Dmitry Ryndyk. December 20, 2007, Dresden. In collaboration with Pino D Amico, Klaus Richter, and Gianaurelio Cuniberti

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1 Memory effect in electron-vibron systems Dmitry Ryndyk December 20, 2007, Dresden In collaboration with Pino D Amico, Klaus Richter, and Gianaurelio Cuniberti Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 1

2 Outline I. Motivation: nano-memory, experiments II. III. IV. Atomistic modelling Electron-vibron model Outlook: DQD, MQD, oligophenyls V. Conclusions Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 2

3 I. Motivation: nano-memory, experiments II. III. IV. Atomistic modelling Electron-vibron model Outlook: DQD, MQD, oligophenyls V. Conclusions Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 3

4 Nano-memory / single-electron electron memory Silicon single-electron electron memory L. Guo,, E. Leobandung,, S.Y. Chou,, Science (1997) SP1 proteins and Au nanoparticle hybrids D. Porath s group, The Hebrew University, Jerusalem Problem: stability (life-time) of charged state. Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 4

5 Charge-memory effect in Cu-NaCl NaCl-Au(Ag) systems J. Repp et al., Science (2004), F. E. Olsson et al., PRL (2007) Au / Ag NaCl Cu DFT calculation of neutral and charged state. Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 5

6 Conformational memory effect P. Liljeroth,, J. Repp,, G. Meyer, Science (2007) Bistability of hydrogen position (chemical bonds) in single naphthalocyanine molecule. Results of STM experiments and DFT calculations. Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 6

7 Nonequilibrium switching E. Lörtscher, H.B.. Weber, H. H Riel,, PRL (2007) Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 7

8 I. Motivation: nano-memory, experiments II. Atomistic modelling III. IV. Electron-vibron model Outlook: DQD, MQD, oligophenyls V. Conclusions Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 8

9 From ab initio and DFT to semi-empirical empirical models Ab initio Semi-empirical empirical Hˆ = Hˆ Hˆ Hˆ Hˆ Hˆ L LM M MR R Geometry optimization and vibrational modes. For this purpose DFT is good. Calculation of the I-V I V curves from DFTNGF codes: TranSIESTA,, SMEAGOL, gdftb. Parameters of the semi-empirical empirical model from ab initio codes: Gaussian, GAMESS, HyperChem. Gate V () L t VR () t V t α gate () V = V V n, σ electronic states bias L R Effective model of leads. Anderson-Hubbard Hamiltonian. ˆ = " ε ˆ ˆ αβ α β αβ α β αβ α β H d d U nˆ nˆ Hleads Htun Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 9

10 Stage I: DFT, geometry optimization Neutral state Charged state Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 10

11 Stage II: I: DFT, vibrational modes Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 11

12 Stage IIII II: ab initio (HF( 2e-integrals integrals) parameterization MO LMO AO (nonorthogonal!) MO (orthogonal) LMO (localized) ˆ = " ε ˆ ˆ αβ α β αβ α β αβ α β H d d U nˆ nˆ Hleads Htun Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 12

13 I. Motivation: nano-memory, experiments II. Atomistic modelling III. Electron-vibron model IV. Outlook: DQD, MQD, oligophenyls V. Conclusions Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 13

14 Vibrons and electron-vibron interaction t αβ ε α 0 ( ε ) α Hˆ ev = ε x Hˆ = ω a a λ a a d V ˆx ε β α, β electronic states ˆx normal mode Diagonal coupling α xˆ dαdα ( ) α d α ˆ αβ Hev tαβ xˆ dαdβ ˆ Hˆ pˆ mω0 xˆ = =ω 2m 2 Off - diagonal coupling t = x ( ) 0aa ˆ (0) M = εα( xˆ) dαdα tαβ( xˆ) dd α β α α β H HV = ω0a a λ a a dαdβ ( ) Hˆ = ω a a λ a a d d q V q q q αβ q q α β q qαβ Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 14

15 Standard Model: semi-empirical empirical or ab initio Hˆ Hˆ Hˆ Hˆ Hˆ Hˆ = L LM M MR (0) R Hˆ M = ( εα eϕα() t ) dαdα tαβ dαdβ α α β α Gate V () L t VR () t V t gate () V = V V bias L R n, σ electronic states ( ε ) Hˆ = = ev () t c c i L( R) ikσ i ikσ ikσ kσ Hˆ im = Vik σα, cik σdα hc.. kσα, ( ) ϕ = V η V V δ V α R α L R α gate ˆ ( C ) HM = U nˆ nˆ α β αβ α β ( ) Hˆ = ω a a λ a a d d q V q q q αβ q q α β q qαβ charge redistribution dissipation of vibrons ( ) ˆ q = " ε ˆ ˆ ˆ ˆ αβ α β ωq q q αβ α β λαβ q q α β leads tun αβ q α β qαβ H d d a a U n n a a d d H H Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 15

