dr. max mustermann referat kommunikation marketing verwaltung daniel steininger ag strunk /...
DESCRIPTION
Coulomb peaks when state is aligned within the bias window Without excited states: Excited states included: „Coulomb Diamond“ pattern Additional steps in Current Coulomb Blockade:TRANSCRIPT
Dr. Max MustermannReferat Kommunikation & Marketing Verwaltung
Daniel SteiningerAG Strunk / Institut für Exp. und Angewandte PhysikFAKULTÄT FÜR PHYSIK
Shot noise of excited states in a CNT quantum dot
5µm
Pd
PdRe QDS D
Gate
𝑉 𝑏
𝑉 𝑔
𝐶𝑔
𝐶 𝑠 𝐶𝑑
𝑅𝑑𝑅𝑠
Double Quantum Dot Layout:source, drain, SC central contact, 2 sidegatesOperated as single quantum dot (QD)
Condition for nonzero Conductance:
𝑉 𝑔𝑎𝑡𝑒
𝜇 𝑆
𝜇 𝑁 +1
𝑉 𝑏𝑖𝑎𝑠
𝜇 𝐷𝜇 𝑁
𝑉 𝑔𝑎𝑡𝑒
𝜇 𝑆
𝜇 𝑁 +1
𝑉 𝑏𝑖𝑎𝑠
𝜇 𝐷
𝜇 𝑁
𝑉 𝑔𝑎𝑡𝑒
𝜇 𝑆
𝜇 𝑁 +1
𝑉 𝑏𝑖𝑎𝑠
𝜇 𝐷
𝜇 𝑁
𝜇𝑁∗
Transport dominated by Coulomb Blockade:
Sample setup:
- e-beam lithography- Metallization:
Sputter (Re)Thermal (Pd)
Coulomb peaks when state is aligned within the bias window
Without excited states: Excited states included:
„Coulomb Diamond“ pattern Additional steps in Current
Coulomb Blockade:
⟨ 𝐼 ⟩𝐼 (𝑡) ⟨ 𝐼 ⟩𝐼 (𝑡)
Average Current is the same for a) and b), while is different.
, where is the number of electrons in lead .
time derivative of the average number of electrons time derivative of variance of the number of electrons
Noise:
Noise gives additional information which is discarded in standard DC measurements
a) b)
Sources of Noise:
1/f Noise
low frequencies, strongly suppressed for
Thermal Noise
𝑺𝑰 𝟏/ 𝒇
Shot NoiseConsequence of charge quantization.Electrons are randomly transmitted or reflected in the conductor. Current fluctuations
For electrons passing a tunnel barrier with transmission probability :
transfer of electrons is completely random and is described by a Poissonian distribution
𝑡
1−𝑡
(Schottky formula)
Sub-/Super Poissonian Noise:
We use the Fano factor to express deviations from the Poisson value
Sub-poissonian (F < 1 ):
-Ballistic transport (no scattering), e.g. open channel in a QPC ()-Transport throught double barrier systems (QDs)
for symmetric barriers for asymmetric coupling
Super-poissonian (F > 1):
-Electron bunching due to cotunneling and/or blocking states (see later…)
Measurement Circuit:
Low frequencies (lock-in) High frequencies (noise)
4.2K 300K20mK
Spectrum Analyzer
66uH15
0Ω
2.0nF
1KΩ
2.2nF10nF
50Ω
22nF
22nF MITEQ – AU 1447
coax.
DC1100Ω
1kΩ100kΩ
1KΩ
10KΩ
LI 1
DMM1
~
10M
Ω
100kΩ
1.1nF
I-V
130 pF
π-filter
π-filter
π-filter
ATF - 34143
x1100
Sample
1Ω
RLC-Circuit Cryo-Amp frequency-Splitter
~100Hz
-Dilution Cryo-
Gain: 1.09
high-frequencies
low-frequencies
System calibration (in situ):
Thermal (equilibrium) noise of a known Resistor ().
Differences in peak amplitude visible down to T=20mK
SV vs T:
Linear dependence:
Two different slopes of the Coulomb diamonds – Two CNTs?
