S. Y. Hsu (S. Y. Hsu ( 許世英許世英 ) ) and K. M. Liu(and K. M. Liu( 劉凱銘劉凱銘 ))

May 29, 2007

NSC95-2112-M-009-040 and NSC94-2120-M-009-002

Department of Electrophysics, National Chiao Tung UniversityHsinchu , Taiwan

I

e-

A coherent electron system

I

tkxVtxV sin),( 0

PRB 27, 6083 (1983)

Pumping in a Quantum Device

left reservoir

left reservoir

right reservoir

V(t)

DC current

A phenomena when the dc current is generated in the system with the local perturbation only, without a global driving (bias).

Quantum system

Thouless pump : a traveling wave

IntroductionIntroduction 2DEG2DEG Gate-confined nanostructuresGate-confined nanostructures Historical review on charge pumpingHistorical review on charge pumping

Experimental results and discussionExperimental results and discussion Pumping and Rectification in our QDPumping and Rectification in our QD

Summary Summary

E1

energy

Ec

Ef

0.2eV

Structure of GaAs/AlGaAs grown by MBE

10 nm, GaAs Cap

15 nm, δ- doping layer, Si, 2.6x1018 cm-2

60 nm, spacer AlGaAs x=0.37

1500 nm, buffer layer GaAs

0.3mm GaAs substrate

8 nm, spacer AlGaAs

2DEG

Two Dimensional Electron Gas

Our wafers were grown by Dr.Umansky in Heiblum’s group at Wiezmann Institute in Israel.

GaAs/AlGaAs 0.3KGaAs/AlGaAs 0.3K

carrier density carrier density nnss 2.4x102.4x101111 cmcm-2-2

mobility mobility 1.8x101.8x106 6 cmcm22/Vs/Vs

Fermi wavelength Fermi wavelength λλFF 51.451.4 nm nm

mean free path mean free path ee ~14 ~14 mm

2DEG specification

The 2DEG systems are generally formed by GaAs/AlGaAs heterostructure and contain a thin conducting layer in the interface.

Photo-lithography E-beam lithography

0.5m

190m

metal gates

contact pads

mesa

Gate confined nanostructuresApplying negative voltages on the metal gates fabricated above a

two dimensional electron gas(2DEG),

a quasi-1D quantum conductor is formed.

e-Source Drain

Vg

Three dimensional representation of V.

For a parabolic confining potential22ym

2

1)y(V o

m2

k

2

1n(x)E

2x

2

on

Energy dispersion for 1D channel En (for n=1,2,3) vs. longitudinal wavevector kx. Electrons in the source and drain fill the available states up to chemical potenti

als s and d, respectively.

kx

-1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.00.0

2.0k

4.0k

6.0k

8.0k

10.0k

12.0k

14.0k

16.0k

18.0k

20.0k

R ()

VSG (V)

1D2D

T=0.3K

-1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.40

1

2

3

4

5

6

7

8

9

10

11

12

G (

2e2

/h)

VSG (V)

Split gates confined QPC : dgap=0.3m and channel=0.5 m

dssd

eI

V

IG

Two terminal Landauer formula

Each plateau corresponds to an additional mode as integer multiples of half the Fermi wavelength

N: integerh

2e )(ET

h

2eG

2

F

N

1nn

2

N

Quantum dots can be formed by placing two quantum point contacts in series in between source and drain and confining

electrons in between to a small area characterized by F<L<.

A coherent system

Quantized Pumping in narrow channel using SAWs

I=nef, f=2.728GHz

Pinched-off regime

SAW generating transducer

2DEGSplit gate

A

-Shilton et al.,

J. Phys. C. 8, L531(1996), PRB62, 1564 (2000).

Surface Acoustic Waves

Electrons reside in potential valleys and are carried by the SAW.

Each plateau corresponds to a discrete number of electrons in an electron packet.

Adiabatic Charge Pumping in a QD

For an open confined cavity with two parameters modifying wavefunction with a phase shift ,

use S-matrix and treat the ac field as a weak perturbation

qpc1 qpc2

2,1 1,

*2,1, Im

2

sin

acac

acac

V

S

V

SVVeI

2,1, sin acac VVI PRB 58, 10135 (1998).

