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Dynamics of Vibrational Excitation in the C 60 - Single Molecule Transistor

Dynamics of Vibrational Excitation in the C 60 - Single Molecule Transistor. Aniruddha Chakraborty. Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore-560012, India. http://www.ipc.iisc.ernet.in/~anirud. Plan of the talk.

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Dynamics of Vibrational Excitation in the C 60 - Single Molecule Transistor

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  1. Dynamics of Vibrational Excitation in the C60 - Single Molecule Transistor Aniruddha Chakraborty Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore-560012, India. http://www.ipc.iisc.ernet.in/~anirud

  2. Plan of the talk 1. What is C60 - single molecule transistor? 2. Experimental results 3. Our work 4. Conclusions

  3. C60 - Single Molecule Transistor C60 molecule Sphere, diameter 0.7 nm. 12 pentagons and 20 hexagons. Park et al. Nature 497, 57 (2000).

  4. Conductance gap Different step heights Asymmetric 5 meV Current Vs Voltage Plot at 1.5K Park et al. Nature 497, 57 (2000).

  5. ‘Two photon’ Process Energy Nuclear Coordinate (0,3) (0,2) (0,1) (0,0) (0,2) Energy Current (0,1) (0,0) Voltage Center of mass motion

  6. Theoretical analysis by Park et al. Lennard-Jones potential for Au-Cinteraction: Chem. Phys. Lett. 214, 569 (1993) Lennard-Jones Lennard-Jones+Coulomb Energy Center of mass motion Park et al. Nature 497, 57 (2000).

  7. Coulomb interaction Hollow sphere Carbon atoms smeared into a continuum Extra electron is uniformly distributed Point charge at the center

  8. Why Not? Why not electronic excitation? Very high energy Why not internal vibrational excitation? Lowest energy mode: 33meV Why not rotational excitation? No net dipole moment

  9. Theoretical Analysis by Boese et al. Local system= quantum dot+ harmonic oscillator Local system + Bosonic Bath+two electronic reservoirs Boese et al. Europhys. Lett. 54, 668 (2001).

  10. The Model ‘Two photon’ Process (Resonance Raman Spectroscopy) Kramers-Heisenberg-Dirac formula Second order Perturbation theory Perturbation (Light) C60 - Single Molecule Transistor Perturbation (electron hopping)

  11. The Hamiltonian Internal vibrational modes of C60 are not considered. Position dependence of LUMO energy is neglected.

  12. Perturbation (electron hopping)

  13. Geometry independent. Energy Center of mass motion

  14. Kramers-Heisenberg-Dirac type formula Temperature effect neglected 1.5K =0.13 meV Contributing factors to the vibrational excitation (a) The displacement of the equilibrium position (b) The position dependence of the electron hopping matrix element *Boese et al. Europhys. Lett. 54, 668 (2001).

  15. C60 trapped between gold electrodes No experimental information available

  16. Van der Waals interaction between C60 and Au electrode *Buckingham potential for Au-C interaction Hollow sphere Carbon atoms smeared into a continuum Metal assumed to form a continuum 0.5 Energy ( eV ) 0.0 Chem. Phys. Lett. 214, 569 (1993) -0.5 6 8 10 12 14 *Acknowledgement: Hao Tang (CEMES/CNRS, France).

  17. Van der Waals interaction: C60 trapped between gold electrodes Choice of d Best distance – maximum binding energy Approximate Potential Analysis by Park et al. Energy Center of mass motion

  18. Image interaction Hollow sphere Carbon atoms smeared into a continuum Extra electron is uniformly distributed Point charge at the center Force Calculation (convergent Series) Images placed at larger and larger distances. Classical Electrodynamics: J. D. Jackson; 3rd ed. (1999).

  19. Approximate Potentials Energy Analysis by Park et al. Center of mass motion

  20. Current Vs Voltage Plot 8 6 Current (arb. units) 4 2 0 0 5 10 15 20 Voltage (meV) Qualitative agreement !

  21. Van der Waals interaction between C60 and Gold electrode Hollow sphere Carbon atoms smeared into a continuum Metal assumed to form a continuum 0.5 Larger radius – effect of protrusion is less Smaller radius – C60 won’t stable on top 0.25 Energy ( eV ) 0.0 -0.25 9 11 13 15 17

  22. Van der Waals interaction: C60 trapped between Gold electrodes Choice of d Best distance – maximum binding energy Analysis by Park et al. Energy Center of mass motion

  23. Image Interaction Hollow sphere Carbon atoms smeared into a continuum Extra electron is uniformly distributed Point charge at the center + = Classical Electrodynamics: J. D. Jackson; 3rd ed. (1999).

  24. Image Interaction Force Calculation (convergent Series) Each reflection on the sphere, reduces the images change. With each reflection the images change sign. Images from reflection between parallel electrodes : placed at larger and larger distances. seven generated from a set of SIX successive reflections 32760 images five

  25. Approximate Potentials Energy Analysis by Park et al. Center of mass motion

  26. Current Vs Voltage Plot 8 6 Current (arb. units) 4 2 0 0 5 10 15 20 Voltage (meV) Qualitative agreement !

  27. Current Vs Voltage Plot 8 6 Current (arb. units) 4 2 0 0 5 10 15 20 Voltage (meV) Qualitative agreement !

  28. Contribution from hopping matrix element (0,3) (0,2) Current (0,1) (0,0) Voltage

  29. Electrode geometry & hopping matrix element *Boese et al. Europhys. Lett. 54, 668 (2001). (0,1) Current (0,0) Voltage

  30. Only Qualitative Agreement ! Double well problem! Energy Internal modes! Center of mass motion

  31. Conclusions 1. Two possible mechanisms for vibrational excitation. (a) The displacement of equilibrium position (b) The position dependence of the electron hopping matrix element 2. Our results are in qualitative agreement with experiment. A. Chakraborty, K. Kumar and K. L. Sebastian, Phys. Rev. B 68, 085411 (2003). A. Chakraborty, Chapter 2, Ph.D thesis, IISC, Bangalore, India, 2005.

  32. Acknowledgements ( Indian Institute of Science, India ) Prof. K.L. Sebastian ( University of Pennsylvania, USA ) Keshav Kumar Hao Tang ( CEMES/CNRS, France ) CSIR ( New Delhi, India )

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