Electronic structures of 1D systems

1. From atom wire and molecular bridges to scanning probe microscopy Electronic structures of 1D systems M.Tsukada Waseda Univ outline 1 Introduction 2 Theoretical methods (RTM,NEGF) 3 Quantum transport in atomic wire eigen channels, quantization 4 Transport through molecules resonant tunneling, Coulomb blockade 5 Large loop current in molecules 6 Some topics of CNT cap, junction, helical shape, persistent current 7 Effect of molecular vibration 8 Magnetism of atomic wire 9 Theory of SPM what and how SPM sees the nano-world? 10 Summary and outlook The 1st A3 Foresight Summer School June 19-22, Seoul National Univ.

2. quantization Coherent vs Dissipation Atomic wires STM,AFM,KFM Contact problem Loop current Atomistic observation Resonant tunneling Molecular bridges Atom manipulation Explore functions View of the systems treated in this lecture Local gates Control of level postions

3. Trends of nano-technology Invention of transistor Road of IC, LSI Molecular quantum bit Down sizing by top down source drain Tunnel junction Economical and physical limit gate Electronics using single molecule Characterization by SPM Novel quantum function Provided by Prof.Y.Wada Bottom up

4. Atom and Molecular bridge structures 1 Bottom up formation of nano-devices 2 Novel functionality utilizing enhanced Quantum nature Nonlocality Nature of electron transport? Quantum entangled state Multiplicity Single electron process Coherent transport Dissipation processes Light emission FET, Switching, Sensing … Instantaneous State transition Reduction of wavepacket Theory can play very essential role for exploring these new area

5. Electron number in molecule Electrode Molecule Electrode Coherent TransportvsDissipative Hopping Transport Uncertainty relation Strong bottle neck even for strong coupling Phase of the state Dissipative Hopping Transport Single electron process Weak bottle neckEffective interaction between the states around EF Coherent quantum transport Competition or Coexistence of the two regimes?

6. Quantum Conductance of Au Point Contact Lars Olesen Quantization value of conductance W tip wetted with Au Au surface Retraction of the tip from the surface

7. Left electrode wave Right electrode wave Concept for the First-principles Recursion Transfer Matrix Method With an appropriate boundary condition, are calculated From the right and left electrode wave-functions DFT potential determined. This is equivalent to Non-equlibrium Green’s function approach.

8. First-Principles RTMmethod details Laue representation of the wave Transfer matrix Matrix difference equation Coefficient matrix Ratio matrix Recursion relation

9. Left electrode wave Right electrode wave RTMmethod details　２ Left jellium electrode Right jellium electrode at the boundary in the right electrode From the recursion relation By multipling All the transefer matrix is solved

10. Exact solvable case

11. Open-Nonequilibrium System

12. Tunnel Current Density and Barrier Calculation with First principles RTM Barrier above Fermi level Current is confined In a narrow channel !! d=12au Vs=2V N.Kobayashi, K.Hirose and M.Tsukada, J.J.Appl. Phys. 35(1996)3710

13. what happens at the atomic contact？ Vs=2V

14. Barrier height and current density

15. Conductance at the atomic contact Conductance at the contact is close to the value of the quantization unit

16. 0V 5V 8V Atom extraxtion by the tip Surface bias Na tip Na surface Electron cloud is pushed out from the nagative tip When a bridge structure of the electron cloud is formed, the atom just ahead of the tip feels a strong puliing force

17. The change of electron density by bias voltage Surface negative Total charge Surface positive

18. Reduction of the Potential Barrier by the bias Tip height 8au=0.42nm Tip negative Potential barrier is remarkably reduce by the applied bias voltage Tip positive

19. Quantization unit= Eigen Channel decomposition Left electrode wave initial Reflection coeff. matrix Transmission coeff. matrix Diagonalize Eigen-channels Unitary transformation of the original channnel Conductance Landauer formula In the eigen channel rep. Transmission Probability of the channel i If

20. Conductance of Jellium Cylinder

21. Quantized conductance in semiconductor mesoscopic system Increase of negative gate voltage Narrowing of the channel width at C Numer of the channnels decreases one by one Conductance Gate Voltage Gate voltage

22. Quantum conductance of Al,Na atomic wire 0.99 0.47X2

23. Channel DOS and Channel Transmission of Al Atom Wire

24. Channel DOS and Channel Transmission of Na Atom Wire

25. Loop current seen in the bent Al atomic wire Impossible in the flame work of classical electromagnetic theory Remarkable Quantum Effect

26. Very fast calculation ! constructed from Inclusion of Non-Local Term in RTM A particular solution with one nonlocal term (αlm) present. atom α lm Transform into integral form (decomposition) GE,I(r,r’) ;Green’s function for the local pseudo-potential system and is present at small regimes.

27. Dependence of the Conductance on the Length of atomic-wires Density of States N=1 Dot Si N=2 N=4 Mixed atoms at the contact determine the magnitude of conductances. N=6 Wire 1D wire

28. Conductance through Al atomic-wires with various atoms mixed at contacts K.Hirose,N.Kobayashi, M.Tsukada, Phys.Rev.B69 (2004) 2454121 First principles RTM calculation with non-local pseudo-potential Al Na Cl

29. Where does the bias drop in the wire ? Potential difference Bias = 5V without wire Charge difference ( ) Local polarization (s-orbital) Bias drop is determined by the local polarization. Spread-out (p-orbital) One impurity gives a significant influence!

