Transcript 投影片 1 - National Tsing Hua University

S. Y. Hsu (許世英) and K. M. Liu(劉凱銘)
Department of Electrophysics, National Chiao Tung University
Hsinchu , Taiwan
NSC95-2112-M-009-040 and NSC94-2120-M-009-002
May 29, 2007
Pumping in a Quantum Device
V(t)
left
reservoir
left
reservoir
e-
Quantum system I
right
reservoir
DC current
A coherent electron system
V ( x, t )  V0 sinkx  t 
I
Thouless pump : a traveling wave
PRB 27, 6083 (1983)
A phenomena when the dc current is generated in the system
with the local perturbation only, without a global driving (bias).
Introduction



2DEG
Gate-confined nanostructures
Historical review on charge pumping
Experimental results and discussion

Pumping and Rectification in our QD
Summary
Two Dimensional Electron Gas
Structure of GaAs/AlGaAs
grown by MBE
The 2DEG systems are generally formed
by GaAs/AlGaAs heterostructure and
contain a thin conducting layer
in the interface.
10 nm, GaAs Cap
8 nm, spacer AlGaAs
15 nm, δ- doping layer, Si, 2.6x1018 cm-2
60 nm, spacer AlGaAs
x=0.37
1500 nm, buffer layer
GaAs
0.2eV
E1
2DEG
2DEG specification
Ec
Ef
0.3mm GaAs substrate
energy
Our wafers were grown by
Dr.Umansky in Heiblum’s group
at Wiezmann Institute in Israel.
GaAs/AlGaAs 0.3K
carrier density ns
2.4x1011 cm-2
mobility 
1.8x106 cm2/Vs
Fermi wavelength λF
51.4 nm
mean free path e
~14 m
Photo-lithography
mesa
E-beam lithography
190m
contact pads
metal gates
0.5m
Gate confined nanostructures
Applying negative voltages on the metal gates fabricated above a
two dimensional electron gas(2DEG),
a quasi-1D quantum conductor is formed.
Three dimensional
representation of V.
Source e
Drain
Vg
1  2 2
For a parabolic confining potential V( y)  m  o y
2
2 2
1
 kx

E n (x)   n  o 


2
2m
kx
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
potentials s and d, respectively.
Split gates confined QPC : dgap=0.3m and channel=0.5 m
12
20.0k
11
18.0k
T=0.3K
16.0k
10
9
8
12.0k
7
2
G (2e /h)
14.0k
R ( )
10.0k
8.0k
1D
6.0k
2D
4.0k
2.0k
0.0
-1.1
6
5
4
3
2
1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
VSG (V)
I
eI
G

Vsd s  d
2e 2 N
2e 2
G
 Tn (E F )  N
h n 1
h
0.0
0
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
VSG (V)
Two terminal Landauer formula
N: integer
Each plateau corresponds to an additional mode as
integer multiples of half the Fermi wavelength
-0.4
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
Surface Acoustic Waves
SAW
generating
transducer
2DEG
Split gate
-Shilton et al.,
J. Phys. C. 8, L531(1996), PRB62, 1564 (2000).
I=nef, f=2.728GHz
Pinched-off regime
A
 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
Brouwer (1998)
Vac,1sin(t)
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
Vac,2sin(t+)
emissivity
The charge Q(m) entering or
leaving the cavity through contact
m(m=1,2) in an infinitesimal time:
After Fourier Transform,
integrating over one period
and change of variables
dn(m)
Q(m,  )  e
X  ,
dX
S *
dn(m) 1

Im
S 


dX
2  m
X
e sin  Vac ,1 Vac , 2
S * S
I 
  Im
 1 
2
Vac ,1 Vac , 2
I   sin  Vac,1 Vac, 2
PRB 58, 10135 (1998).
Electron pumping in an open dot using two RF signals
Switkes et al., Science 283, 1905 (1999)
Ibias=0
Vacsin(t)
Vacsin(t+)
V()  sin()
 σ(A0)  f. slope~3pA/MHz (20 electrons/cycle)
 For small driving amplitude, σ(A0) Vac2.
Rectification of displacement currents
Brouwer, PRB63, 12130 (2001).
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.
dX1
dX 2
I(t)  C1
 C2
dt
dt
Average over one period, T 
2

