1. Title Transport Through Single Molecules: Resonant Transmission, Rectification, Spin Filtering, and Tunneling Magnetoresistance Harold U. Baranger, Duke University with Rui Liu, San-Huang Ke, and Weitao Yang Thanks to Michael Fuhrer and Larry Sita, U. Maryland molecule lead 1 lead 2 V I Conductance? I-V curve?e-e interactions? Vibrations?Devices?

2. How to contact?? How to contact a molecule?? Comp. Tech. self-assembled alkanethiol monolayers-PRB 48, 1711 (1993) mechanically controllable break junction –Science 278,252 (1997) electromigration junction – APL 75, 301 (1999)

3. Expt. Examples Examples: Experiments on Conjugated Molecules Comp. Tech. Reed & Tour groups, Science 278, 252 (97) Reichert, et al. (Karlsruhe) APL 82, 4137 (03) Rawlett, et al. APL 81, 3043 (02) Organic molecules: gap of order 1 V

4. Method (1) Theoretical Approach: Two Main Ingredients Comp. Tech. 1. Transmission of incident flux: Single-particle electron states Energy of relevant states are in window determined by eV about Fermi energy Consider flux impinging on molecule from lead 1 How much gets transmitted? 2. Electronic structure from Density Functional Theory in local approx. Use Kohn-Sham theory to get self-consistent equilibrium density & structure Reliable! lots of experience in quantum chemistry Use Kohn-Sham single-particle states for transmission – NOT JUSTIFIED! For non-equilibrium, get self-consistent density matrix by filling states coming from lead 1 to  1 and states coming from lead 2 to  2 molecule lead 1 lead 2 V I 11 22

5. Method (2) Computational Methods Comp. Tech. molecule lead 1lead 2 extended molecule Semi-infinite leads at constant  (no voltagle drop); no spin polarization Extended molecule: include large amount of leads in the “molecule” First-principles DFT theory using SIESTA program (Double-zeta plus polarization basis set, optimized Troullier-Martins pseudopotentials, PBE version of GGA functional for exchange-correlation) Transmission from Green function built from Kohn-Sham orbitals San-Huang Ke, H.U.Baranger, and W. Yang, PRB (2004) Datta group, PRB (2001); Ratner group, Chem. Phys. (2002); Guo group, PRB (2003)

6. Benzene: T Simple case: 1 Carbon ring + S to bond to Au Comp. Tech. [San-Huang Ke]

7. Benzene: I-V Additional Au makes a difference: T(E) resonance and NDR! Comp. Tech. [San-Huang Ke] transmission resonance at Fermi energy negative differential resistance

8. Benzene: ldos Image resonant state Comp. Tech. Surface of constant local density of states: (ie. one contour of a 3d contour plot) [San-Huang Ke]

9. Metallocenes Metallocenes: Organometallic Sandwich Complexes Comp. Tech. M=Fe: ferrocene 6 electrons in levels in box S=0 M=Co: cobaltocene 7 electrons in levels in box S=1/2 [Rob Toreki, Organometallic HyperTextBook]

10. Fcene: data 1 Experiment: I-V of a phenyl-ethynyl-ferrocene complex Comp. Tech. [Getty, Engtrakul, Wang, Fuhrer, and Sita; U. Maryland] !!!

11. Fcene: data 2 Experiment: I-V of Ferrocene-OPE compared to OPE Comp. Tech. !!! [Getty, Engtrakul, Wang, Fuhrer, and Sita; U. Maryland]

12. Fcene: calc Conductance of Ferrocene-OPE: Calculation Comp. Tech. resonance at the Fermi energy [Rui Liu]

13. Fcene: calc 2 Conductance of Fc-OPE: Experiment & Calculation Comp. Tech.

14. Fcene: control But what about the OPE control? – It ALSO conducts… Comp. Tech. This embarassing result is an example of a long-standing problem in the theory of transport through molecules: theory says fully conjugated molecules should conduct, while experiment shows that they do not. Not clear why: because of using the Kohn- Sham wave-functions to find the transmission? local exchange-correlation? (derivative discontinuity) … The fact that the Fc molecule avoids this embarassment is an important clue…

15. Cobaltocene Cobaltocene: One more electron in a nice place… Comp. Tech. lowest energy bonding state: increasing energy e 2g a 1g ’e 1u

16. Rectifier: I-V Cobaltocene Rectifier Comp. Tech. Rectifier: Conducts under forward bias, but not under reverse bias [Rui Liu]

17. Rectifier: T, ldos Transmission Resonances in Cobaltocene Rectifier Comp. Tech. Density of states projected on molecule Transmission (E,V) Resonance A ( HOMO at V=0):Resonance B ( LUMO at V=0): [Rui Liu]

18. Rectifier: potential Potential Drop and Charge Distribution in Rectifier Comp. Tech. [Rui Liu]

19. Spin active molecule Use Cobaltocene’s Spin: Molecular Spintronics Comp. Tech. Goal: Move spin active parts from leads into molecules Apply B field to align spin of cobaltocene; Current is spin polarized Cobaltocene spin filter:

20. diCo: energetics Spintronic Switch in a Molecule with 2 Cobaltocenes Comp. Tech. diCo diCo-2C Ground state => S=0 (super-exchange*). The more insulating the spacer, the smaller the energy difference. B field needed to excite molecule from S=0 to S=1 depends on spacer * The term used for the indirect exchange coupling of unpaired spins via orbitals having paired spins. MoleculeE (S=1) – E (S=0) Inverting B field (g=2) DiCo 12 meV120 T DiCo-2C 2 meV 20 T DiCo-4C~0.1 meV ~1 T Energetics of the singlet-triplet splitting

21. diCo: T Transmission of di-Cobaltocene Molecules: A Good Switch and Spin-Valve! Comp. Tech. [Rui Liu] diCo diCo-2C

22. Conclusion Conclusions Comp. Tech. Lessons we have learned on molecular electronics and spintronics: Contact atomic structure does matter! additional Au caused a dramatic increase of conductance Ferrocene containing molecule has good conductance! first case of agreement between theory and experiment Cobaltocene has a very nice additional electron: * resonance near the Fermi energy of Au * unpaired spin to use for spintronics Rectifier, spin filter, and spintronic switch using cobaltocene Credits: Rui Liu, San-Huang Ke, Weitao Yang, and HUB Expt: Michael Fuhrer, Larry Sita, and their team