Sample Characterization:
Stability diagram:
90 meV80 meV
10 meV20 meV
𝐿𝐶𝑁𝑇 ≈h𝑣𝐹
4 𝛿 =𝟖𝟒𝟎𝒏𝒎
𝐿𝐶𝑁𝑇 ≈h𝑣𝐹
4 𝛿 =𝟖𝟓𝒏𝒎
Two sets of Coulomb diamonds:
S D𝐿𝑄𝐷1
𝐿𝐶𝑁𝑇
𝐿𝑄𝐷 2
Possible configuration:
2 CNTs in parallelAPL 78, 3693 (2001)
1𝜇𝑚
geometric length of the CNT
5µm
Current:
dI/dV:
Stability Diagram:
Excited states
∆𝐸 ≈1𝑚𝑒𝑉
What kind of excitations? Electronic or Vibronic?
Yar et al. PRB 84, 115432 (2011)
Pro vibronic: - excitations are equidistant - alternating pattern: pos./neg. dI/dV
Pro electronic: -CNT lies on a substrate - fits
𝑃1≈0.284
𝑃2≈0.268
𝑃3≈0.175𝑃4≈0.91
Comparison Franck-Condon model 𝑃𝑛=𝑒−𝑔𝑔𝑛
𝑛 ! 𝑔=12 ( 𝑥𝑥0 )
2
𝒈=𝟏 .𝟗 : From experiment:
Step heights fit Franck-Condon modelfor electron-phonon coupling Sapmaz et al. PRL 96, 026801 (2006)
20mK 4.2K 300K
Spectrum Analyzer
66uH15
0Ω
2.0nF
1KΩ
2.2nF10nF
50Ω
22nF
22nF MITEQ – AU 1447
coax.
DC1100Ω
1kΩ100kΩ
1KΩ
10KΩ
LI 1
DMM1
~
10M
Ω
100kΩ
1.1nF
I-V
130 pF
π-filter
π-filter
π-filter
ATF - 34143
x1100
Sample
Noise Measurements:
1Ω
Low frequencies (lock-in) High frequencies (noise)
RLC-Circuit Cryo-Amp f-Splitter
66uH
2.0nF
coax.
> Remove distortions by cutting> Do Lorentzian fit> Extract amplitude and convert to current noise
> Complete spectrum for every data point (pixel)
Data Processing:
Current
Averaging time: t=10s
Current noise
Fano-Map:
- Pattern of different Fano factors - Super Poissonian noise on excited states- Enhanced Fano factors on NDC-areas
Modelling/Simulations required to explain this pattern and distinguish different mechanisms (vibronic or electronic)
1
1.8
1.21.5 - 2.0
1.0 0.5 - 1.0
1.0
𝜇 𝑆
𝑉 𝑏𝑖𝑎𝑠
𝜇 𝐷t
𝜏1>𝜏 0
𝜏 0
𝜏 0
𝜏 0
Origin of Super Poissonian Noise (F>1):
A state with longer lifetime prevents electrons on higher states from tunneling (blocking state)
Once the electron tunnels out of the dot, all electrons with higher energy can tunnel out
Current flow is blocked again for Increase of noise, while average current remains constant
Increase of Fano factor
𝐼 ≠0 𝐼=0 𝐼 ≠0 𝐼=0 𝐼 ≠0
……
DC Current: dI/dV:
Fano Factor: Current Noise (SI):
Different gate regime:
Very large Fano factors observed in this gate regime ()
Steps in Fano Factor:
1 2 3
3
2
1
Bias Voltage
F=0.5
F=1
F=10
SI vs Current:
1 2 3
3
F=0.5
F=1
F=10
2
1
Current
F=0.5
F=1
F=10
Summary:
• Home built noise setup at mK-temperatures- DC-/AC-/Noise-measurements simultaneously- Very high resolution ()
• Plenty of additional information beyond standard DC transport:- Shot Noise suppression / enhancement in Coulomb blockade regime- Very high Fano factors on excited states
Outlook:• Modelling our experimental results• Repeat measurements with higher quality QDs (suspendended CNTs)• Use two amplifier chains to increase resolution (cross-correlations)
2 amps already implemented, waiting for samples!
Spectrum Analyzer
1.
2.
Thank you for your attention!