Mechanically Assisted Single-ElectronicsRobert Shekhter

Göteborg University, Sweden

*

• Nanoelectromechanics of CB structures - classical approach:Coulomb blockade of single-electron tunneling (SET)Nanoelectromechanical coupling in SET devicesShuttling of single electronsShuttling of magnetization and Cooper pairs

• Quantum nanoelectromechanics:Quantum theory of shuttle instabilitySpin-dependent tunneling in CB structures; shuttling of a spin--polarized electronsInterferometry of quantum vibrations

Millikan’s Oil-Drop Experiment(Nobel Prize in 1923)

The electronic charge as a discrete quantity:

In 1911, Robert Millikan of the University of Chicago published* the details of an experiment that proved beyond doubt that charge was carried by discretepositive and negative entities of equal magnitude, which he called electrons.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.

*Phys. Rev. 32, 349-397 (1911); se also http://nobelprize.org/physics/laureates/1923/press.html

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

Gate

DotElectron

Attraction to the gate

Repulsion at the dot

Cost

At

the energy cost vanishes!

Coulomb blockade

Single-electron transistor (SET)

Submicron SET-Sensors

• CB primary termometer (based on thermal smearing of the CB) in a range 20mK-50K (δT~3%) (T.Bergsten et al. Appl.Phys.Lett. 78, 1264 (2001) Y.Pekola, J.Low Temp.Phys. 135, (2004))

• Most sensitive electrometers (based on SET sensitivity to the gate potential Vg): δq~(M.Devoret et al., Nature 406, 1039 (2000)).

• CB current meter (based on SET oscillations in time) (J.Bylander et al. Nature 434, 361 (2005) )

6 1/ 210 eHz− −

Nature 425, 628 (2003)

Single molecular transistors with OPV5 and fullerenes

Self-assembled metal-organic composites

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

Materials properties:

Electrical –heteroconducting

Mechanical - heteroelastic

Electronic features:

Quantum coherence

Coulomb correlations

11 12 11/ , 1, 10 10R M R MRC sτ ω τ ω−= −

Electromechanical coupling

Basic characteristics

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 associatedwith single-charge tunneling effects

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

Nanoelectromechanical Devices

CNT-Based Nanoelectromechanics

A suspended CNT has mechanical degrees of freedom => study electromechanical effects on the nanoscale.

V. Sazonova et al., Nature 431, 284 (2004)

B. J. LeRoy et al., Nature 432, 371 (2004)

Milliken’s Set-up o Nanometer Length Scale

0

( ) ( ) 0.TEW dt Q t X t

T= >∫

If W exceeds the dissipated power an

instability occurs

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

Stable Shuttle Vibrations

pumping

dissipation

W

Shuttle vibrations

2A

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

=

The Electronic Shuttle

Shuttling of magnetization

Mechanically mediated superconducting coupling

M1 M2m L. Y. Gorelik et al., PRL(2003).

Mechanically mediated magnetic coupling

L.Gorelik et al. Nature (2001); A. Isacsson et al. PRL 89, (2002)

How does mechanics contribute to tunneling of Cooper pairs?

Is it possible to maintain a mechanically-assisted supercurrent?

Gorelik et al. Nature 2001

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:

Δ

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= − + Δ

=Δ =

Δ = +

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 > = > + + >

Single Cooper Pair Box

Coherent superposition of two “nearby” charge states [2n and 2(n+1)] 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 Coulomb

blockade is lifted by the gates.

How does it work?

[ ]0 0

Between the leads Coulomb degeneracy is lifted producingan additional "electrostatic" phase shift

(1) (0)dt E Eχ± = −∫

Shuttling between coupled superconductors

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

⎛ ⎞= ±⎜ ⎟⎝ ⎠

∑

[ ] [ ]0

Louville-von Neumann equationDynamics:

, ( )i H Htρ ρ ν ρ ρ∂ = − − −∂

Relaxation suppresses the memory of initial conditions.

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

What about shuttling magnetization?Is it possible to control the effective magnetic coupling

between two magnets by means of a mediator nanomagnet?

M1 M2m

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

L. Y. Gorelik et al., Phys. Rev. Lett. (2003).

1,2 1Mm

ω= >>

Ω

Conclusions

• Electronic and mechanical degrees of freedom of nanometer- scale structures can be coupled.

• Shuttling of single electrons developes as a result of nanoelectromechanical instability in NEM-SET devices.

• Phase coherence between remote superconductors and magnets can be supported by shuttling of Cooper pairs and shuttling of magnetization.

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

Nanoelectromechanical instability

0( ) exp{ }x t x i t tω α= +

1 1( ) ( )R LL RL R L R

C CdQ dQ Q VI Idt dt C R R C R R

= + ⇒ = + + −

MExQ

dtdxx

dtxd )(22

2

+−−= γωWeak electromechanical coupling

1{ }2 thr

α γ γ= −1

)(;);/(2 20

1

+=== −

xxxfCRf RRthr ωωω

ηωγ

))(1(10,1

λtxRR LR ±= −−

12 22

II: Mechanically mediated superconductive coupling

Formulation of the problem

nn Sp }{∧

= ρρ

})()({2,1

1''''∑

=±=

−=∂∂

snn

nsnnn

snn

n xGxGt

ρρρ

MExQ

dtdxx

dtxd )(22

2

+−−= γω

∑=n

nnexQ ρ)(

Distribution of phase differences as a function of number of rotations. Suppression of quantum fluctuations of

phase difference

A. Isacsson et al. PRL 89, 277002 (2002)

Dephasing: A.Romito, F.Plastina & R.Fazio, PR B68, 140502(R) (2003)

Part 1

Classical Nanomechanics Caused by Single-Electrons