16 Single-level level model I ( ) Ĥ = " ε d d ω a a λ a a d d 0 0 ( λ ) " ε E( nm, ) = n ω m ω L ΓL ε 0 ΓR R ε n =1 n = 0 ev ε 1 ω 0 left (tip) x x 1 0 ρε ( ) right (substrate) Memory? Switching / noise? M. Galperin,, M.A. Ratner,, A. Nitzan,, Nano Lett.. (2005) A. Mitra, I. Aleiner,, A.J. Millis,, PRL (2005) Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 16

17 Single-level level model II: zero voltage λ 2 ( a a) 10 ω 0 Γ M = m e m M 0m 2 0,0 1, m mm ' mm ' ' g 2 λ = ω Γ # ω m g=0.1 g=1 g= m Franck-Condon blockade,, J. Koch & F. von Oppen g 2 (τγ) τ 1 10 τ λ/ω 0 τ Zero voltage: bistability Finite voltage: switching n 1 0 τ 00 τ 10 = Γ τ = Γ m'0 10 m'0 m' m' t Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 17

18 Single-level level model III: finite voltage Symmetric 0.6 n L ΓL ε 0 ΓR R (τγ) τ τ 10 0 t τ 1 00 Asymmetric ev/ω 0 L ΓL ΓR R L ΓL ε 0 ΓR R ε 1 Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 18

19 Single-level level model IV: I switching 1.0 V τ S t p ev/ω 0 L ΓL ε 0 Γ R 0 0 R L Γ Γ R (τγ) τ 1 10 n 1 τ 10 0 t τ 1 00 L ε 1 R Memory effect in electron-vibron systems Dresden, 20 December 2007 D. A. Ryndyk Memory effect in electron Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 19

20 Single-level level model V: NGF method Γ % ω 0 Nonequilibrium current J 2e = R (,) t t e < im Vik σα, Gα, ikσ $ kσα, Nonequilibrium Green functions G G = d c < α,ikσ α ikσ G = d d < ( RA, ) < ( RA, ) αβ α β < < ( RA, ) n ev/ω 0 J i= L( R) = ie d ε Tr ε ε 2π G G $ G = G G Σ G < 0 R A ( ε ev ) ( ) f ( ε ev ) ( ) G ( ε ) { Γ } i i i R( A) R( A) R( A) R( A) R( A) 0 0 G = G Σ G < R < A Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 20

21 I. Motivation: nano-memory, experiments II. III. Atomistic modelling Electron-vibron model IV. Outlook: DQD, MQD, oligophenyls V. Conclusions Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 21

22 Oligophenyl molecules Benzene Molecular junction Molecular diode Rectification fluorine hydrogen M.A. Reed et al., Science 278, 278, 252 (1997) Triphenyl Molecular switch M. Elbing et al., al., Proc. Natl. Acad. Sci. Sci. USA 102, 102, 8815 (2005) F. Pump and G. Cuniberti, Surface Science (2007) B. Song, D.A. Ryndyk, G. Cuniberti, PRB (2007) D. A. Ryndyk Memory effect in electronelectron-vibron systems systems Dresden, 20 December 2007 Complex Quantum Systems Institute for Theoretical Physics Universität Regensburg 22

23 Effective multi-qd models & vibrations From atomistic to effective multi quantum dot model L tl t ε R t R R ε L Include vibrons ε α ε β t p αβ ˆ mω0 xˆ ˆx ( ) ˆ q = " ε ˆ ˆ ˆ ˆ αβ α β ωq q q αβ α β λαβ q q α β leads tun αβ q α β qαβ H d d a a U n n a a d d H H 0aa Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 23 Hˆ = =ω 2m 2 ˆ (0) M = εα( xˆ) dαdα tαβ( xˆ) dd α β α α β H α, β electronic states ˆx normal mode

24 Molecular spin-valve and spin-correlation effects Spin-blockade Spin-memory L tl t ε R t R R ε L U L tl ε L t ε R t R R Charge-memory effect J. Repp, et al.,, Science (2004) Conformational-memory memory effect J. Repp, et al.,, Science (2007) Spin-memory effect? Current is suppressed in P case by combined action of Coulomb blockade and Pauli exclusion principle. L tl ε L t U ε R t R R L tl ε L t U ε R t R R Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 24

25 I. Motivation: nano-memory, experiments II. III. IV. Atomistic modelling Electron-vibron model Outlook: DQD, MQD, oligophenyls V. Conclusions Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 25

26 Conclusions! Simple polaron model of the charge-memory effect is considered! Crossover between memory and switching is investigated? Interplay of vibrons with charging effects and spin effects in multi-level level systems? Application to oligophenyl systems and recent experiments? Nonequilibrium ab initio theory This work is supported by SPP 1243 Quantum Transport at the Molecular Scale SFB 689 Spin phenomena in reduced dimensions Klaus Richter Pino D Amico Gianaurelio Cuniberti thank you for attention Complex Quantum Systems Institute for Theoretical Physics Universität t Regensburg 26