Dr. Max MustermannReferat Kommunikation & Marketing Verwaltung
Daniel SteiningerAG Strunk / Institut fรผr Exp. und Angewandte PhysikFAKULTรT FรR PHYSIK
Shot noise of excited states in a CNT quantum dot
5ยตm
Pd
PdRe QDS D
Gate
๐ ๐
๐ ๐
๐ถ๐
๐ถ ๐ ๐ถ๐
๐ ๐๐ ๐
Double Quantum Dot Layout:source, drain, SC central contact, 2 sidegatesOperated as single quantum dot (QD)
Condition for nonzero Conductance:
๐ ๐๐๐ก๐
๐ ๐
๐ ๐ +1
๐ ๐๐๐๐
๐ ๐ท๐ ๐
๐ ๐๐๐ก๐
๐ ๐
๐ ๐ +1
๐ ๐๐๐๐
๐ ๐ท
๐ ๐
๐ ๐๐๐ก๐
๐ ๐
๐ ๐ +1
๐ ๐๐๐๐
๐ ๐ท
๐ ๐
๐๐โ
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:
โCoulomb Diamondโ pattern Additional steps in Current
Coulomb Blockade:
โจ ๐ผ โฉ๐ผ (๐ก) โจ ๐ผ โฉ๐ผ (๐ก)
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
๐บ๐ฐ ๐/ ๐
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
๐ก
1โ๐ก
(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 laterโฆ)
Measurement Circuit:
Low frequencies (lock-in) High frequencies (noise)
4.2K 300K20mK
Spectrum Analyzer
66uH15
0ฮฉ
2.0nF
1Kฮฉ
2.2nF10nF
50ฮฉ
22nF
22nF MITEQ โ AU 1447
coax.
DC1100ฮฉ
1kฮฉ100kฮฉ
1Kฮฉ
10Kฮฉ
LI 1
DMM1
~
10M
ฮฉ
100kฮฉ
1.1nF
I-V
130 pF
ฯ-filter
ฯ-filter
ฯ-filter
ATF - 34143
x1100
Sample
1ฮฉ
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 โ Two CNTs?
Sample Characterization:
Stability diagram:
90 meV80 meV
10 meV20 meV
๐ฟ๐ถ๐๐ โh๐ฃ๐น
4 ๐ฟ =๐๐๐๐๐
๐ฟ๐ถ๐๐ โh๐ฃ๐น
4 ๐ฟ =๐๐๐๐
Two sets of Coulomb diamonds:
S D๐ฟ๐๐ท1
๐ฟ๐ถ๐๐
๐ฟ๐๐ท 2
Possible configuration:
2 CNTs in parallelAPL 78, 3693 (2001)
1๐๐
geometric length of the CNT
5ยตm
Current:
dI/dV:
Stability Diagram:
Excited states
โ๐ธ โ1๐๐๐
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
๐1โ0.284
๐2โ0.268
๐3โ0.175๐4โ0.91
Comparison Franck-Condon model ๐๐=๐โ๐๐๐
๐ ! ๐=12 ( ๐ฅ๐ฅ0 )
2
๐=๐ .๐ : 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
0ฮฉ
2.0nF
1Kฮฉ
2.2nF10nF
50ฮฉ
22nF
22nF MITEQ โ AU 1447
coax.
DC1100ฮฉ
1kฮฉ100kฮฉ
1Kฮฉ
10Kฮฉ
LI 1
DMM1
~
10M
ฮฉ
100kฮฉ
1.1nF
I-V
130 pF
ฯ-filter
ฯ-filter
ฯ-filter
ATF - 34143
x1100
Sample
Noise Measurements:
1ฮฉ
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
๐ ๐
๐ ๐๐๐๐
๐ ๐ทt
๐1>๐ 0
๐ 0
๐ 0
๐ 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
๐ผ โ 0 ๐ผ=0 ๐ผ โ 0 ๐ผ=0 ๐ผ โ 0
โฆโฆ
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:
โข Home built noise setup at mK-temperatures- DC-/AC-/Noise-measurements simultaneously- Very high resolution ()
โข Plenty of additional information beyond standard DC transport:- Shot Noise suppression / enhancement in Coulomb blockade regime- Very high Fano factors on excited states
Outlook:โข Modelling our experimental resultsโข Repeat measurements with higher quality QDs (suspendended CNTs)โข 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!
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