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 Kada
no –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.
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