T
Equivalent circuit for the experiment
of Switkes et al..
DC
Vrec
1
I(t)
  dt
T 0 G(t)

1 
G
G 


dX1dX 2 2  C1
 C2

2 S
G   X2
 X1 
Experimental details
9
8
7
qpc2
6
5
qpc1
2
G(2e /h)
qpc1
qpc2
4
3
2
Vg1
Vg2
1
0
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Vg(volt)
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 QPC
n2: mode number on the right QPC
Measurements : Low frequency modulation technique
(1) Pumping mode
(2) Rectification mode
FG
FG
1m
1m
qpc1
Vacsin(t+1)
qpc2
qpc1
qpc2

Vacsin(t+2)
FG
FG
A
Vsdsin(t+1)
A

Vacsin(t+2)
6.0n
A typical plot of I().
in the pumping mode
4.0n
I    I p sin   0   I 0
I (Amp)
2.0n
0.0
-2.0n
in the rectificat ion mode
I    I rect sin   *   I *
-4.0n
-6.0n
0
90
180
270
360
 (deg)
450
540
630
720
Vac1sin(t)
Vac1sin(t)
reservoir
reservoir
I
I’=?
wider
Vac2sin(t+)
Vac2sin(t+)
I   sin  Vac1 Vac 2
Experimental results
I DC  2f Vac,1 Vac,2
DC current amplitude Ip & Irect vs. ac driving amplitude Vac
DC current amplitude Ip & Irect vs. ac driving frequency f
for different couplings between dot and its reservoir.
(n1, n2).
Pumped current amplitude Ip vs. ac driving amplitude Vac
N=(2,2), f=7MHz
Ip (Amp)
10n
I p  Vac 
1.99
1n
100p
10p
Good resolution
as small as few pA.
1p
1m
10m
Vrms
ac (volt)
It’s in weak pumping regime.
IpVac2, in good agreement with the theoretical prediction.
The relation extends well over a very wide current range,
3 orders in magnitude.
Rectification current amplitude Irect vs. Vac
ac
Vfg =25mV;f=5MHz
-9
 
I rect  V
0
Irect(A)
10
SD .95
ac
10
-10
-4
-3
10
10
SD
Vac (volt)
I rect  V
SD
ac
Consistent with the theoretical prediction.
Pumped current amplitude Ip vs. ac driving frequency f
for different (n1, n2)
10.0n
(1,1)
(2,2)
(3,3)
Ip (Amp)
8.0n
6.0n
Vac =15mV
4.0n
2.0n
0.0
0
1M
2M
3M
4M
5M
6M
7M
8M
f (Hz)
Ip is roughly linearly dependent with frequency.
Ip is smaller for larger Ntot.
Rectification current amplitude Irec vs. ac driving frequency f
for different (n1, n2)
7.0n
sd
6.0n
(1,1)
(1,2)
(2,2)
(3,3)
(4,4)
5.0n
Irect(A)
FG
Vac=1mV, Vac =25mV
4.0n
3.0n
2.0n
1.0n
0.0
0.0
1.0M
2.0M
3.0M
4.0M
5.0M
f(Hz)
Irect decreases with f for f1MHz and slightly increases with f for f>1MHz.
Irect increases with N (conductance), but saturates for Ntot4.
Dependence of Ip on the coupling bet. dot and its environments
Comparing with
(1,1) trace,
10.0n
(1,1)
(1,2)x 1.5
(1,3)x 2
(2,2)x 2
(3,3)x 3
8.0n
I*p(A)
6.0n
multiply other traces
with a factor (n1+n2)/2
4.0n
2.0n
0.0
0.0
2.0M
4.0M
6.0M
8.0M
f(Hz)
Ip is scaling with the ratio between mode numbers.
Why do n1 and n2 influence Ip?
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.
The escaping rate of electron in the dot
esc

n1  n 2 

2 
 N tot
1
Ip 
N tot
 The escaping rate esc increases with mode number linearly,
and electrons are more likely to escape to the reservoirs.
With shorter dwell time, the coherent effect is reduced.
Therefore,
quantum pumping is suppressed w/. increasing Ntot.
Summary
The dc current characteristics of pumping and rectification
effects are drastically different in our systems.
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)