Abstract
Using the nonequilibrium Keldysh Green's function formalism, we show that the nonequilibrium charge transport in nanoscopic quantum networks takes place via 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.
Highlights
Using the non-equilibrium Keldysh Green’s function formalism, we show that the non-equilibrium charge transport in nanoscopic quantum networks takes place via 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
V I We show that nanoscopic quantum networks possess current eigenmodes which possess distinct spatial current
Summary
In order to study the effects of dephasing [2, 18] on the spatial current patterns in nanoscopic networks, we consider the electron-phonon interaction [see Eq(1)] [19] and employ the high-temperature approximation ω0 ≪ kBT (with ω0 → 0) introduced in Ref.[20] In this case, the self-energy is related to the full Green’s function via ΣK,r = γGK,r, where γ = 2g2kBT /ω0, such that the dephasing process is controlled by a single parameter, γ (a derivation of the Green’s functions in this approximation is presented in Appendix A). We demonstrated that the rich variety of spatial current patterns arises from the interplay between the network’s geometry and electronic structure, the leads’ location and width, and the dephasing time, and can be selected via gating or through constrictions These results suggest new venues for custom-designing current patterns and their transport properties at the nanoscopic, local level. We introduce the superoperator D [20] which, when operating on a Green’s function matrix, returns the same matrix with all elements set to zero except for the diagonal elements in the network, e.g.,
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