4 Coulomb blockade

G [arb. u.]
4.4 Coulomb blockade in quantum dots 85
-1 0 1 2 3
V G
Fig. 4.10. Linear conductance of a QD as a function of the gate voltage at different
temperatures T =0.01EC, T =0.03EC, T =0.05EC, T =0.1EC, T =0.15EC
(lower curve).
A typical behaviour of the conductance as a function of the gate voltage
at different temperatures is shown in Fig. 4.10. In the resonant tunneling
regime at low temperatures T ≪ ∆ɛ the peak height is strongly
temperature-dependent. It is changed by classical temperature dependence
(constant height) at T ≫ ∆ɛ.
4.4.2 Transport at finite bias voltage
At finite bias voltage we find new manifestations of the interplay between
single-electron tunneling and resonant free-particle tunneling.
Now, let us consider current-voltage curve of the differential conductance
(Fig. 4.12). First of all, Coulomb staircase is reproduced, which is more pronounced,
than for metallic islands, because the density of states is limited by
the available single-particle states and the current is saturated. Besides, small
additional steps due to discrete energy levels appear. This characteristic behaviour
is possible for large enough dots with ∆ɛ ≪ EC. If the level spacing
is of the oder of the charging energy ∆ɛ ∼ EC, the Coulomb blockade steps
and discrete-level steps look the same, but their statistics (position and height
distribution) is determined by the details of the single-particle spectrum and
interactions [27].
Finally, let us consider the contour plot of the differential conductance
(Fig. 4.12). Ii is essentially different from those for the metallic island
(Fig. 4.9). First, it is not symmetric in the gate voltage, because the energy
spectrum is restricted from the bottom, and at negative bias all the levels are