double quantum dot as a thermoelectric generator · references 1. double quantum dot as a minimal...
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Double quantum dot as a thermoelectric generator
Stefan Donsa Abinitio DГA Workshop, Baumschlagerberg 01.09.2013
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Starting Point
• Modelling of an experimental realized double quantum dot in a GaAs/Al0.33Ga0.67As heterostructure (Hübel et. al. 2007, 2008)
• Good match of theory and experiment for the conductivity
• Calculate other thermoelectric coefficients; especially thermopower
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Basic concept
• Kondo effect leads to enhanced thermoelectric coefficients
• One dot n-type, other dot p-type thermoelectric device
• External heat gradient leads to a total current
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Scheme
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Kondo effect in quantum dots
• Lower conductivity in bulk materials
• Quantum tunneling with „spin flip“ leads to non-vanishing thermoelectric coefficients in quantum dots
Initial Final
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Model Hamiltonian
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ˆˆ
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kR
kRkRR
kRkR
kR
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i
iii
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chcaV
cc
nnUnnUnH
• Anderson impurity
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Meir – Wingreen formula
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)()(
1)(
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)(1)(
)(²)(
0
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TI
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TIeTG
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hI i
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2
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Calculations
• Spectral functions via NRG
• Assymetric hybridization
• T=25mK
• Changing one gate voltage effects both quantum dots
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Results
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Thermopower
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Spectral functions
0
/
3
0
2
i
i
BB
iA
ddATk
e
kTS
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Applications 1
• Energy scale μeV
• Temperatur scale mK
• Uninteresting except for Peltier cooling at very low temperatures
• Basic research
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Applications 2
• Reducing size to nm => rescaling of energy and temperature scale
• Multiple connected quantum dots connected via a common back electrode
• Integration on computer chips for the cooling of waste heat and power generation
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Problems & Outlook
• Small thermopower
• Figure of merit is not too high
• Calculated for specific parameters
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Problems & Outlook
• Small thermopower
• Figure of merit is not too high
• Calculated for specific parameters
• Calculate spectral functions for different parameter sets
• Go to lower temperatures
![Page 16: Double quantum dot as a thermoelectric generator · References 1. Double quantum dot as a minimal thermoelectric generator , S. Donsa, S. Andergassen, K. Held arxiv/1308.4882 (2013)](https://reader030.vdocuments.mx/reader030/viewer/2022040121/5eb7e17b668f3c5ee60b59f8/html5/thumbnails/16.jpg)
References
1. Double quantum dot as a minimal thermoelectric generator , S. Donsa, S. Andergassen, K. Held arxiv/1308.4882 (2013)
2. Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992)
3. A. Hübel, J. Weis, W. Dietsche, and K. v. Klitzing, Appl. Phys. Lett., 102101 (2007); A. Hübel, J. Weis, and K. von Klitzing, Physica E (Amsterdam) , 1573 (2008)
4. A. Hübel, K. Held, J. Weis, and K. v. Klitzing, Phys. Rev. Lett., 186804 (2008).