Mechanically Assisted Single-Electronics Robert Shekhter In - - PowerPoint PPT Presentation

Mechanically Assisted Single-Electronics

Robert Shekhter

In collaboration with

L.Gorelik* and M.Jonson

Göteborg University, *)Chalmers University

*

• Mechanics caused by single electrons
• Nanoelectromechanical SET device: Shuttle instability
• Mechanical transportation of Cooper pairs
• Transport in magnetic NEM-SET device

Milikan’s Oil Drop Experiment (Nobel Prize in 1923)

The electronic charge as a discrete quantity: In 1910, Robert Millikan of the University of Chicago published the details of an experiment that proved beyond doubt that charge was carried by discrete positive and negative entities each of which had an equal magnitude. The charge on the trapped droplet could be altered by briefly turning on the X-ray

• tube. When the charge changed, the forces on the droplet were no longer balanced

and the droplet started to move.

Electrically controlled single-electron charging

Experiment:

L.S.Kuzmin, K.K.Likharev, JETP Lett. 45, 495(1987): T.A.Fulton, C.J.Dolan, PRL, 59,109(1987); L.S.Kuzmin, P.Delsing, T.Claeson, K.K.Likharev, PRL,62,2539(1989); P.Delsing, K.K.Likharev, L.S.Kuzmin & T.Claeson, PRL, 63, 1861, (1989)

Theory:

R.S., Soviet Physics JETP 36, 747(1973); I.O.Kulik, R.S., Soviet Physics JETP 41, 308(1975); D.V.Averin, K.K.Likharev, J.Low Temp.Phys. 62, 345 (1986)

• H. Park et al., Nature 407, 57 (2000)

Quantum ”bell” Single C60 Transistor

• A. Erbe et al., PRL 87, 96106 (2001);

Here: Nanoelectromechanics caused by or associated with single-charge tunneling effects

• D. Scheible et al. NJP 4, 86.1 (2002)

Nanoelectromechanical Devices

Silicon nanopillars for mechanical single-electron transport

• D. V. Scheible, R. H. Blick APL 84, 4632 (2004)

CNT-Based Nanoelectromechanics

• !"# $$"%

&'() *+,# $$"%

Electro-mechanical instability

( ) ( )

.

T

E W dt Q t X t T = >

• If W exceeds the

dissipated power an instability occurs

Gorelik et al., PRL, 80, 4256(1998)

Quantum Shuttle Instability

λ γ γ d Γ ≡ <

thr

Quantum vibrations, generated by tunneling electrons, remain undamped and accumulate in a coherent “condensate” of phonons, which is classical shuttle oscillations.

k eE d 2 =

Shift in oscillator position caused by charging it by a single electron charge

(1)D.Fedorets et al., PRL, 95, 057203-1, 2005 (2) D. Fedorets et al. PRL, 92, 166801 (2004) (3) D. Fedorets, PRB 68, 033106 (2003) (4) T. Novotny et al. PRL, 90 256801 (2003)

Phase space trajectory of shuttling. From Ref. (4) eV

e ω η ω η

[ ]

2 / , ) ( 2 / ˆ ˆ ) )( ˆ ( , ] ˆ [ ) (

, / , 2 2 , ,

eV e T x T x p H a c c a x T H H c c x eE H a a H H H H H

R L x R L v k k k T v Dot k k k k Leads T Dot Leads

± = = + = + = + − = − = + + =

+ + + +

• µ

µ ε µ ε

λ α α α α α α α α α µ

The Hamiltonian: Time evolution in Schrödinger picture:

( )

• ≡

≡ ) ( ˆ ) ( ˆ ) ( ˆ ) ( ˆ ˆ ) ( ˆ

1 10 01

t t t t t Tr t

leads

ρ ρ ρ ρ σ ρ

Theory of Quantum Shuttle

)] ( ˆ , [ ) ( ˆ t H i t

t

σ σ − = ∂

Reduced density operator Total density operator Dot x Lead Lead

Generelized Master Equation

: ˆ0 ρ

density matrix operator of the uncharged shuttle

: ˆ1 ρ

density matrix operator of the charged shuttle

1 1 1 1 1

ˆ ) ˆ ( ) ˆ ( } ˆ ), ˆ ( { ] ˆ , ˆ [ ˆ ˆ ) ˆ ( ˆ ) ˆ ( } ˆ ), ˆ ( { ] ˆ , ˆ [ ˆ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ

