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

62 J.M. Elzerman et al.
lock-in signal (arb. units)
-0.96
τ = 15 µs
a
100
-0.96 0
1
b
45
2
90
3
4
180
5
6
300
N =1
-1.12
0
0 τ (µs) 370
N =0
V -1.13
M (V)
-0.76
7
8
f = 4.17 kHz 7 6 5 4
2
3
-0.76
3
4
5
6
7
8
f = 41.7 kHz 7 6 5 4
2
3
-1.07 VM (V) -1.40
V R (V)
0
1
2
c
dip height (%)
V R (V)
-0.96
0
1
2
-0.76
3
4
5
6
7
8
f = 41.7 Hz 7 6 5 4
2
3
-1.07 VM (V) -1.40
Fig. 22. Lock-in detection of electron tunnelling. (a) Lock-in signal at f =1/(2τ)
versus VM for different pulse times, τ, withVP = 1 mV. The dip due to the electron
response disappears for shorter pulses. (Individual traces have been lined up horizontally
to compensate for a fluctuating offset charge, and have been given a vertical
offset for clarity.) (Inset) Height of the dip versus τ, as a percentage of the maximum
height (obtained at long τ). Circles: experimental data. Dashed lines indicate the
pulse time (τ ≈ 120 µs) for which the dip size is half its maximum value. Solid line:
calculated dip height using Γ =(40µs) −1 .(b) Lock-in signal in grayscale versus
VM and VR for VP =1mVandf =4.17 kHz. Dark lines correspond to dips as in
(a), indicating that the electron number changes by one. White labels indicate the
absolute number of electrons on the dot. (c) Sameplotasin(b), but with larger
pulse repetition frequency (f =41.7kHz). (d) Sameplotasin(b), but with smaller
pulse repetition frequency (f =41.7Hz)
for Γ in the analytical expression given above, we obtain the solid line in the
inset to Fig. 22a, which nicely matches the measured data points.
We explore several charge transitions in Fig. 22b, which shows the lock-in
signal in grayscale for τ = 120 µs, i.e. f =4.17 kHz. The slanted dark lines
correspond to dips as in Fig. 22a. From the absence of further charge transitions
past the topmost dark line, we obtain the absolute electron number
starting from zero. In the top left region of Fig. 22b, the right tunnel barrier
(between gates R and T ) is much more opaque than the left tunnel barrier
(between M and T ). Here, charge exchange occurs only with the left reservoir
(indicated as “reservoir” in Fig. 21a). Conversely, in the lower right region
V R (V)
d