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)

Nanoelectromechanical Devices Quantum ”bell” Single C 60 Transistor A. Erbe et al ., PRL 87 , 96106 (2001); D. Scheible et al. NJP 4 , 86.1 (2002 ) H. Park et al ., Nature 407 , 57 (2000) Here : Nanoelectromechanics caused by or associated with single-charge tunneling effects

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 ( ) ( ) 0 T 0 If W exceeds the dissipated power an instability occurs Gorelik et al., PRL, 80 , 4256(1998)

Quantum Shuttle Instability Quantum vibrations, generated by tunneling electrons, remain undamped and accumulate in a coherent “condensate” of phonons, which is e η ω classical shuttle oscillations. eV η ω d γ < γ ≡ Γ thr λ Phase space trajectory of shuttling. From Ref. (4) Shift in oscillator position eE = d caused by charging it by a (1)D.Fedorets et al., PRL, 95 , 057203-1, 2005 2 k single electron charge (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)

Theory of Quantum Shuttle The Hamiltonian: x = + + H H H H Leads Dot T � + = ε − µ H ( ) a a α α α α Leads k k k α , k Dot + = ε − + ˆ H [ eE x ] c c H , Lead Lead Dot 0 v � + + = ˆ + H T ( x )( a c c a ) α α α T k k α , k Time evolution in [ ] 2 2 Schrödinger picture: = ˆ + ˆ H p x / 2 v µ λ x / = µ = µ ± T ( x ) T e , eV / 2 ∂ σ = − σ ˆ ˆ ( t ) i [ H , ( t )] L , R 0 L , R t � � ρ ˆ ρ ˆ ( t ) ( t ) Total density operator � � ( ) 0 01 ρ ˆ ≡ σ ˆ ≡ ( t ) Tr t � � leads � ρ ˆ ρ ˆ � ( t ) ( t ) Reduced density operator 10 1

Generelized Master Equation ρ ˆ 0 : density matrix operator of the uncharged shuttle density matrix operator of the charged shuttle ρ ˆ 1 : At large voltages equations for are local in time: ρ ρ ˆ 0 ˆ , 1 ∂ ρ ˆ = − + ρ ˆ − Γ ρ ˆ + Γ ρ ˆ Γ + ρ ˆ ˆ ˆ ˆ ˆ i [ H eE x , ] { ( x ), } ( x ) ( x ) L − + γ t 0 v 0 L 0 R 1 R 0 Free oscillator dynamics Electron tunnelling Dissipation ∂ ρ ˆ = − − ˆ ρ ˆ − Γ ˆ ρ ˆ + Γ ˆ ρ Γ ˆ + ρ ˆ i [ H eE x , ] { ( x ), } ( x ) ( x ) L − + γ t 1 v 1 R 1 L 0 L 1 ρ ˆ ≡ ρ ˆ − ρ ˆ γ γ : describes shuttling of electrons i [ ] [ [ ] ] { } − 0 1 ρ ≡ − ρ − ρ ˆ ˆ ˆ ˆ ˆ ˆ ˆ L x , p , x , x , γ α α α ρ ˆ ≡ ρ ˆ + ρ ˆ : 2 2 describes vibrational space. + 0 1 λ << λ << γ << Approximation: x / 1 , eE / k 1 , 1 0

Stable Shuttle Vibrations W Shuttle vibrations pumping dissipation 2 A

Shuttling of electronic charge > In s ta b ility o c c u rs a t V V a n d d e v e lo p s in to a lim it c y c le c o f d o t v ib ra tio n s . B o th V a n d v ib ra tio n a l a m p litu d e a re c d e te rm in e d b y d is s ip a tio n . = eN ω I 2 [ VC Int 2 ] = N e

Experimental observation of shuttling Externaly driven NEMS AC resonance : D.V.Scheible, R.H.Blick, Appl.Phys.Lett. 84 , 4632, (2004); F.Pistolesi, R.Fazio, PRL 94 ,036806,(2005) Internaly driven NEMS 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)

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: → ω ∆ h = • No quasiparticles are produced • Large fluctuations of the charge are suppressed by the Coulomb blockade: → E = E J C

Possible setup configurations Supercurrent between the H leads kept at a fixed phase difference L.Y.Gorelik et al.,Nature, 411 ,454,(2001) Coherence between isolated remote leads created by a single Cooper pair shuttling n n L R A.Isacsson et al., PRL, 89 , 277002, (2002)

Shuttling between coupled superconductors = + H H H C J 2 � � 2 ( ) e Q x = + H 2 n � � C � � 2 ( ) C x e � ˆ s = − Φ − Φ H E ( )cos( x ) J J s = s L R , Dynamics: Louville-von Neumann equation � � δ x L R . = ± ( ) exp � � E x E ∂ ρ J 0 � � [ ] [ ] λ = − ρ − ν ρ − ρ i H , ( H ) 0 ∂ t Relaxation suppresses the memory of initial conditions.

= Average current in units I 2 ef as a function of 0 χ Φ electrostatic, , and superconducting, , phases Black regions – no current. The current direction is indicated by signs

Mechanically-assisted superconducting coupling

Distribution of phase differences as a function of number of 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? M 1 M 2 m By electrically controlling the tunnel barriers the effective interaction between M 1 and M 2 can be made ferromagnetic or antiferromagnetic M ω = 1,2 >> 1 Ω m L. Y. Gorelik et al., PRL (2003).

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 I 2 ef as a function of 0 χ Φ electrostatic, , and superconducting, , phases Black regions – no current. The current direction is indicated by signs