Dynamics of Vibrational Excitation in the C 60 - Single Molecule Transistor Aniruddha Chakraborty Department of Inorganic and Physical Chemistry Indian.

Slides:

Advertisements

Similar presentations

Understanding Complex Spectral Signatures of Embedded Excess Protons in Molecular Scaffolds Andrew F. DeBlase Advisor: Mark A. Johnson 68 th Internatinal.

Advertisements

“Rotational Energy Transfer in o - / p -H 2 + HD” Renat A. Sultanov and Dennis Guster BCRL, St. Cloud State University St. Cloud, MN June 20, 2007 OSU.

Cohen & Fano (CF) Model CF-I: Monoelectronic Process CF-II: LCAO for the bound molecular state CF-III: Free Wave for the ejected electron H H Interferences.

Molecular Bonds Molecular Spectra Molecules and Solids CHAPTER 10 Molecules and Solids Johannes Diderik van der Waals (1837 – 1923) “You little molecule!”

Cphys351 c4:1 Chapter 4: Atomic Structure The Nuclear Atom The Atom as the smallest division of an element quantization of electric charge oil drop experiments.

Emergent Majorana Fermion in Cavity QED Lattice

№4. Soap film Create a soap film in a circular wire loop. The soap film deforms when a charged body is placed next to it. Investigate how the shape of.

METO 621 Lesson 6. Absorption by gaseous species Particles in the atmosphere are absorbers of radiation. Absorption is inherently a quantum process. A.

The Hybrid Quantum Trajectory/Electronic Structure DFTB-based Approach to Molecular Dynamics Lei Wang Department of Chemistry and Biochemistry University.

Quantum Monte Carlo Simulation of Vibrational Frequency Shifts in Pure and Doped Solid para-Hydrogen Lecheng Wang, Robert J. Le Roy and Pierre- Nicholas.

Molecular Modeling: Molecular Mechanics C372 Introduction to Cheminformatics II Kelsey Forsythe.

TEST GRAINS AS A NOVEL DIAGNOSTIC TOOL B.W. James, A.A. Samarian and W. Tsang School of Physics, University of Sydney NSW 2006, Australia

Computational Solid State Physics 計算物性学特論第２回 2.Interaction between atoms and the lattice properties of crystals.

Generation of short pulses

P461 - Molecules 21 MOLECULAR ENERGY LEVELS Have Schrod. Eq. For H 2 (same ideas for more complicated). For proton and electron 1,2 real solution: numeric.

Chemistry 6440 / 7440 Vibrational Frequency Calculations.

Raman Spectroscopy and Thin Films Alexander Couzis ChE5535.

Introduction to Infrared Spectrometry Chap 16. Infrared Spectral Regions Table 16-1 Most used – 15.

Activation energies and dissipation in biased quantum Hall bilayer systems at. B. Roostaei [1,2], H. A. Fertig [3,4], K. J. Mullen [2], S. Simon [5] [1]

Simulation of X-ray Absorption Near Edge Spectroscopy (XANES) of Molecules Luke Campbell Shaul Mukamel Daniel Healion Rajan Pandey.

Rodolfo Jalabert CHARGE AND SPIN DIPOLE RESONANCES IN METALLIC NANOPARTICULES : collective versus single-particle excitations R. Molina (Madrid) G. Weick.

Crystal Lattice Vibrations: Phonons

F. Cheung, A. Samarian, W. Tsang, B. James School of Physics, University of Sydney, NSW 2006, Australia.

Lecture 6 Raman spectra of carbon nanotubes. Infrared (IR) spectroscopy IR 700 nm3500 nm400 nm Visible light IR IR spectra can be used to identify the.

Vibrational and Rotational Spectroscopy

Objectives of this course

Magnetopolaronic effects in single-molecule transistor

Towards Single Molecule Electronics

Monte Carlo Methods: Basics

Einstein A coefficients for vibrational-rotational transitions of NO

Lecture 9 Energy Levels Translations, rotations, harmonic oscillator

Absorption Spectra of Nano-particles

1 Materials Science Concepts MATS-535 Electronics and Photonics Materials Scope a – Atomic Structure and Atomic Number b – Bonding and Type of Solids Dr.

1 B. RAM PRASAD, MANGALA SUNDER KRISHNAN Department of Chemistry, Indian Institute of Technology Madras, Chennai , India. AND E. ARUNAN Department.

Ch ; Lecture 26 – Quantum description of absorption.

Supercurrent through carbon-nanotube-based quantum dots Tomáš Novotný Department of Condensed Matter Physics, MFF UK In collaboration with: K. Flensberg,

INTERFERENCE AND QUANTIZATION IN SEMICLASSICAL VIBRATIONAL RESPONSE FUNCTIONS Scott Gruenbaum Department of Chemistry and Chemical Biology Cornell University.

Rotational spectra of molecules in small Helium clusters: Probing superfluidity in finite systems F. Paesani and K.B. Whaley Department of Chemistry and.

MODELING MATTER AT NANOSCALES 3. Empirical classical PES and typical procedures of optimization Classical potentials.

Van der Waals and Electrostatic Forces Acting on a Carbon Nanotubes Research Center for Applied Sciences, Academia Sinica,Taipei, Taiwan contact: Evgeny.

Various trajectories through the potential energy surface.

