
Microscopic theory of
nonequilibrium electronic transport under
timedependent bias through the molecule (or quantum
dot) embedded between two semiinfinite metallic
electrodes is developed in the nonorthogonal
singleparticle basis set using abinitio formalism
of Greens functions. The equilibrium zeroth order
electron Green’s function and selfenergy are
corrected by the corresponding timeinhomogeneous
dynamical contributions, derived in Hartree
approximation in steadystate linearresponse
regime. It was shown that nonorthogonality
contributes to these dynamical contributions by
introducing terms related to the central
regionelectrode interface, appearing only in
timedependent case. The expression for current is
also derived, where nonorthogonalinduced dynamical
correction gives an additional current, not present
in the orthogonal description. It is shown that the
obtained expression for current is gaugeinvariant
and demonstrated that the omission of the additional
current violates charge conservation. It is also
shown that the additional current term vanishes in
orthogonal case. This approach
includes approximations that are to be performed on
two particle Green’s functions in order to avoid
infinite BBGKY hierarchy and to meet the
requirements for calculated selfenergy, such as
conservation laws, self interaction and self
screening free property, as much as it is possible.
In order to describe physical system more
realistically, we try to go beyond known
approximations, or at least to improve them. Once
the time dependent potential in dot is calculated,
we have the basis to determine alternating current
through the dot and its relation with applied
voltage in linear and higher orders.
Since the quantum dots are a physical systems where
the size and the charge quantization meet together,
it is desirable to develop a theories which reduce a
selfinteraction error, allowing to explore the
single charge effects, which is one of the focuses
of my work.
In the density functional theory,
it is desirable to work with quantities represented
in nonorthogonal basis set. The reason is that the
nonorthogonality provides the most localized
description and the linearscaling computation.
Although the orbitals belonging to the same atom and
to nighboring atoms are, without an interaction,
expected to be orthogonal, an interatomic
interaction leads to nonorthogonal behaviour and
the overlap emerging. Any attempt to reintroduce
orthogonality by means of a linear combination of
nonorthogonal orbitals, would lead to orthogonal
functions which have a wider extent than
nonorthogonal one, thus spoiling the picture of
localized basis set and leading to Hamiltonian with
matrix elements which are spread on more distant
sites than in nonorthogonal case. Without working
with localized orbitals, the Hamiltonian division on
separate contributions from electrodes and molecule
as well as from the interfaces projections, would be
meaningless. Beside the computational advantages and
clear physical picture, it is known that
nonorthogonality between atomic orbitals produce
nontrivial effects on chemical bonds strength,
resonance molecular energies, sensitivity of bond
orders and charge densities in heteromolecules. It
is also strongly involved in population analysis
problem.
In steady state transport, as
long as there is no a single molecular orbital that
couples appreciably to the electrodes, the
nonorthogonality has no influence on final results
for transmission or current. The situation
significantly changes when we have to deal with time
dependent transport where charge starts to pile up
in central region consisting of a molecule with
additional neighboring parts of electrodes, chosen
in such a way to provides complete screening of a
molecule. The nonorthogonality introduces a problem
due to nonunique definition of the time dependent
partial charges associated with electrodes and
central region, which is a consequence of
nonorthogonality between complementary subspaces,
making the corresponding projectors nonHermitian.
Furthermore, it is known that the coupling strength
and the current decreases. Additionally, we have
obtained that the interfaces nontrivially
contributes, giving rise the displacement current,
producing the capacitive response only due to
nonorthogonality, and its influence on transport
properties is one of the topics of present work. 