András Halbritter. Budapest University of Technology and Economics, Department of Physics

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1 Electron transport in single-molecule unctions András Halbritter Budapest University of Technology and Economics, Department of Physics Coworkers: Prof. György Mihály Dr. Szabolcs Csonka Péter Makk Attila Geresdi Máté Vigh András Gyenis László Pósa Zoltán Balogh András Magyarkuti Béla Horváth Tibor Halász Sándor Bacsa László Takács This work is connected to the scientific program of the " Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" proect. This proect is supported by the New Széchenyi Plan (Proect ID: TÁMOP-4..1/B-09/1/KMR Electron transport in single-molecule unctions András Halbritter Budapest University of Technology and Economics, Department of Physics Future perspectives: Single molecule transistor Electrode Insulator ~7nm Electrode 1 Electrode arrangement Present goal: Atomic and molecular switches understanding the architecture of matter and electron transort at the scale of single atoms and molecules Molecular sensors? 1

2 Electron transport in single-molecule unctions András Halbritter Budapest University of Technology and Economics, Department of Physics Literature: Juan Carlos Cuevas and Elke Scheer: Molecular Electronics: An Introduction to Theory and Experiment N. Agrait, A. L. Yeyati, and J. M. van Ruitenbeek: Quantum properties of atomic-sized conductors, Physics Reports 377, 81 (003 (condmat/00839 Moore's law, driving force of nanoelectronics Micro world Micro mechanics bacteria Visible world 1mm 100µm The size of the building blocks shows an exponential decrease in nanoelectronics Gordon E. Moore Mesoscopic systems Nano world Top-down apprach Bottom-up apprach self organization, chemistry (biology!

3 Creating atomic-sized gaps - break unctions During the rupture of a metallic wire at the final stage a single atom connects the two sides A possible method to create high stability atomic-sized unctions: Mechanically Controllable Break Junction technique An atomic-sized contact can be created by pushing an STM tip into the sample surface With a nanofabricated break unction a displacement ratio of 1:10 5 can be reached z x/10 5! Advantage: precisely tunable electrode separation, easy statistical averaging z x/100! MCBJ technique (as we use it sample wire Epoxy drop Piezo x contact pad epoxy sample beam Bending beam Differential screw (coarse positioning molecules 3

4 Creating atomic-sized gaps - electromigration Danger: formation of a metallic grain, which alone acts as a SET. Gentle breaking process is essential at the final steps T. Taychatanapat et al., Nano Lett., 7, 3, 007 Advantages: extreme stability, possibility for gate electrode, "mass" production Reminder: Landauer formula µ L ^ t in L out R µ R The system is considered as two ideal quantum wires with quantized transverse modes connected by a small constriction, characterized by a transmission matrix out R = ˆt in L transmission matrix The conductance is given by the Landauer formula: e = Tr( ˆ ˆ e G t t = h h T i i= 1..N In the appropriate eigenchannel basis the conductance can be given as a sum transmission eigenvalues, the so called mesoscopic PIN code In semiconductor DEG heterostructures the Fermi wavelength is large due to the small electron density, λ F 40nm. -> a "smooth", adiabatic contact can be made by e- beam lithography -> conductance quantization is observed λ F In metals the Fermi wavelength is comparable to the lattice constant. According to a simple approximation (3D Sharvin formula a single-atom contact has a conductance in the range of conductance quantum, G e /h. Due to the atomic granularity of the matter such a small contact cannot be treated as an adiabatic one. 4

5 Single molecule unctions? Idea: single molecule unction Reality: Changing gate voltage Molecule Electrode Anchoring group Tuning electrode separation I? Piezo V Every piece of information is important to puzzle out the microscopic details! Measuring I-V curve Dosing molecules e (transparent unctions i subgap structure -> i (low T unctions 5

6 Conductance histograms e (transparent unctions i subgap structure -> i (low T unctions By repeated opening and closing of the unction thousands of conductance vs. electrode separation traces are recorded Au conductance traces conductance histogram From the conductance traces a histogram is constructed. Peaks in the histogram correspond to stable, frequently occuring atomic configurations. After dosing molecules the appearance of a new peak reflects the stable molecular configurations. R.H.M. Smit et al. Nature 419, 906 (00 e (transparent unctions i subgap structure -> i (low T unctions Conductance fluctuations T 0 The partial electron waves reflected by impurities in the electrodes cause a random interference process, which can be tuned by bias voltage. Its amplitude depends on the channel transmissions. Example: Pt-H unctions Single channel, T=97% The new molecular configuration has a single perfectly transmitting channel. It must be a single molecule, as parallel molecules would have more channels. Statistical information! B. Ludoph et al. Phys. Rev. Lett., 8, 1530 (1999; A. Halbritter et al. Phys. Rev. B, 69, (004 R.H.M. Smit et al. Nature 419, 906 (00 S. Csonka, A. Halbritter et al. Phys. Rev. Lett (004 6

