Figure 4 shows the Ohmic conductance through two dots which are identical in all respects apart from a relative energy off-set of 0.4 U. In order to be able to interpret the conductance plots more easily the average occupation numbers for the four single-particle states are also plotted.
In the limit of negligible coupling between the dots, the occupation for
each dot is determined solely by the coupling to the adjoining reservoir.
This is identical to the single dot case (cf figure 3).
The Ohmic conductance displays peaks at all the single particle energy levels
and at the same energies displaced by U. Similar to the conductance through
a single dot (see figure 2), the peaks come in pairs
separated by the Zeeman energy 
. As it has been explained
for the single dot, one of the peaks of each pair is suppressed as a
result of the Coulomb blockade in the dot. However, it is apparent from
figure 4a that there is also a modulation of the height of
pairs of peaks. For instance the first major peak is noticeably
larger than the second peak. The current path that gives rise to the
first major peak encompasses the levels 
and 
. At
the chemical potential at which the second major peak occurs, the first
dot will be virtually completely occupied and the Coulomb blockade will
be in place. Therefore the dominant contribution to the current will
come from the energy levels 
and . In the case of
figure 4a the dominant levels for the second peak are
energetically further apart than those for the first peak, which explains
why the second pair of peaks is slightly suppressed.
In short, the form of the conductance plot for negligible inter-dot coupling
can be understood by realising that electrons contribute to the
transport only when the Coulomb barrier is overcome in both the first and
the second dot.
As the coupling between the dots is increased, the energy levels in the dots
start to interact, repelling one another.
The conductance peaks are shifted in energy.
When the coupling between the dots becomes appreciable compared to the
energy level difference 
for the decoupled dots,
the number of peaks in the conductance can increase to a number that
is greater than the total number of single particle energy levels.
This is a result of the fact that the amount by which a level is repelled
depends on the energy difference with the level by which it is repelled.
For instance, an original level at an energy can be repelled to
two different resultant energies depending on whether it interacts with
level or 
. This causes a conductance peak both to
shift in energy and to split. This is particularly significant when a
level is repelled into opposite directions by the two possible levels it
could interact with. This happens at intermediate values of the chemical
potential. This explains why splitting can start to be observed for the
middle peak pairs of figure 4c but not for the peaks at more
extreme values of the chemical potential.
In figure 5 the current through the two dots is plotted as a function of the chemical potential in the left reservoir, keeping the chemical potential in the right reservoir fixed. The I-V characteristics are studied as the coupling between the dots is increased.
In the limit of negligible coupling the occupation of each dot is
completely determined by the tunnelling of electrons to and from the
adjoining reservoir. The barrier between the dots is clearly the current
limiting segment, so that the current is proportional to 
(see
figure 5a). Transport can proceed because the wavefunctions
corresponding to the levels in the first dot can leak slightly into the
second dot and vice versa, thus creating current paths.
This explains why there is a marked increase in the current
at 
, 
and
. Note that no current step occurs at
, even though an extra current path becomes
available. This is most easily comprehended by drawing a distinction
between the number of current paths and the number of effective
current paths. A current path consists of a composite state which
is a mixture of a state in the first dot and one in the second dot.
A current path can be said to be effective when it can be used constantly.
For example, it is true that a second current path becomes available
at . However, the number of effective paths
remains fixed at 1, since the Coulomb blockade in the first dot prevents
the paths from being used simultaneously.
The most notable feature of figure 5a is the region of
negative differential conductance around 
. This
is the energy at which the single particle levels in the first dot
are both likely to be occupied. The dominant current
contribution arises from the interaction of the levels 
with the levels 
. As these states are energetically further separated
than the levels 
and , this means that there is less overlap
of the wavefunctions in the two dots which accounts for the drop in current.