Quantum Transport at Nanoscale

Transport in nanoscale systems is fundamentally di«erent than that encountered in macroscopic systems, due to the quantum mechanical nature of charge carriers over very small length scales. For dimensions much longer than the mean free path of carriers, charge transport is essentially di«usive and well described by the Boltzmann transport equation (BTE) or similar such kinetic equation approach, in which collisions are numerous and treated as instantaneous and memoryless. ¡is picture changes as we approach the nanoscale. As characteristic dimension shrinks below the phase coherence length of carriers in a material (which is of course a strong function of temperature), the exact nature of the quantum states of the system began to manifest themselves. A major e«ect is quantization of motion due to concnement, which leads to reduced dimensionality of charge carriers, and associated changes in the quasiparticle energy and density of states. Quantum interference e«ects also become important, which manifest themselves as quantum |uctuations, conductance quantization, tunneling phenomena, etc. ¡e discrete nature of charge itself becomes important for nanoscale systems, and the many-body interaction of a particle with its environment (which may be phenomenologically related to a “capacitance”) leads to single-electron phenomena such as Coulomb blockade and single-electron tunneling.