Transcript AAMP - Latvijas universitāte

Low-frequency excitation of
quantum dots: charge pumping
Slava Kashcheyevs
theory
Bernd Kästner (PTB, Braunschweig, Germany)
Mark Buitelaar (University of Cambridge, UK)
AAMP’2008, Ratnieki, Latvia
exp.
Outline
 What we have...
quantum dots
 What we
do...
”pump” ~ 0.1-1GHz
 What we
get...
electrical current
 What we learn...
electronic structure
metrological goals
quantum dots
conducting 2D
electron gas
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)
Experimental results
I=e×f
V1
V2(mV)
V2
 Fix V1 and V2
 Apply Vac on top of V1
V1
V2
 Measure the current I(V2)
Theory steps - I
ε0
ε0(t) , ΓL (t) and ΓR (t)
 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 - II
 For 1 level it is possible to
use exact Floquet solution
 A rate equation is valid for
max (ΓL, ΓR, h f ) << kT
ε0(t) , ΓL (t) and ΓR (t)
 We solve for P(t), separate the current into L-R
components and integrate over one period
Theory steps - results
Three main regimes:
I / (ef)
A. Adiabatic:
h f << min Γ
negligible
current
B. Optimal:
I→ef
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
Experimental data
 Peak-and-dip structure
 Correlated with Coulomb blockade peaks
 Reverse wave direction => reverse polarity
Experiment
and theory
Interpretation: a “molecule”!
Interpretation and a model
 Two-level system
 Adiabatic transfer:
– level-to-level
– level-to-lead
Two-parameter adiabatic pumping
Charge per period Q
Brouwer formula
PRB 58 (1998)
is easy to obtain
analytically
Q is an integral over
the area enclosed by
the pumping contour
Theory results for pumping
(0,0)
(1,0)
(0,1)
(1,1)
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
Δ
Two “triple points”
0.3
One “quadruple point”
1
3
Γ/Δ
 If Δ is less than ΓL or ΓR (or both), the two dots
are not resolved in a conductance measurement
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