By fabricating a single-electron transistor onto a mechanical system in a high magnetic field, it is shown that one can manipulate both the mechanical spring constant and damping constant by adjusting a potential of a nearby gate electrode. The spring constant effect is shown to be usable to control the resonant frequency of silicon-based nanomechanical resonators, while an additional damping constant effect is relevant for the resonators built upon carbon nanotube or similar molecular-sized materials. This could prove to be a very convenient scheme to actively control the response of nanomechanical systems for a variety of applications including radio-frequency signal processing, ultrasensitive force detection, and fundamental physics explorations.

1.
D. W.
Carr
,
S.
Evoy
,
L.
Sekaric
,
H. G.
Craighead
, and
J. M.
Parpia
,
Appl. Phys. Lett.
75
,
920
(
1999
).
The Roukes group at Caltech has measured a 650 MHz silicon carbide resonator (private communication).
2.
J.
Yang
,
T.
Ono
, and
M.
Esashi
,
Appl. Phys. Lett.
77
,
3860
(
2000
).
3.
A. N.
Cleland
and
M. L.
Roukes
,
Appl. Phys. Lett.
69
,
2653
(
1996
).
4.
Z.
Zhang
,
M. L.
Roukes
, and
P. C.
Hammel
,
J. Appl. Phys.
80
,
6931
(
1996
).
5.
T. D.
Stowe
,
K.
Yasumura
,
T. W.
Kenny
,
D.
Botkin
,
K.
Wago
, and
D.
Rugar
,
Appl. Phys. Lett.
71
,
288
(
1997
).
6.
A. N. Cleland and M. L. Roukes, in Proceedings of ICPS-24, edited by D. Gershoni (World Scientific, Singapore, 1999).
7.
K. Schwab, in Proceedings of the International Conference on Solid State Implementations of Quantum Computing, Sydney, Australia, January 2001 (to be published).
8.
C. T.-C.
Nguyen
,
A.-C.
Wong
, and
H.
Ding
,
Dig. Tech. Pap.-IEEE Int. Solid-State Circuits Conf.
448
,
78
(
1999
).
9.
M.
Zalalutdinov
,
B.
Ilic
,
D.
Czaplewski
,
A.
Zehnder
,
H. G.
Craighead
, and
J. M.
Parpia
,
Appl. Phys. Lett.
77
,
3287
(
2000
).
10.
S.
Evoy
,
D. W.
Carr
,
L.
Sekaric
,
A.
Olkhovets
,
J. M.
Parpia
, and
H. G.
Craighead
,
J. Appl. Phys.
86
,
6072
(
1999
).
11.
Single Charge Tunneling, edited by H. Grabert and M. H. Devoret (Plenum, New York, 1991).
12.
The SET properties are simulated using the model described in
M.
Amman
,
R.
Wilkins
,
E.
Ben-Jacobs
,
P. D.
Maker
, and
R. C.
Jaklevic
,
Phys. Rev. B
43
,
1146
(
1991
),
and simplified in:
M. P.
Blencowe
and
M. N.
Wybourne
,
Appl. Phys. Lett.
77
,
3845
(
2000
).
13.
D. V. Averin and K. K. Likharev, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb (Elsevier, Amsterdam, 1991).
14.
The capacitance between the resonator and gate electrode can be approximated by CG(x)=(12×10−12l)/log[4x/w], where w is the width of the electrodes of length l, separated by x [F. E. Terman, Radio Engineers’ Handbook (McGraw–Hill, New York, 1943)].
15.
For VDS≈e/CΣ, one can approximate IDS=(e/4RJCΣ){sin[2πn(x)]+1}, thus ∂IDS/∂x≈(π/4)(e/RJCΣ)(∂n/∂x)cos[2πn(x)]≈(π/4)(VG/RJCΣ)(∂CG/∂x)cos[2πn(x)]. The Lorentz spring constant can be estimated to be kL≈(π/4)(VGBl/RJCΣ)(∂CG/∂x)cos[2πn(x)]. This agrees with the numerical simulation of the SET within ∼10%.
16.
S.
Evoy
,
A.
Olkhovets
,
L.
Sekaric
,
J. M.
Parpia
,
H. G.
Craighead
, and
D. W.
Carr
,
Appl. Phys. Lett.
77
,
2397
(
2000
).
17.
This effect can estimated to the 20% level: for VDS≈e/CΣ, the dynamic impedance of the SET is ∼∂IDS/∂VDS≈2RJ−1, this will lead to Qmax≅ω0m/β=2ω0mRJ/(Bl)2.
18.
A. N.
Korotkov
,
Phys. Rev. B
49
,
10381
(
1994
).
19.
M. H.
Devoret
and
R. J.
Schoelkopf
,
Nature (London)
406
,
19
(
2000
).
20.
M.
Bockrath
,
D. H.
Cobden
,
P. L.
McEuen
,
N. G.
Chopra
,
A.
Zettl
,
A.
Thess
, and
R. E.
Smalley
,
Science
275
,
1922
(
1997
).
21.
Y.
Takahashi
,
M.
Nagase
,
H.
Namatsu
,
K.
Kurihara
,
K.
Iwdate
,
K.
Nakajima
,
S.
Horiguchi
,
K.
Murase
, and
M.
Tabe
,
Electron. Lett.
31
,
136
(
1995
).
22.
D. W.
Carr
,
S.
Evoy
,
L.
Sekaric
,
H. G.
Craighead
, and
J. M.
Parpia
,
Appl. Phys. Lett.
77
,
1545
(
2000
).
23.
D.
Rugar
and
P.
Grutter
,
Phys. Rev. Lett.
67
,
699
(
1991
).
24.
This application will be described elsewhere.
25.
A. D. Armour, M. P. Blencowe, and K. Schwab, Physica B (to be published).
This content is only available via PDF.
You do not currently have access to this content.