Fission Collective Dynamics in a Microscopic Framework Kazimierz Sept 2005 H. Goutte, J.F. Berger, D. Gogny CEA Bruyères-le-Châtel Fission dynamics with.

1 Statistical Mechanics and Multi- Scale Simulation Methods ChBE Prof. C. Heath Turner Lecture 18 Some materials adapted from Prof. Keith E. Gubbins:

1 CE 530 Molecular Simulation Lecture 14 Molecular Models David A. Kofke Department of Chemical Engineering SUNY Buffalo

Thomas Halverson and Bill Poirier Texas Tech University Department of Physics

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh) Nuclear and Radiation Physics Why nuclear physics? Why radiation.

How do you build a good Hamiltonian for CEID? Andrew Horsfield, Lorenzo Stella, Andrew Fisher.

Electron-hole duality and vortex formation in quantum dots Matti Manninen Jyväskylä Matti Koskinen Jyväskylä Stephanie Reimann Lund Yongle Yu Lund Maria.

Vibrational Motion Harmonic motion occurs when a particle experiences a restoring force that is proportional to its displacement. F=-kx Where k is the.

Charge pumping in mesoscopic systems coupled to a superconducting lead

Development of a cavity ringdown spectrometer for measuring electronic states of Be clusters JACOB STEWART, MICHAEL SULLIVAN, MICHAEL HEAVEN DEPARTMENT.

Tao Peng and Robert J. Le Roy

Metastable molecular hydrogen anion The lowest states (i.e. the ones with longest life-time) are collected in the table below. The same values were found.

Infrared Spectra of Anionic Coinage Metal-Water Complexes J. Mathias Weber JILA and Department of Chemistry and Biochemistry University of Colorado at.

The many forms of carbon Carbon is not only the basis of life, it also provides an enormous variety of structures for nanotechnology. This versatility.

modes Atomic Vibrations in Crystals = Phonons Hooke’s law: Vibration frequency   f = force constant, M = mass Test for phonon effects by using isotopes.

C 60 - Single Molecule Transistor Aniruddha Chakraborty Indian Institute of Technology Mandi, Mandi , Himachal Pradesh, India.

Chapter 8. Molecular Motion and Spectroscopy

Introduction to Infrared Spectroscopy

The gerade Rydberg states of molecular hydrogen Daniel Sprecher, 1 Christian Jungen, 2 and Frédéric Merkt 1 1 Laboratory of Physical Chemistry, ETH Zurich,

Why do molecules form? Molecular bonds Rotations Vibrations Spectra Complex planar molecules Molecules CHAPTER 9 Molecules Johannes Diderik van der Waals.

Tunable excitons in gated graphene systems

Quantum Phase Transition of Light: A Renormalization Group Study

Production of an S(α,β) Covariance Matrix with a Monte Carlo-Generated

物理化學 Physical Chemistry matter logic change study origin

Solid state physics Lecture 3: chemical bonding Prof. Dr. U. Pietsch.

Diatomic molecules

武汉物数所理论交叉学术交流系列报告 (第一三四期)

Quantum Mechanical Treatment of The Optical Properties

Perturbation Theory Lecture 5.

Presentation transcript:

Dynamics of Vibrational Excitation in the C 60 - Single Molecule Transistor Aniruddha Chakraborty Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore , India.

Plan of the talk 1. What is C 60 - single molecule transistor? 2. Experimental results 3. Our work 4. Conclusions

Park et al. Nature 497, 57 (2000). C 60 - Single Molecule Transistor C 60 molecule Sphere, diameter 0.7 nm. 12 pentagons and 20 hexagons.

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

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

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

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

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

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

The Model Perturbation (electron hopping) ‘Two photon’ Process (Resonance Raman Spectroscopy) Perturbation (Light) Kramers-Heisenberg-Dirac formula Second order Perturbation theory C 60 - Single Molecule Transistor

The Hamiltonian Internal vibrational modes of C 60 are not considered. Position dependence of LUMO energy is neglected.

Perturbation (electron hopping)

Center of mass motion Energy Geometry independent.

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

trapped between gold electrodes C 60 No experimental information available

Van der Waals interaction between C 60 and Au electrode *Buckingham potential for Au-C interaction *Acknowledgement: Hao Tang (CEMES/CNRS, France) Energy ( eV ) Chem. Phys. Lett. 214, 569 (1993) Hollow sphere Carbon atoms smeared into a continuum Metal assumed to form a continuum

Van der Waals interaction: C 60 trapped between gold electrodes Energy Center of mass motion Approximate Potential Analysis by Park et al. Choice of d Best distance – maximum binding energy

Classical Electrodynamics: J. D. Jackson; 3rd ed. (1999). 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.

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

Current Vs Voltage Plot Voltage (meV) Current (arb. units) Qualitative agreement !

Van der Waals interaction between C 60 and Gold electrode Energy ( eV ) Hollow sphere Carbon atoms smeared into a continuum Metal assumed to form a continuum Larger radius – effect of protrusion is less Smaller radius – C 60 won’t stable on top

Van der Waals interaction: C 60 trapped between Gold electrodes Van der Waals interaction: C 60 trapped between Gold electrodes Energy Center of mass motion Analysis by Park et al. Choice of d Best distance – maximum binding energy

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

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

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

Voltage (meV) Current (arb. units) Current Vs Voltage Plot Qualitative agreement !

Voltage (meV) Current (arb. units) Current Vs Voltage Plot Qualitative agreement !

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

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

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

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

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