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Slava Kashcheyevs
Bernd Kästner (PTB, Braunschweig, Germany)
Mark Buitelaar (University of Cambridge, UK)
AAMP’2008, Ratnieki, Latvia
Low-frequency excitation of quantum dots: charge pumping
theory
exp.
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Outline
What we have...
What we do...
What we get...
What we learn...
quantum dots
”pump” ~ 0.1-1GHz
electrical current
electronic structuremetrological goals
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conducting 2D
electron gas
quantum dots
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Artificial versus natural atoms Custom “ionic” potential
– easy to manipulate (electrostatics)– less symmetries, hard to know exact shape
Excitation field confined to wires– accurate frequency control– (much) beyond dipole approximation
Coupled to enviroment– the Fermi sea (gapless vacuum!)– sensitive to fluctuations and signals around
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Single-parameter non-adiabatic qunatized charge pumping
Kaestner, VK, Amakawa, Li, Blumenthal, Janssen, Hein, Pierz, Weimann, Siegner, Schumacher
Phys. Rev. B 77, 153301 (2008);Appl. Phys. Lett. 92, 192106 (2008)
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V2(mV)
Fix V1 and V2
Apply Vac on top of V1
Measure the current I(V2)
V1
V2
Experimental results
V1 V2
I = e × f
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Assume some resonable shape for the double-hill Focus on “neutron-hydrogen” transition Construct tunneling Hamiltonian
– each contact is a Fermi black body!
Solve for adiabatic evolution of the level and rates
Theory steps - I
ε0(t) , ΓL (t) and ΓR (t)
ε0
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Theory steps - II
For 1 level it is possible to use exact Floquet solution
A rate equation is valid for max (ΓL, ΓR, h f ) << kT
We solve for P(t), separate the current into L-R components and integrate over one period
ε0(t) , ΓL (t) and ΓR (t)
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Theory steps - results
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I / (ef)
Three main regimes:A. Adiabatic:
h f << min Γ
negligible current
B. Optimal:I → e f
quantization
C. Overdrive:“stuck” charge
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Mid-talk summary
Novel principle of quantized current generation using just one signal
Frequency threshold for current generation (“non-adiabatic blockade of tunneling”)
Work in progress...
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Adiabatic pumping in carbon nanotubes
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Peak-and-dip structureCorrelated with Coulomb blockade peaksReverse wave direction => reverse polarity
Experimental data
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Experimentand theory
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Interpretation: a “molecule”!
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Two-level system Adiabatic transfer:
– level-to-level– level-to-lead
Interpretation and a model
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Two-parameter adiabatic pumping
Charge per period Q
Q is an integral over the area enclosed by the pumping contour
is easy to obtain analytically
Brouwer formulaPRB 58 (1998)
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(0,0)
(0,1)
(1,0)
(1,1)
Theory results for pumping
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Effects of assymetry
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Reduce frequency 5-fold
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Conclusions
Every beast has some beauty...
...if you look at it form the right perspective.
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Experimental findings
At small powers of applied acoustic waves the features grow with power and become more symmetric
For stronger pumping the maximal current saturates and opposite sign peaks move aparpt
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(Static) transmission probability
If Δ is less than ΓL or ΓR (or both), the two dots are not resolved in a conductance measurement
Δ
Γ/Δ310.3
Two “triple points” One “quadruple point”
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Meaning of adiabaticity
Gapped systemGapless system...? Remain close to the ground state.
However, due to gapless excitations (threre is an infinity!) you can end up in a different state
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Work in progress
Want to see quantum effects – Floquet M.Sc. postition
Expreimentalist are pushing for applications – postdoc postion in Braunschweig