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

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

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 V=2.4V

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

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

13. C6H5SC6H5S ELIMINATE CONTACT ON LEFT C 6 H 4 (NO 2 )S

14. -6 -4 -2 0 2 Energy (eV) C 6 H 5 -SC 6 H 4 (NO 2 )-S Energy (eV) -3 -2 -1 0 1

15. 0.6V 0 e 1.8V 1 e 4.2V 1 e

16. V sd = 0.1 V Using a gate voltage Q=0 0.3 0.8 1.2

17. Fowler-Nordheim tunneling J E J/E 2 = Aexp(-B/E) MOS n-Si Metal SiO 2 EFEF EcEc EvEv

18. I V ln(J/E 2 ) 1/E Ohmic Fowler-Nordheim J/E 2 = Aexp(-B/E) I=V/R

19. 8-layer Si(001) Ohmic

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

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

22. I-V curve through SiO 2 nano-film Three regions: (1)0.0 to 0.5V quasi-linear; (2)0.5 to 4.0V non-linear; (3)Over 4.0V quasi-linear

23. Fowler-Nordheim I-V plot

24. Effective potential J The dash-dot lines are boundary EFEF SiO 2 V= 4.0v nano-film V=0.5v

25. 1.2 n m (SiO 2 ) 1.5 n m (SiO 2 ) 0.9 n m (vacuum) 1.2 n m (vacuum) 1.5 n m (vacuum ) 012345 G. Timp et al (Bell Lab) 1998 calculation

26. The Lippmann-Schwinger method t r EVERYWHERE

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

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

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

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