Slava Kashcheyevs Bernd Kästner (PTB, Braunschweig, Germany) Mark Buitelaar (University of Cambridge, UK) AAMP’2008, Ratnieki, Latvia Low-frequency excitation.

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 structuremetrological 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, 153301 (2008);Appl. Phys. Lett. 92, 192106 (2008)

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

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

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)

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 structureCorrelated with Coulomb blockade peaksReverse wave direction => reverse polarity

Experimental data

Experimentand 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 formulaPRB 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 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”

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

Work in progress

Want to see quantum effects – Floquet M.Sc. postition

Expreimentalist are pushing for applications – postdoc postion in Braunschweig