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!