, storage and conversion. In this Colloquium we survey recent advances and present understanding of physical mechanisms of energy transport in nanostructures. We examine basic issues such as thermoelectricity, local temperature and heating, and the relation between energy 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.