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Explore the current operator in quantum transport through this 14-minute lecture from the nanoHUB-U course on Fundamentals of Nanoelectronics Part B. Delve into advanced concepts of non-equilibrium statistical mechanics as applied to nanotransistors, where active regions span just a few hundred atoms. Learn how modern smartphone technology, enabled by billions of nanotransistors, has deepened our understanding of current flow at the atomic scale. Examine the fundamental conceptual issues surrounding resistance on an atomic scale, the interconversion of electricity and heat, thermodynamic principles, and the fuel value of information. Build upon foundational knowledge of linear algebra and differential equations to grasp sophisticated quantum transport phenomena that bridge the gap between quantized conductance in short ballistic conductors and classical Ohm's law in long diffusive conductors.
