Spintronics of Nanomechanical Shuttle

Transcription

1 * Spinronics of Nanomechanical Shule Rober Shekher In collaboraion wih: D.Fedores,. Gorelik, M. Jonson Göeborg Universiy / Chalmers Universiy of Technology Elecromechanics of Coulomb Blockade srucures Nanomechanical Shuling: Quanum approach. Shuling of Spin-Polarized elecrons. Conclusions

2 Nanoelecromechanical Devices Quanum bell Single C 6 Transisor A. Erbe e al., PR 87, 966 ; D. Scheible e al. NJP 4, 86.. Park e al., Naure 47, 57 ere: Nanoelecromechanics caused by or associaed wih single-charge unneling effecs

3 Silicon nanopillars for mechanical single-elecron ranspor D. V. Scheible, R.. Blick AP 84, 463 4

4 CNT-Based Nanoelecromechanics A suspended CNT has mechanical degrees of freedom > sudy elecromechanical effecs on he nanoscale. B. J. eroy e al., Naure 43, 37 4 V. Sazonova e al., Naure 43, 84 4

5 Elecro-mechanical insabiliy W T E dq X > T. If W eceeds he dissipaed power an insabiliy occurs Gorelik e al., PR 998

6 Shuling of elecronic charge Insabiliy occurs a V > V and develops ino a limi cycle of do vibraions. Boh V and vibraional ampliude are deerm ined by dissipaion. c c I enω N In [VC e ]

7 Quanum Nanoelecromechanics of Shule Sysems δxδp h δx X h Mω R X δx If >> hen quanum flucuaions of he R X grain significanly affec nanoelecromechanics. Do we have a shule insabiliy in his case? We will give a posiive answer o his quesion

8 Condiions for Quanum Shuling X ~ > λ. Fullerene based SET ω λ Tunneling X λ Tz..35 lengh Quasiclassical shule vibraions.. Suspended CNT STM ω d 4 z nm d X / λ ω z for SWNT wih μm [μm]

9 Quanum Shule Insabiliy e h ω ev Quanum vibraions, generaed by unneling elecrons, remain undamped and accumulae in a coheren condensae of phonons, which is classical shule oscillaions. h ω d < hr ee k d λ Shif in oscillaor posiion caused by charging i by a single elecron charge References: Phase space rajecory of shuling. From Ref. 3 D. Fedores e al. Phys. Rev. e. 9, D. Fedores, Phys. Rev. B 68, T. Novony e al. Phys. Rev. e

10 [ ] /, /, ] [, /,,, ev T e T p a c c a T c c ee a a R R v k k k T v Do k k k k eads T Do eads ± μ μ ε μ ε λ m The amilonian: Time evoluion in Schrödinger picure: Tr leads σ Theory of Quanum Shule ], [ i σ σ Reduced densiy operaor Toal densiy operaor Do ead ead

11 Generelized Maser Equaion : : densiy mari operaor of he uncharged shule densiy mari operaor of he charged shule A large volages equaions for, are local in ime: i[ v ee, ] {, } R R Free oscillaor dynamics Elecron unnelling Dissipaion i[ v ee, ] { R, } i [, { p, }] [, [, ] : : describes shuling of elecrons describes vibraional space. Approimaion: / λ <<, ee / kλ <<, <<

12 Shule insabiliy n n n d p p p λ h h & & & [ ] [ ] [ ] Tr n p Tr p Tr h Resul: an iniial deviaion from he equilibrium posiion grows eponenially if he dissipaion is small enough: λ d hr hr h < / ; ; ep Afer linearisaion in using he small parameer o /λ one finds:

13 Skech of resuls W A igh dissipaion case > hr d λ W A Tr{ δ Mω A } ω Mω A I π da W A I cl A Widh is ma[d/λ,/λ 3 d]<<, allowing classical inerpreaion ow dissipaion case A/λ Peak posiion same as obained in classical descripion of shule moion, EP

14 Spinronics of Nanomechanical Shule V/ V/ B E Do A. Pasupahy e al., Science 36,86 4 B: magneic field E: elecric field D.Fedores e al., PR, 95, 573-, 5

15 Formulaion of he problem eads T Do bah bahosc ε a a, T a c c a eads k k k T k k, k, k h Do ε d cc cc Ucccc cc cc p

16 Densiy mari for he spin-polarized shule c c Four basic vecor for he elecronic space c c Densiy mari

17 Spin-vibraional dynamics Λ Λ Λ Λ Λ Λ ], [ ], [ ], [ }, { ], [ }, { ], [ }, { ], [ ih i ih i ih i ih i ee i ee i v v R R v v v R R v

18 Phase Diagram

19 Sof Onse of Shule Vibraions

20 ard Onse of Shule Vibraions

21 Conclusions. Magneic Field Conrolled Nanomechanics: In he magneic NEM-SET he shule effecs can be conrolled via eernal magneic field.. Shule and Mied Regimes of Nanomechanical Vibraions: Differen sable regimes of he spinronic NEM-SET operaion are found and analyzed. 3. Magneic Field Induced ysereic Behaviour: Two ypes of ransiions beween sable vibraional regimes as a funcion of he magneic and elecric field are found

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23 alf-meallic Conducors Ferromagneic Meal μ <<E F alf-meallic Conducors E F - 3 K μ >E F Saes wih minoriy spin are empy Meal w.r.. o majoriy spin elecrons; Semiconducor w.r.. minoriy spin elecrons Maerials: Perovskie Manganese Oides

24 Coulomb Promoion of Spin-Dependen Tunneling Posiive di/dv -- a large magneic fields Coulomb blockade Negaive di/dv -- a small magneic fields Coulomb promoion effec I IV, h J I Ih ν β ν ν ν R R

25 Semiclassical and Quanum Regimes of Shuling Pumping of he energy W cl E eeλ h, δ q h mω δ q Quanum correcion o he pumping resuls in quanum par of he shuling energy δw q E E c δ W q W δw cl q Wcl Ec E c 3 h / emωλ h.e >> E c Semiclassical limi.e E c Quanum limi