Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

Semiconductor Few-Electron Quantum Dots as Spin Qubits 37
a b
Current
N-1
N N+1 N+2
Gate voltage
Bias voltage
∆E
N-1 N N+1
E add
Gate voltage
Fig. 8. Transport through a quantum dot. (a) Coulomb peaks in current versus gate
voltage in the linear-response regime. (b) Coulomb diamonds in differential conductance,
dI/dVSD, versusVSD and Vg, up to large bias. The edges of the diamondshaped
regions (black) correspond to the onset of current. Diagonal lines emanating
from the diamonds (gray) indicate the onset of transport through excited states
potential level falls within the bias window. By increasing VSD until both the
ground state as well as an excited state transition fall within the bias window,
an electron can choose to tunnel not only through the ground state, but also
through an excited state of the N-electron dot. This is visible as a change in
the total current. In this way, we can perform excited-state spectroscopy.
Usually, we measure the current or differential conductance while sweeping
the bias voltage, for a series of different values of the gate voltage. Such a
measurement is shown schematically in Fig. 8b. Inside the diamond-shaped
region, the number of electrons is fixed due to Coulomb blockade, and no
current flows. Outside the diamonds, Coulomb blockade is lifted and singleelectron
tunnelling can take place (or for larger bias voltages even doubleelectron
tunnelling is possible, see Fig. 7d). Excited states are revealed as
changes in the current, i.e. as peaks or dips in the differential conductance.
From such a “Coulomb diamond” the excited-state splitting as well as the
charging energy can be read off directly.
The simple model described above explains successfully how quantisation
of charge and energy leads to effects like Coulomb blockade and Coulomb
oscillations. Nevertheless, it is too simplified in many respects. For instance,
the model considers only first-order tunnelling processes, in which an electron
tunnels first from one reservoir onto the dot, and then from the dot to the
other reservoir. But when the tunnel rate between the dot and the leads, Γ ,is
increased, higher-order tunnelling via virtual intermediate states becomes important.
Such processes are known as “cotunnelling”. Furthermore, the simple
model does not take into account the spin of the electrons, thereby excluding
for instance exchange effects. Also the Kondo effect, an interaction between
the spin on the dot and the spins of the electrons in the reservoir, cannot be
accounted for.