30. Resonant tunneling Coherent coupling Electrode Molecule Electrode Internal deg. of freedom Free electrons Localized spin Free electrons Degenrate states Resonant tunneling and quantum coherencemolecular bridges Kondo state Quantum entanglement Large loop current Persistent current

31. Resonant Tunneling,Bottle neck of the coherent transport, and Coulomb blockade

32. 100% transmission, if the energy is exactly tuned at resonant tunneling Double tunnel junctions and bridge systems Contribution to the conductance from the Whole energy range In proportion to the width of the resonance!

33. Nano-structures sandwiched between the planer electrodes First Principles Recursion Transfer Matrix Method N.Kobayashi and M.Tsukada, Jpn. J.Appl. Phys., 38 (1999) 3805

34. Removing vacuum gap・・・ 1D character is appeared!

35. Dimension crossover by the bottleneck Band conduction １-dimensional Resonant tunneling ０-dimensional

36. Transmission Prob. Channel transmission spectra １Dim Channel Atomic wire with good contact Atom or molecular bridge with poor contact And resonant tunneling systems

37. Tunneling through Kondo Resonant State Phase shift of Symmetric, Antisymmetric Scattering waves When the energy crosses with the resonant level, Phase shift abruptly increses by Resonant tunneling Kondo resonant peak always sticks to the Fermi level, thus transmission probability is almost unity over wide range of the gate voltage. A.Kawabata, in Transport phenomena in Mesoscopic Systems, (Springer, ‘91)

38. Single molecular bridge How electron flows through electrode-molecule-electrode? 1)Coherent throughout whole systems resonant tunneling process 2)Incoherentwith the electrodes、but coherentwithin the molecule？ 3)Incoherent both between the molecule and electrodes, as well as within the molecule Intra -molecular hopping the same as small molecular aggregates Coherent in the hole system Transmission assisted by molecular states Partially coherent within a molecule Coulomb blockade, single electron processes Organic molecular thin film(EL) Dissipated hopping

39. Coulomb blockade and single electron process Phase and electron number(charge) are conjugate quantities with each other Energy change just after the tunneling event of an electron Probability of the electron tunneling Based on a naïve assumption that electron with the energy E sees the Fermi level of the counter electrode shifted with the energy Ec

40. I Coulomb blockade and single electron process2 Zero bias conductance anormaly More accurate treatment with including the coupling with external electromagnetic environment Equivalent to the many-harmonic- oscillators system Hamiltonian of the whole system

41. Coulomb blockade and single electron process3 Zero bias conductance anormaly Dissipation spectral fumction Tunneling probability between electrodes Correlation function of phase Tunneling current

42. Coulomb blockade and single electron process4 Multi-junctions and Coulomb diamond No tunneling If above 4 energies are all positive electron tunneling is prohibited

43. Current STM tip Al oxide In fine particle T=4.2K Al substrate -0.2 0.0 0.2 Voltage (V) Single electron tunneling process Wilkins et al Phys. Rev.Lett. 63 (1989)801 Many other examples; Ag cluster/GaAs surface Dye molecules embedded in oxides thin film

44. Coulomb blockade and resonant tunneling Energy of n-th ionized state

45. Density Functional, First-Principles RTM and Non-Equilibrium Green’s Function calculations for the molecular bridges

46. S S I-V characteristic 1 0 h HOMO-LUMO 4 0 0 e 2 2 8 2 0 0 e c n 6 a t 0 c u 4 d n - 2 0 0 o C 2 - 4 0 0 0 - - - - 4 2 0 2 4 4 2 0 2 4 V o l t a g e V V o l t a g e V DOS [eV-1] Energy [eV] Conductance of Benzene di-thiolate First-Principles RTM method by Hirose (NEC) Semi-infinite jellium electrode Differential conductance Exp. Reed et al

47. I-V Characteristics with various contacts 1. close to good contact d=2 a.u. I-V characteristic Differential conductance 1 0 h 4 0 0 HOMO-LUMO state e 2 A 2 8 d ｵ e 2 0 0 c t n n 6 e a t r 0 c r u u 4 d C n - 2 0 0 o C 2 - 4 0 0 0 - - - - 4 2 0 2 4 4 2 0 2 4 V o l t a g e V V o l t a g e V 2. bad contact d=8 a.u. I-V characteristic average local effective potential 1 0 5 V e A d molecule ｵ 0 5 l a t i t n n e - 5 e r tunneling regime 0 t r tunneling o u P C - 1 0 - 5 - 1 5 - - - 1 5 1 0 5 0 5 1 0 1 5 - 1 0 - - 4 2 0 2 4 D i s t a n c e a . u . V o l t a g e V Strong non-linear behavior Effect of the local tunnel barrier disapepearence

48. Non-equlibrium Green’s function approach for Molecular bridges current Transmission function Retarded ….Advanced Green’s function Vertex Lesser Green’s function Electron density distribution Segment current between i and j

49. Transmission function Resonant tunneling metallization of the molecule Transmission spectrum of phenalenyl molecule

50. -0.5 0.0 0.5 eV -0.5 0.0 0.5 eV Connection of Phenalenyl moleculesto the electrodes K.Tagami, L.Wang and M.Tsukada, NANO LETTERS 4 (‘04) 209 SOMO level Source/drain coreesponds to nodes of SOMO transmission transmission