Current Eigenmodes and Dephasing in Nanoscopic Quantum Networks

Using the non-equilibrium Keldysh Green's function formalism, we show that the non-equilibrium charge transport in nanoscopic quantum networks takes place via {\it current eigenmodes} that possess characteristic spatial patterns. We identify the microscopic relation between the current patterns and the network's electronic structure and topology and demonstrate that these patterns can be selected via gating or constrictions, providing new venues for manipulating charge transport at the nanoscale. Finally, decreasing the dephasing time leads to a smooth evolution of the current patterns from those of a ballistic quantum network to those of a classical resistor network.