7 e (transparent unctions i subgap structure -> i (low T unctions Shot noise T 1-T G G G Example: Pt-H unctions The average transmission probability is T. However, if current is measured, we can never detect the transmission of fractional charge: the electron is either fully transmitted, or fully reflected. ~ N = T 1+ ~ ~ T N ( 1 T ( 1 T = T 1+ ( 1 T H.E. van den Brom et al. Phys. Rev. Lett., 8, 156 (1999 D. Dukic, J.M. van Ruitenbeek, Nano Letters, 6, 789 (006. N 0 = T 0 T The shot noise measurement shows that the selected configuration indeed has a single, almost perfectly transmitting channel. Information on a given contact! e (transparent unctions i subgap structure -> i (low T unctions Point-contact spectroscopy Discrete vibrational mode: g(e hω excitation spectrum HD D E di/dv hω ev d I/dV hω Pt Pt ev Isotope shift of the vibration energies clerly shows that a H and not dissociated H atoms are sitting in the unction Pt Pt H R. H. M. Smit et al. Nature 419, 906 (00 D. Dukic et al., Phys. Rev. B 71 (005, R

8 e (transparent unctions i subgap structure -> i (low T unctions A benchmark system: Pt-H unctions Conductance of a single H molecule R.H.M. Smit et al. Nature, (00. Conclusions: Conductance histogram -> new molecular configuration single Vibr. spectroscopy -> hydrogen molecule hydrogen Shot noise, cond. fluct. -> single channel molecule + ab initio simulations -> the molecule is aligned parallel with the axis e (transparent unctions i subgap structure -> i (low T unctions Role of the electrodes - PdH In PdH unctions the histogram shows two new peaks, and the cond. fluct. donotvanishat1g 0, allthough the electronic structure of Pd isvery similar to Pt. Count (a.u Pd+H Pt+H Conductance (e /h Conductance fluctuation (a.u. Reason: the hydrogen dissolves in the Pd lattice, which completely changes the DOS of the electrodes. (The dissolution is detected by pointcontact spectroscopy on large unctions The bandstructureof thecontacting electrodes strongly affect the conductance of the molecular contact! Sz. Csonka, A. Halbritter et al., Phys. Rev. Lett. 93, (004. 8

9 I Subgap structure e (transparent unctions i subgap structure -> i (low T unctions Further application: strict confrontation of simulations with reality. (See poster of P. Makk, D. Visontai, L. Oroszlany, D. Zs. Manrique, Sz. Csonka, J. Cserti, C. Lambert, A. Halbritter /3 E. Scheer Nature 394, 154 (1998 P. Makk, A. Halbritter et al., Phys. Rev. B 78, (008. ev By fitting the subgap structures the whole mesoscopic PIN code can be determined. The same I-V curve shows inelastic degrees of freedom at higher bias {0.70, 0.14, 0.08, 0.05, 0.04 Conductance histograms of largemolecules Pioneering measurement on bipyridine molecules: B. Xu, & N.J. Tao, Science (003 e (transparent unctions i subgap structure -> i Limited experimental information, but a systematic variation of the molecules is possible (length, binding group, side group, etc. Example: length dependence (alkanediamine molecules with different number of methylene groups: (low T unctions Venkataraman et al., Nano Lett., 6, 3 (006 9

10 e (transparent unctions i subgap structure -> i (low T unctions Conductance as a function of molecular length oligophenyleneimine molecules with diff. length Coherent transport: L T 1 n. L T n -B n L n Gn Ae G1 Incoherent transport (Ohm's law: 1 n G n = G / n OPI1-5: coherent transport exponential dependence of G on the length no T dependence OPI6-10: incoherent hopping linear dependence of G on the lenth exponential T dependence, activated behavior Seong Ho Choi, et al., Science 30, 148 (008; 1 Dependence of conductance on conformation e (transparent unctions i subgap structure -> i Tuning twist agle by chemical design Conductance depends on the delocalization of the orbitals, π conugated molecules are good candidates for high transmission As the twist angle increases, the conductance decreases, T(ε ~ t^, t~cosθ The effect of substituents does not matter, the real effect comes from the π π overlap (low T unctions L. Venkataraman et al., Nature 44, (006 10

