Shuttling of Single Electrons and Cooper Pairs · Quantum ”bell” Single C60 Transistor A. Erbe...
Transcript of Shuttling of Single Electrons and Cooper Pairs · Quantum ”bell” Single C60 Transistor A. Erbe...
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Shuttling of Single Electrons and Cooper Pairs
Robert Shekhter
In collaboration with:
L. Gorelik and M. Jonson
Chalmers University of Technology / Göteborg University
• Electromechanical coupling in Coulomb Blockade structures
• Shuttling of electrons by a movable dot (PRL,1998)• Shuttling of Cooper pairs by a movable Single Cooper
Pair Box (Nature (2001); PRL (2002) ) • Shuttling of Magnetization between nanomagnets• Discussion and conclusion
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Motivation
Molecular manufacturing – a way to design materials on the nanometer scale
Encapsulated 4 nm Au particles self-assembled into a 2D array supported by a thin film, Anders et al., 1995
Scheme for molecular manufacturing
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Basic characteristics
Materials properties:
Electrical – heteroconducting
Mechanical - heteroelastic
Electronic features:
Quantum coherence
Coulomb correlations
Electromechanical coupling
11 12 -1R , 1, 10 10 sM R MRCτ ω τ ω= ≈ ≈ −
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Tunneling through a metal-organic single-electron device (experiment)
From Han et al., Chem. Phys. Lett. 1998
Specifics of Coulomb Blockade (CB) in molecularly coated dots:
• More emphasized (flat plateaus, sharp edges)
• More pronounced with bias increase
• In some cases – hysteretic I-V curves
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Electro-mechanical instability
0
( ) ( ) 0.TEW dt Q t X t
T= >∫
If W exceeds the dissipated power an
instability occurs
Gorelik et al., PRL 1998
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Shuttling of electronic charge
In s ta b i l i ty o c c u r s a t a n d d e v e lo p s in to a l im i t c y c leo f d o t v ib r a t io n s . B o th a n d v ib r a t io n a l a m p li tu d e a r e d e te rm in e d b y d i s s ip a t io n .
c
c
V VV>
2I eNω=
Int 2
][VCNe
=
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Single C60 TransistorQuantum ”bell”
A. Erbe et al., PRL 87, 96106 (2001) H. Park et al., Nature 407, 57 (2000)
Conclusion: Strong electroelastic effects imply that electrical and mechanical phenomena are coupled on the nanometer length scale – new physics!
Here: Nanoelectromechanics caused by or associatedwith single-charge tunneling effects
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Electromechanical couplingExperiments:
• Artificial systems - mechanical oscillator, f=340 Hz, Tuominen et al., PRL 1999
• Tunneling through a vibrating C60 molecule, f=1.2 THz, Park et al., Nature 2000
• Mechanical manufacturing of nanoshuttle, Erbe et al., PRL 2001
Theory:
• Gate controlled shuttling, Nishiguchi, PRB 2001
• Shuttle instability induced by a resonantly tunneling electron, Fedorets et al., Europhys. Lett. 2002
• Quantum shuttle, Armour et al., PRB, 2002
• Shuttling of Cooper pairs by a movable single-Cooper- pair box, Gorelik et al., Nature 2001; Isacsson et al., PRL (in press)
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How does mechanics contribute to tunneling of Cooper pairs?
Is it possible to maintain a mechanically-assisted supercurrent?
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To preserve phase coherence only few degrees of freedom must be involved.
This can be achieved provided:
• No quasiparticles are produced
• Large fluctuations of the charge are suppressed by the Coulomb blockade: CJ EE <<→
∆<<→ ωh
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Coulomb Blockade of Cooper Pair Tunneling
20
Parity Ef
( ) ( )
0fe
, 2,
c1
t2
{
c g N
N
E N E N V
N nN n
α= − + ∆
=∆ =
∆ = +
At 2 1 Coulomb Blockade is lifted, and the ground state
is with respect to addition degenerate one extrof Coopea r PairgV nα = +
1 2 S in g le | C o o p e r P a i r B| o1 x| n nγ γΨ > = > + + >
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Single Cooper Pair Box
Coherent superposition of two succeeding charge states can be created by choosing a proper gate
voltage which lifts the Coulomb Blockade,
Nakamura et al., Nature 1999
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Movable Single Cooper Pair Box
Josephson hybridization is produced at the trajectory turning points since near these points the CB is lifted by
the gates.
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Possible setup configurations
Supercurrent between the leads kept at a fixed
phase difference
H
Ln Rn
Coherence between isolated remote leads
created by a single Cooper pair shuttling
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Shuttling between coupled superconductors
[ ] [ ]0
Louville-von Neumann equationDynamics:
, ( )i H Htρ ρ ν ρ ρ∂= − − −
∂
22
,
.0
( )22 ( )
ˆ( ) cos ( )
( ) exp
C J
C
sJ J s
s L R
L RJ
H H H
e Q xH nC x e
H E x
xE x E δλ
=
= +
= +
= − Φ −Φ
= ±
∑
Relaxation suppresses the memory of initial conditions.
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How does it work?
[ ]0 0
Between the leads Coulomb degeneracy is lifted producingan additional "electrostatic" phase shift
(1) (0)dt E Eχ± = −∫
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0Average current in units as a function of electrostatic, , and superconducting, , phases
2I efχ
=Φ
Black regions – no current. The current direction is indicated by signs
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Mechanically-assisted superconducting coupling
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Distribution of phase differences as a function of number of rotations. Suppression of quantum fluctuations of
phase difference
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To avoid decoherence:
• Electromagnetic perturbations should be screened
• Gates should be free from dynamic charged defects
• Single-electron tunneling should be suppressed
9 8
Estimates from below can be extracted from the experiNakamura et al., Na
ment by :
10ture 200
10
0 sφτ− −= −
Recent experiments by Saclay group demonstrate even longer decoherence times,
D. Vion et al., cond-mat/0205343610 sϕτ−≈
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What about shuttling magnetization?
Is it possible to control the effective magnetic couplingbetween two magnets by means of a mediator nanomagnet?
M1 M2m
By mechanically controlling the tunnel barriers and hence the exchange coupling between the magnetic moments M1,2 and m at the turning points the effective interaction between M1 and M2 can be made ferromagneticor antiferromagnetic
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Conclusions• Electronic and mechanical degrees of freedom of nanometer-scale structures can be coupled.
• Such a coupling may result in an electro-mechanical instability and “shuttling” of electric charge
• Phase coherence between remote superconductors can be supported by shuttling of Cooper pairs.
• Magnetization can be shuttled by a mediator nanomagnet to provide controllable FM or AFM coupling between cluster magnetic moments