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Low-frequency excitation of quantum dots: charge pumping

theory. exp. Low-frequency excitation of quantum dots: charge pumping. Slava Kashcheyevs Bernd K ä stner (PTB, Braunschweig, Germany) Mark Buitelaar (University of Cambridge, UK) AAMP’2008, Ratnieki, Latvia. Outline. What we have ... What we do ... What we get ...

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Low-frequency excitation of quantum dots: charge pumping

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  1. theory exp. Low-frequency excitation of quantum dots: charge pumping Slava Kashcheyevs Bernd Kästner (PTB, Braunschweig, Germany) Mark Buitelaar (University of Cambridge, UK) AAMP’2008, Ratnieki, Latvia

  2. Outline • What we have... • What we do... • What we get... • What we learn... quantum dots ”pump” ~ 0.1-1GHz electrical current electronic structure metrological goals

  3. quantum dots conducting 2D electron gas

  4. 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

  5. Single-parameter non-adiabatic qunatized charge pumping Kaestner, VK, Amakawa, Li, Blumenthal, Janssen, Hein, Pierz, Weimann, Siegner, SchumacherPhys. Rev. B 77, 153301 (2008);Appl. Phys. Lett. 92, 192106 (2008)

  6. V1 V2(mV) V2 Experimental results I = e ×f • Fix V1and V2 • Apply Vacon top of V1 • Measure the current I(V2) V1 V2

  7. ε0 Theory steps - I • 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 ε0(t), ΓL (t) and ΓR (t)

  8. 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)

  9. Theory steps - results

  10. Three main regimes: Adiabatic:h f << min Γnegligible current Optimal:I → e fquantization Overdrive:“stuck” charge I / (ef)

  11. 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...

  12. Adiabatic pumping in carbon nanotubes

  13. Experimental data • Peak-and-dip structure • Correlated with Coulomb blockade peaks • Reverse wave direction => reverse polarity

  14. Experiment and theory

  15. Interpretation: a “molecule”!

  16. Two-level system Adiabatic transfer: level-to-level level-to-lead Interpretation and a model

  17. Two-parameter adiabatic pumping Charge per period Q Brouwer formulaPRB 58 (1998) is easy to obtain analytically Q is an integral over the area enclosed by the pumping contour

  18. (0,0) (1,0) (0,1) (1,1) Theory results for pumping

  19. Effects of assymetry

  20. Reduce frequency 5-fold

  21. Conclusions Every beast has some beauty... ...if you look at it form the right perspective.

  22. 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

  23. Two “triple points” One “quadruple point” 0.3 Γ/Δ 1 3 (Static) transmission probability • If Δ is less than ΓL or ΓR (or both), the two dots are not resolved in a conductance measurement Δ

  24. Meaning of adiabaticity • Gapped system • Gapless system...? • Remain close to the ground state. However, due to gapless excitations (threre is an infinity!) you can end up in a different state

  25. Work in progress • Want to see quantum effects – Floquet M.Sc. postition • Expreimentalist are pushing for applications – postdoc postion in Braunschweig

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