11 Role of the anchoring group pure amine thiol nitrile Venkataraman et al., Nano Lett., 6, 3 (006 e (transparent unctions i subgap structure -> i (low T unctions Generally gold electrodes and thiol (SH linking groups are used Problemswiththiol: Low conductance Not so well-defined binding site Amine (NH group gives much better defined plateaus and histogram peak Amine group is selective to low coordinated Au sites Isonitrile (NC aslo gives less well-defined configurations Further possibility: fullerene-based groups (larger conductance, higher stability due to multiple bonds Vibration modes of large molecules e (transparent unctions i subgap structure -> i C.R. Arroyo PRB 81, (010 Point contact spectroscopy: transparent unction back-scattering decrease of conductance 1 T=1 E E IETS, Inelastic tunneling spectr. tunnel unction forward-scattering increase of conductance 1 T<<1 E E (low T unctions -k +k -k +k -k di/dv hω ev +k -k +k di/dv hω Crossover at T=0.5. Experiment: O. Tal et al., PRL 100, (008 ev 11

12 e (transparent unctions i subgap structure -> i (low T unctions A small island between the source, drain and gate electrodes e N ECoulomb ( N = C A characteristic charging energy is needied to add an extra electron to the island. The island can be single molecule! V SD C 60 n- C 60 -(n+1 Example: C 60 single electron transistor in an electromigration unction (J. Park et al., Nature 407, 57 (000 Conductance as a function of source-drain and gate voltage -> Coulomb diamond structure Equidistant lines with 5mV spacing parallel to the diamond edges. Vibration of the molecule with respect to the electrodes V G Atomic chain formation e (transparent unctions i subgap structure -> i In some metals the last plateau in the conductance trace is extremely long, much longer than a typical atom-atom distance. The distribution of the length of the last plateau shows peaks at equidistant displacements with a spacing of.5 Å. If a single-atom contact is pulled, it does not break, but a monoatomic chain is pulled from the electrodes. A. I. Yanson et al. Nature, 395, 783 (1998 atom-atom distance:.5å (low T unctions Hydrogen molecules pulling a chain of gold atoms (Sz. Csonka, A. Halbritter et al., Phys. Rev. B 73, (006. 1

13 Trace histograms e (transparent unctions i subgap structure -> i Study on the binding of fullerine anchoring groups to gold electrodes. D trace histograms show significantly more information than the traditional histograms. (low T unctions C.A. Martin et al., JACS 130, (008 D correlation histograms e (transparent unctions i subgap structure -> i (low T unctions A. Halbritter, P. Makk et al. PRL (010 13

14 Trace index: r Bin index: i Conductance histogram= 1 = N i r = N r i( r R number of all traces e (transparent unctions i subgap structure -> i (low T unctions Data file for all traces: 60MByte loss of information! Histogram data file: 60kByte N i (r: number of data points in bin "i" on trace "r" (histogram for trace "r" e (transparent unctions i subgap structure -> i r C i, = colorscale i, Au i i ( Ni( r Ni ( N ( r N r r r ( N ( r N ( N ( r N i i r r r r (low T unctions -1 C i, 1 diagonal: C i,i =1 If N i and N are independent -> C i, =0 For anticorrelated configurations C i, <0 For positive correlations C i, >0 14

15 Positive correlation: If we have plateau in bin "i" we also have a plateau in bin "", if there is no plateau at "i" than no plateau at "" e (transparent unctions i subgap structure -> i i Negative correlation: If we have plateau in bin "i" we also have a plateau in bin "", if there is no plateau at "i" there is also no plateau at "" i (low T unctions i i e (transparent unctions i subgap structure -> i (low T unctions Experimental examples: Ni contact: Only two peaks in the histogram, rich structure in the correlation plot. Correlated shifting of the plateas Regular narrowing of the unction from high conductance. A. Halbritter, P. Makk et al. PRL (010 G [e /h] Conductance d c Displacement C i, Displacement [nm] G [e /h] Pt-CO molecular unction: Single-atom peak is negatively correlated with the molecular configurations The two molecular configurations are positively correlated with each other See poster of Z. Balogh! a b Normalized counts

16 Conclusions A wide range of characterization methods is available: Conductance histograms MesoscopicPIN code Vibrational spectroscopy Quantum dot physics Novel statistical methods Ab initio simulations... All the ingredients of the molecular unction are important! Molecule Electrode Anchoring group 16