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.

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

conducting 2D electron gas quantum dots

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

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

V 2 (mV)  Fix V 1 and V 2  Apply V ac on top of V 1  Measure the current I(V 2 ) V1V1 V2V2 Experimental results V1V1 V2V2 I = e × f

 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 ε 0 (t), Γ L (t) and Γ R (t) ε0ε0

Theory steps - II  For 1 level it is possible to use exact Floquet solution  A rate equation is valid for max ( Γ L, Γ R, h f ) << kT  We solve for P(t), separate the current into L-R components and integrate over one period ε 0 (t), Γ L (t) and Γ R (t)

Theory steps - results

I / (ef) Three main regimes: A.Adiabatic: h f << min Γ negligible current B.Optimal: I → e f quantization C.Overdrive: “stuck” charge

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...

Adiabatic pumping in carbon nanotubes

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

Experiment and theory

Interpretation: a “molecule”!

 Two-level system  Adiabatic transfer: –level-to-level –level-to-lead Interpretation and a model

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 formula PRB 58 (1998)

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

Effects of assymetry

Reduce frequency 5-fold

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

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

(Static) transmission probability  If Δ is less than Γ L or Γ R (or both), the two dots are not resolved in a conductance measurement Δ Γ/ΔΓ/Δ Two “triple points”One “quadruple point”

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

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