Electrical Transport Through Single Molecules Harold U. Baranger, Duke University Title with Rui Liu, San-Huang Ke, and Weitao Yang Thanks to S. Getty, M. Fuhrer and L. Sita, U. Maryland Conductance? I-V curve? e-e interactions? Vibrations? Devices? role of contact atomic structure agreement between experiment and theory metal atoms are good for conduction!
How to contact a molecule?? How to contact?? self-assembled alkanethiol monolayers-prb 48, 1711 (1993) mechanically controllable break junction Science 278,252 (1997) electromigration junction APL 75, 301 (1999)
Examples: Experiments on Conjugated Molecules Expt. Examples 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
Theoretical Approach: Two Main Ingredients 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? Method (1) µ 1 µ 2 I lead 1 molecule lead 2 V 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 µ 1 and states coming from lead 2 to µ 2
Computational Methods molecule lead 1 lead 2 Method (2) extended molecule Semi-infinite leads at constant µ (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 Comp. basis set, Tech. 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)
Vary surface [(111) or (100)], adsorption site, linking atom (S, Se, or Te), type of lead (thin, infinite surface, surface+protrusion) Benzene: structures [San-Huang Ke] Simple case: 1 Carbon ring + S to bond to Au
Transmission for benzenedithiol+au: Surface+protrusion Benzene: T [San-Huang Ke]
Additional Au makes a difference: T(E) resonance and NDR! Benzene: I-V transmission resonance at Fermi energy negative differential resistance [San-Huang Ke]
Image resonant state Benzene: ldos Surface of constant local density of states: (ie. one contour of a 3d contour plot) ρ ( r, ) = E F constant [San-Huang Ke]
Carbon nanotube Metal electrode contact How good NT-met can the electrical struc contact be? Does it depend on the metal? Try to make an ideal contact, to set a bound: assume metal wets tube, many strong bonds are formed! 3 terminal transmission [San-Huang Ke]
Au Pd (5,5) Tube 7 layers of Au or Pd 5x5, 3Term, 7L excellent contact!! [San-Huang Ke]
(5,5) Tube: Evolution with width of metal electrode 5x4, 3Term, 3/5L [San-Huang Ke]
(10,0) Tube Doped and undoped 2 Terminal 10x0, 2Term [San-Huang Ke]
(10,0) Tube: 3 Terminal Transmission 10x0, 3Term Again, Pd make a better contact than Au [San-Huang Ke]
Metallocenes: Organometallic Sandwich Complexes Metallocenes 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]
Experiment: I-V of a phenyl-ethynyl-ferrocene complex Fcene: data 1!!! [Getty, Engtrakul, Wang, Fuhrer, and Sita; U. Maryland; PRB `05]
Experiment: I-V of Ferrocene-OPE compared to OPE Fcene: data 2!!!!!! [Getty, Engtrakul, Wang, Fuhrer, and Sita; U. Maryland]
Conductance of Ferrocene-OPE: Calculation Fcene: calc resonance at the Fermi energy [Rui Liu]
But what about the OPE control? It ALSO conducts Fcene: control 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? (ie. self-interaction?) failure to include interactions in transport calculation? The fact that the Fc molecule avoids this embarassment is an important clue
Cobaltocene: One more electron in a nice place lowest energy bonding state: Cobaltocene increasing energy e 2g e 2g a 1g e 1u
Cobaltocene Rectifier Rectifier: Conducts Rectifier: under forward bias, I-V but not under reverse bias [Rui Liu]
Transmission Resonances in Cobaltocene Rectifier Density of states projected Rectifier: on molecule T, ldos Transmission (E,V) Resonance A (HOMO at V=0): Resonance B (LUMO at V=0): [Rui Liu]
Potential Drop in Rectifier Rectifier: potential [Rui Liu]
Spin active molecule Use Cobaltocene s Spin: Molecular Spintronics Goal: Move spin active parts from leads into molecules Spin active molecule Cobaltocene spin filter: Apply B field to align spin of cobaltocene; Current is spin polarized
Spintronic Switch using Ferromagnetic Metals Spintronic switch Density of states at E F for Majority (minority) spin state Also works if N is an insulator: Tunneling Magneto-Resistance (TMR)
Spintronic Switch in a Molecule with 2 Cobaltocenes dico: energetics dico dico-2c Energetics of the singlet-triplet splitting Molecule E(S=1) E(S=0) Inverting B field (g=2) DiCo 12 mev 120 T DiCo-2C 2 mev 20 T DiCo-4C ~0.1 mev ~1 T 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.
Transmission of di-cobaltocene Molecules: A Good Switch and Spin-Valve! dico: T dico dico-2c [Rui Liu]
Conclusions Though the methods Conclusion used are, in general, not quantitative, we have learned some general lessons: Contact atomic structure does matter! additional Au caused a dramatic increase of conductance Excellent Pd/Nanotube contact; even ideal Au is good Ferrocene containing molecule has good conductance! Cobaltocene has a very nice additional electron: * resonance near the Comp. Fermi energy Tech. of Au * unpaired spin to use for spintronics Credits: Rui Liu, San-Huang Ke, Weitao Yang, and HUB Expt: Stephanie Getty, Michael Fuhrer, Larry Sita, and team