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Transport Through Single Molecules: Resonant Transmission,

Rectification, Spin Filtering, and Tunneling Magnetoresistance with Rui Liu, San-Huang Ke, and Weitao Yang

Thanks to Michael Fuhrer and Larry Sita, U. Maryland lead 1

I molecule lead 2

V

Conductance?

Vibrations?

I-V curve?

e-e interactions?

Devices?

How to contact a molecule??

How to contact??

Comp. Tech.

• 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

Science 278, 252 (97)

Comp. Tech.

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

Method (1)

1. Transmission of incident flux: m

1

• Single-particle electron states

• Energy of relevant states are in lead 1 window determined by eV about

I molecule

Fermi energy

• Consider flux impinging on molecule from lead 1

2 m 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 m

1 and states coming from lead 2 to m

2

Computational

Methods lead 1 molecule

Method (2)

lead 2 extended molecule

• Semi-infinite leads at constant m

(no voltagle drop); no spin polarization

• Extended molecule: include large amount of leads in the “molecule”

• First-principles DFT theory using SIESTA program

Comp. Tech.

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)

Simple case: 1 Carbon ring + S to bond to Au

Benzene: T

Comp. Tech.

[San-Huang Ke]

Additional Au makes a difference: T(E) resonance and NDR!

Benzene: I-V

Comp. Tech.

transmission resonance at Fermi energy negative differential resistance

[San-Huang Ke]

Image resonant state

Benzene: ldos

Comp. Tech.

Surface of constant local density of states:

(ie. one contour of a 3d contour plot)

( r

, E

F

)

 constant

[San-Huang Ke]

Metallocenes: Organometallic Sandwich Complexes

Metallocenes

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]

Experiment: I-V of a phenyl-ethynyl-ferrocene complex

Fcene: data 1

!!!

Comp. Tech.

[Getty, Engtrakul, Wang, Fuhrer, and Sita; U. Maryland]

Experiment: I-V of Ferrocene-OPE compared to OPE

Fcene: data 2

!!!

Comp. Tech.

[Getty, Engtrakul, Wang, Fuhrer, and Sita; U. Maryland]

Conductance of Ferrocene-OPE: Calculation

Fcene: calc

resonance at the Fermi energy

Comp. Tech.

[Rui Liu]

Conductance of Fc-OPE: Experiment & Calculation

Fcene: calc 2

Comp. Tech.

But what about the OPE control? – It ALSO conducts…

This embarassing result is an

Fcene: control

problem in the theory of transport through molecules: theory says fully conjugated molecules should conduct, while experiment shows that

Comp. Tech.

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…

Cobaltocene: One more electron in a nice place… lowest energy bonding state:

Cobaltocene

Comp. Tech.

increasing energy e

2g e

2g a

1g

’ e

1u

Cobaltocene Rectifier

Comp. Tech.

[Rui Liu]

Transmission Resonances in Cobaltocene Rectifier

Density of states projected on molecule

Rectifier: T, ldos

Comp. Tech.

Resonance A ( HOMO at V=0): Resonance B ( LUMO at V=0):

[Rui Liu]

Potential Drop and Charge Distribution in Rectifier

Rectifier: potential

Comp. Tech.

[Rui Liu]

Goal: Move spin active parts from leads into molecules

Spin active molecule

Cobaltocene spin filter:

Comp. Tech.

Apply B field to align spin of cobaltocene; Current is spin polarized

Spintronic Switch in a Molecule with 2 Cobaltocenes

diCo: energetics

diCo diCo-2C

Energetics of the singlet-triplet splitting

Comp. Tech.

Inverting B field (g=2)

DiCo 12 meV 120 T

DiCo-2C 2 meV

DiCo-4C ~0.1 meV

20 T

~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.

diCo

Transmission of di-Cobaltocene Molecules:

A Good Switch and Spin-Valve!

diCo: T

Comp. Tech.

diCo-2C

[Rui Liu]

Conclusions

• 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:

Comp. Tech.

* 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

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