Brouwer (1998)Vac,1sin(t)

Vac,2sin(t+)

The charge Q(m) entering or leaving the cavity through contact m(m=1,2) in an infinitesimal time:

*Im2

1)(

,)(

),(

SX

S

dX

mdn

XdX

mdnemQ

m

emissivity

After Fourier Transform, integrating over one period and change of variables

Electron pumping in an open dot using two RF signals Switkes et al., Science 283, 1905 (1999)

Vacsin(t)

Vacsin(t+)

V() sin()

Ibias=0

σ(A0) f. slope~3pA/MHz (20 electrons/cycle)

For small driving amplitude, σ(A0) Vac2.

Rectification of displacement currents

Brouwer, PRB63, 12130 (2001).

Equivalent circuit for the experiment of Switkes et al..

The two ac gates coupled to the reservoir via stray capacitances C1 and C2. At low frequency, ac X1 and X2 generate

displacement current through the dot.

dt

dXC

dt

dXCI(t) 2

21

1

Average over one period,

12

2122

S

1

T

0

DCrec

X

G C

X

G C

G

1dXdX

2

G(t)

I(t)dt

T

1V

2

T

qpc1 qpc2

Vg1 Vg2

The quantized conductance of each QPC is clearly present.

Quantum dot is formed by placing two QPCs in series.

We can adjust transmission mode number N=(n1, n2) for the “open” quantum dot.

n1: mode number on the left QPCn2: mode number on the right QPC

Experimental details

Vacsin(t+2)

Vacsin(t+1)

A

1m

FG

FG

qpc2qpc1

Vacsin(t+2)

Vsdsin(t+1)

A

1m

FG

FG

qpc2qpc1

Measurements : Low frequency modulation technique(1) Pumping mode (2) Rectification mode

A typical plot of I().

**

00

sin

modeion rectificat in the

sin

mode pumping in the

III

III

rect

p

reservoir reservoirI I’=?

wider

Vac1sin(t)

Vac2sin(t+)

Vac1sin(t)

Vac2sin(t+)

21 sin acac VVI

Experimental results

DC current amplitude Ip & Irect vs. ac driving frequency f

for different couplings between dot and its reservoir.(n1, n2).

2,1, 2 acacDC VVfI

DC current amplitude Ip & Irect vs. ac driving amplitude Vac

Pumped current amplitude Ip vs. ac driving amplitude Vac

It’s in weak pumping regime. IpVac

2, in good agreement with the theoretical prediction.

The relation extends well over a very wide current range, 3 orders in magnitude.

Good resolution as small as few pA.

99.1acV pI

Rectification current amplitude Irect vs. Vac

Consistent with the theoretical prediction.

SDacrect VI

95.SDacV rectI

Ip is roughly linearly dependent with frequency.

Ip is smaller for larger Ntot.

Vac =15mV

Pumped current amplitude Ip vs. ac driving frequency f

for different (n1, n2)

Irect decreases with f for f1MHz and slightly increases with f for f>1MHz.

Irect increases with N (conductance), but saturates for Ntot4.

Rectification current amplitude Irec vs. ac driving frequency f

for different (n1, n2)

Dependence of Ip on the coupling bet. dot and its environments

Comparing with (1,1) trace,

multiply other traces with a factor (n1+n2)/2

Ip is scaling with the ratio between mode numbers.

Why do n1 and n2 influence Ip?

2

nn 21

esc

The escaping rate of electron in the dot

n1 and n2 are transmission mode numbers of

both “entrance” leads of the “open” dot, respectively.

For the larger mode number, electrons have stronger coupling strength between dot and reservoirs.

totNtot

p N

1 I

With shorter dwell time, the coherent effect is reduced. Therefore, quantum pumping is suppressed w/. increasing Ntot.

The escaping rate esc increases with mode number linearly, and electrons are more likely to escape to the reservoirs.

The dc current characteristics of pumping and rectification effects are drastically different in our systems.

Summary

The pumping current decreases with increasing transmission mode numbers of the two QPCs due to the dephasing of the coherent electrons in the dot by rapid motions of entering and leaving the dot.

The observed DC current in the pumping mode is mainly from the pumping effect.

symmetric arrangement of pumping gates relative to both entrance leads of the dot

Acknowledgments:

Dr. C.S. Chu (Theoretical support)

Dr. V. Umansky (High mobility 2DEG support)