Time-dependent quantum transport in nanosystems : a nonequilibrium Green's function approach

Abstract

A time-dependent extension to the Landauer–Büttiker approach to study transient quantum transport in arbitrary junctions composed of leads and conducting devices is developed. The nonequilibrium Green’s function approach is employed for describing the charge and heat transport dynamics. The importance of the developed method is that it provides a closed formula for the time-dependent density matrix in both electronic and phononic systems. In the electronic case the nonequilibrium conditions are due to a switch-on of a bias voltage in the leads or a perturbation in the junction whereas in the phononic case the central region of interest is coupled to reservoirs of di erent temperatures. In both cases the time-dependent density matrices, and furthermore other transport properties such as local charge and heat currents, may be evaluated without the necessity of propagating individual singleparticle orbitals or Green’s functions More precisely, an analytic solution to the Kadano –Baym equations of motion for both electronic and phononic Green’s functions describing an arbitrarily shaped and sized noninteracting lattice connected to an arbitrary number of noninteracting wide-band terminals, also of arbitrary shape and size, is provided. In the electronic case, the initial equilibrium state is properly described by the addition of an imaginary track to the Keldysh time contour, on which the equation of motion is described. From the solution the time-dependent electron and phonon densities and currents within the junction are extracted. The final results are analytic expressions as a function of time, and therefore no time propagation is needed – either in transient or in steady-state regimes. As the formalism allows for studying time-dependent transport in noninteracting but arbitrary molecular systems coupled to wide band leads, several applications are presented and discussed. Especially, transient charge dynamics in graphene nanoribbons of di erent geometries is studied. The transient time scales are found to exceed several hundreds of femtoseconds while displaying a long time oscillatory motion related to multiple reflections of the density wave in the nanoribbons at the ribbon–lead interface. This finding strongly vouches for the need for a fully timedependent description of the quantum transport processes. The time-dependent current through a graphene nanoribbon has a shape that scales with the length of the ribbon and is modulated by fast oscillations described by intra-ribbon and ribbon–lead transitions. Furthermore, time-dependent quantum transport is studied in curved graphene nanoribbons. The curvature is found to trigger temporally and spatially focused electric currents which might prove pivotal for a robust design of graphene sensors and circuitries. Further simulations in a superconducting benzene-like molecule attached to normal metal leads show formation of Cooper pairs within the molecule related to Andreev reflection processes. In addition, transient heat transport in atomic chains is studied where the transient oscillations are found to be related to the transitions between the chain’s vibrational modes.