PowerPoint - Duke University
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
