First-principles investigation of alternating current density distribution in molecular devices

Abstract

Using the nonequilibrium Green's function (NEGF) formalism, we derive the current density formula for ac quantum transport by including the self-consistent Coulomb interaction. It is well known that the Coulomb interaction is very important in determining ac current in nanostructures. As pointed out by B\uttiker that the Coulomb interaction must be included to conserve the ac current. Theoretically, the displacement current can be accounted for by including a self-consistent Hartree term in the Hamiltonian as well as the exchange and correlation term while the ac current is calculated from particle current, i.e., $\ensuremath{\langle}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{I}}_{\ensuremath{\alpha}}(t)\ensuremath{\rangle}=q\ensuremath{\langle}d{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{N}}_{\ensuremath{\alpha}}/dt\ensuremath{\rangle}$ where ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{N}}_{\ensuremath{\alpha}}$ is the number operator of the $\ensuremath{\alpha}$ lead. For the ac current density, however, the Coulomb interaction contributes in two ways. As the case of ac current, the self-consistent Coulomb interaction has to be included in the conventional particle current density. In addition, we have to consider the displacement current density explicitly, which is proportional to the time derivative of displacement field. Once the ac current density is obtained, one can calculate the ac current by integrating it over a cross-section area along the transport direction. It is shown that ac current obtained from the total ac current density is conserved and equal to that calculated directly from the lead using NEGF theory. We have applied our formalism to calculate ac current density for nanodevices by combining the density functional theory (DFT) with NEGF theory. Specifically, we have calculated the ac current density to the first order of frequency in a molecular device Al-${\mathrm{C}}_{4}$-Al from first principles. It is found that Al-${\mathrm{C}}_{4}$-Al system exhibits inductive-like behavior under ac bias in the low-frequency limit. Furthermore, nonequilibrium charge distribution is obtained that enables us to study electrochemical capacitance of the molecular devices.