Mesoscopic Nano-Electro-Mechanics of Shuttle Systems

Transcription

1 * Mesoscopic Nano-Electro-Mechanics of Shuttle Systems Robert Shekhter University of Gothenburg, Sweden Lecture1: Mechanically assisted single-electronics Lecture2: Quantum coherent nano-electro-mechanics Lecture3: Mechanically assisted superconductivity

2 Electric Weak Links (EWL) Electronic transmission through small regions of material determines electric transport between bulk conductors Microbridges EWL with current concentration J A/ cm Coulomb Blockade structures EWL with electric charge concentration

3 Mesoscopic Phenomena (Examples) 3/23 Persistent currents (in the ground state) -Microscopic scale: Electrons move in atomic orbitals, may generate net magnetization -Macroscopic scale: No current in the ground state of bulk sample -Mesoscopic scale: Persistent currents in the ground state Josephson effect (supercurrent passing through SNS-region) -A supercurrent may flow between two superconductors separated by a non-superconducting region of mesoscopic size Coulomb blockade (due to discreteness of electronic charge) -Microscopic scale: Electrons have finite charge e, Coulomb interactions give rise to large ionization energies of atoms -Macroscopic scale: Electron liquid, charge discreteness not important -Mesoscopic scale: Coulomb blockade of tunneling through granular samples Mesoscopic samples contain a large number of atoms but are small on the scale of a temperature-dependent coherence length. On such scales electronic and mechanical phenomena coexist: Mesoscopic Nanoelectromechanics

4 References Book: Andrew N. Cleland: Foundation of Nanomechanics Springer,2003 (Chapter7,esp.7.1.4, Chapter 8,9); Reviews: R.Shekhter et al.: Low.Tepmp.Phys. 35, 662 (2009); J.Phys. Cond.Mat. 15, R 441 (2003) J. Comp.Theor.Nanosc., 4, 860 (2007)

5 Lecture 1 Mechanically Assisted Single Electronics Outline Electric charge quantization in solids (important historical events) Nanoelectromechanical coupling due to tunneling of single electrons Shuttling of single electrons in NEM-SET devices

6 Lecture 1: Mechanically assisted single-electronics 6/23 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 discrete positive 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, (1911) See also

7 Lecture 1: Mechanically assisted single-electronics 7/23 Electrically Controlled Single-Electron Charging Dot e 2 /C 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)

8 Lecture 1: Mechanically assisted single-electronics 8/23 Electron Coulomb Blockade Gate Dot Cost Repulsion at the dot Attraction to the gate At the energy cost vanishes! Single-electron transistor (SET)

9 Lecture 1: Mechanically assisted single-electronics 9/23 Single Molecular Transistors with OPV5 and Fullerenes Nature 425, 628 (2003)

10 Lecture 1: Mechanically assisted single-electronics 10/23 Self-Assembled Metal-Organic Composites Molecular manufacturing a way to design materials on the nanometer scale Encapsulated 4nm Au particles self-assembled into a 2D array supported by a thin film, Anders et al., 1995 Scheme for molecular manufacturing

11 Lecture 1: Mechanically assisted single-electronics 11/23 Basic Characteristics Materials properties: Electronic features: Electrical heteroconducting Quantum coherence Mechanical heteroelastic Coulomb correlations Electromechanical coupling

12 Lecture 1: Mechanically assisted single-electronics 12/23 Nanoelectromechanical Devices Quantum bell Single C 60 Transistor A. Erbe et al., PRL 87, (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

13 Lecture 1: Mechanically assisted single-electronics 13/23 CNT-Based Nanoelectromechanics A suspended CNT has mechanical degrees of freedom => study electromechanical effects on the nanoscale. B. J. LeRoy et al., Nature 432, 371 (2004) V. Sazonova et al., Nature 431, 284 (2004)

14 Lecture 1: Mechanically assisted single-electronics 14/23 Millikan s Set-up on a Nanometer Length Scale If W exceeds the dissipated power an instability occurs Gorelik et al., PRL, 80, 4256(1998)

15 Lecture 1: Mechanically assisted single-electronics 15/23 The Electronic Shuttle

16 Lecture 1: Mechanically assisted single-electronics 16/23 Circuit Model for the Shuttle Electrostatic energy of the charged grain V C 2 L CR En Qn / 2 C Qn, 2 C Qn ne C C L C R Electronic tunneling rate: G s n n e 2 1 R ( x) s 1 E exp n E { E n n ev E n s ( n ev s n) ( n n, )} s L, R R ( x) R exp 1 1 L( R) 0 x

17 Lecture 1: Mechanically assisted single-electronics 17/23 Formulation of the Problem p Sp{ } n n Q ( x) e n np n p t n n s ' n 1 1,2 { G s ' n n ( x) p n ' G s nn ' ( x) p n } 2 d x 2 dx Q( x) E x 2 dt dt M

18 Lecture 1: Mechanically assisted single-electronics 18/23 Nanoelectromechanical Instability dq dq Q 1 1 V CR CL IL IR ( ) ( ) dt dt C R R C R R L R L R R 1 1 x( t) R, L R (1 ) 0 2 d x 2 dx Q( x) E x 2 dt dt M Weak electromechanical coupling: CVE 2 2M 2 1 x( t) x0 exp{ i t t} 1 { } 2 thr thr 2 f ( R / ); R 1 R C; 0 f ( x) x 2 x 1

19 Lecture 1: Mechanically assisted single-electronics 19/23 Stable Shuttle Vibrations W Shuttle vibrations pumping dissipation 2 A

20 Lecture 1: Mechanically assisted single-electronics 20/23 Different Scenarios for a Shuttle Instability SOFT instability HARD instability R 3 2 Only one stable mechanical regime is possible R 3 2 Two regimes of locally stable mechanical operations

21 Lecture 1: Mechanically assisted single-electronics 21/23 Soft Onset of Shuttle Vibrations

22 Lecture 1: Mechanically assisted single-electronics 22/23 Hard Onset of Shuttle Vibrations

23 Lecture 1: Mechanically assisted single-electronics 23/23 Shuttling of Electronic Charge

24