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Quantum Transport: Exploring Phenomena and Methods in Molecular Charging and Film Transport

This study delves into quantum transport phenomena, particularly in charging molecules during transport and through ultra-thin films. Employing the Lippmann-Schwinger method, it explores groundbreaking theoretical frameworks and experimental validations. Key findings include the observation of current suppression and subsequent increase at threshold voltages, as indicated by past studies. Collaborative insights from researchers across institutions, including Vanderbilt University and Oak Ridge National Laboratory, contribute to a comprehensive understanding of transport dynamics, offering new methods for quantifying quantum behavior in nanoscale systems.

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Quantum Transport: Exploring Phenomena and Methods in Molecular Charging and Film Transport

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  1. Explorations in quantum transport – phenomena and methods Sokrates T. Pantelides Department of Physics and astronomy, Vanderbilt University, Nashville, TN and Oak Ridge National Laboratory, Oak Ridge, TN Collaborators: Yoshihiro Gohda Zhong-yi Lu Kalman Varga Supported in part by Department of Energy

  2. MOORE’S LAW

  3. Phenomena (using the Lippmann-Schwinger method) • Charging of molecules during transport (Gohda) • Transport through ultra-thin films (Lu) • New method (Varga)

  4. t r The Lippmann-Schwinger method • Norton Lang, 1981 – • Di Ventra, Lang, and Pantelides, 2000-2002

  5. Theory 0° 90° 0° 90° Experiment: Reed et al (2000) T=190 K T=300 K

  6. Nature 417, 72 (2002) “The current is strongly suppressed up to a threshold V, then it increases in steps”

  7. Coulomb blockade in a quantum dot GaAs-AlGaAs-InGaAs-AlGaAs-GaAs

  8. Barner and Ruggiero, 1987

  9. LUMO LUMO V=2.4V

  10. V=3.6[V] V=1.2[V]

  11. LUMO LUMO AFTER SELF-CONSISTENCY, MOLECULE IS NEUTRAL! ELECTRODES ARE NEUTRAL! EXCITED STATE?

  12. C6H4(NO2)S ELIMINATE CONTACT ON LEFT C6H5S

  13. -3 -2 -1 0 1 -6 -4 -2 0 2 Energy (eV) Energy (eV) C6H5-S C6H4(NO2)-S

  14. 4.2V 1 e 1.8V 1 e 0.6V 0 e

  15. 0.8 1.2 0.3 dQ=0 Using a gate voltage Vsd = 0.1 V

  16. Fowler-Nordheim tunneling M O S J E Ec Ev n-Si EF Metal SiO2 J/E2 = Aexp(-B/E)

  17. J/E2 = Aexp(-B/E) ln(J/E2) 1/E Fowler-Nordheim I I=V/R V Ohmic

  18. 8-layer Si(001) Ohmic

  19. Effective potential 8 layers Si(001) V=0.1v EF EF J V=1.0v V=5.0v The dash-dot lines are boundary

  20. Current vs thickness [Si(001)] Bias=1.0V

  21. I-V curve through SiO2 nano-film • Three regions: • 0.0 to 0.5V quasi-linear; • 0.5 to 4.0V non-linear; • Over 4.0V quasi-linear

  22. Fowler-Nordheim I-V plot

  23. Effective potential nano-film SiO2 J EF V=0.5v V= 4.0v The dash-dot lines are boundary

  24. 1.2 n m (SiO2) 1.5 n m (SiO2) 0.9 n m (vacuum) 1.2 n m (vacuum) 1.5 n m (vacuum) 0 1 2 3 4 5 G. Timp et al (Bell Lab) 1998 calculation

  25. t r EVERYWHERE The Lippmann-Schwinger method

  26. Static external potential DENSITY FUNCTIONAL THEORY FOR STEADY-STATE TRANSPORT (CURRENT-DENSITY FUNCTIONAL) + B.C.

  27. Sink Source Schrödinger equation with imaginary potential: MAP TRANSPORT ONTO AN EIGENVALUE PROBLEM Battery!

  28. Na wire Real-space DFT calculation Jellium electrodes Bias Voltage

  29. Benzene ring -- IV characteristics Experiment (Reed et al.)

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