γ γ

L x x x x eE H i L x x x x eE H i

L L R v t R R L v t

+ Γ Γ + Γ − − − = ∂ + Γ Γ + Γ − + − = ∂

+ − + −

Free oscillator dynamics Dissipation Electron tunnelling : ˆ ˆ ˆ

1

ρ ρ ρ + ≡

+

: ˆ ˆ ˆ

1

ρ ρ ρ − ≡

−

describes vibrational space. describes shuttling of electrons

Approximation:

1 , 1 / , 1 / << << << γ λ λ k eE x

{ } [ ] [ ] [ ]

α α α γ

ρ γ ρ γ ρ ˆ , ˆ , ˆ 2 ˆ , ˆ , ˆ 2 ˆ x x p x i L − − ≡

At large voltages equations for are local in time:

1 0 ˆ

, ˆ ρ ρ

Stable Shuttle Vibrations

pumping dissipation

W

Shuttle vibrations

2

A

Shuttling of electronic charge

In s ta b ility o c c u rs a t a n d d e v e lo p s in to a lim it c y c le

• f d o t v ib ra tio n s . B o th

a n d v ib ra tio n a l a m p litu d e a re d e te rm in e d b y d is s ip a tio n .

c c

V V V >

2 I eNω =

Int 2 ]

[VC

N e =

Experimental observation of shuttling

AC resonance:

D.V.Scheible, R.H.Blick, Appl.Phys.Lett.84, 4632, (2004); F.Pistolesi, R.Fazio, PRL 94,036806,(2005)

DC transport and shot noise(?):

H.Park et al.,Nature, 407,57,(2000); D.Fedorets etal.Europhys.Lett.58,99, (2002); S.Braig,K.Flensberg,PR,68,205324, (2003); F.Pistolesi, PR,69,245409-1,(2004)

Internaly driven NEMS Externaly driven NEMS

How does mechanics contribute to tunneling of Cooper pairs?

Is it possible to maintain a mechanically-assisted supercurrent?

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

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.

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:

ω → ∆ h =

J C

E E → =

Possible setup configurations

Supercurrent between the leads kept at a fixed phase difference

H

L

n

R

n

Coherence between isolated remote leads created by a single Cooper pair shuttling

L.Y.Gorelik et al.,Nature, 411,454,(2001) A.Isacsson et al., PRL, 89, 277002, (2002)

Shuttling between coupled superconductors

2 2 , .

( ) 2 2 ( ) ˆ ( )cos( ) ( ) exp

C J C s J J s s L R L R J

H H H e Q x H n C x e H E x x E x E δ λ

=

= +

• =

+

• = −

Φ − Φ

• =

±

• [

] [ ]

Louville-von Neumann equation Dynamics: , ( ) i H H t ρ ρ ν ρ ρ ∂ = − − − ∂

Relaxation suppresses the memory of initial conditions.

Average current in units as a function of electrostatic, , and superconducting, , phases 2 I ef χ = Φ

Black regions – no current. The current direction is indicated by signs

Mechanically-assisted superconducting coupling

Distribution of phase differences as a function of number

• f rotations. Suppression of quantum fluctuations of

phase difference

Shuttling of magnetization

Is it possible to control the effective magnetic coupling between two magnets by means of a mediator nanomagnet?

M1 M2

m

By electrically controlling the tunnel barriers the effective interaction between M1 and M2 can be made ferromagnetic or antiferromagnetic

• L. Y. Gorelik et al., PRL (2003).

1,2

1 M m ω = >> Ω

Conclusion

• Mechanics and electronics meet on a nanometer

length scale

• Mechanically assisted electronics and electronic

control of nanomechanical performance come from such an interplay

• Three examples:
• 1. Shuttle of single electrons
• 2. Transportation of Cooper Pairs
• 3. Mechanically assisted magnetic coupling

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 (in classical and quantum regimes)

• 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

Average current in units as a function of electrostatic, , and superconducting, , phases 2 I ef χ = Φ

Black regions – no current. The current direction is indicated by signs