Controlled electron transport
through single molecules
H

S (H )

transport
Colin Lambert
Lancaster
University
Outline
•
Motivation
•
SMEAGOL approach to modelling of molecules and contacts
•
Control of electron transport via geometry
Control via ring rotation
Control via contact angle
Control via geometrically-tuned Fano resonances
•
The inverse effect: control of geometry by the transport of
electrons. eg: carbon nanotube windmills
•
Control of electron transport via solvation shells: few-atom
sensing
Motivation
EPSRC Basic Technology programme: To develop a scalable
technology to reliably control transport through single molecules
Technology of Metallic Contacts
• QinetiQ, Malvern
• T. Cox, P. Buckle, I. Sage
Molecular Synthesis
• Durham University
• M.R. Bryce & C. Wang
• Edge gaps typically 8-10 nm
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Molecular Backbone
Gap (~10nm)
(A)
(B)
Tunnel Barrier
Drain
Receptor
Gate
Source
“Mushroom Molecular Necklace”
Molecule Characterization
and Synthesis
• Bangor University
• G. Ashwell
Theory
• Lancaster University
• I. Grace, C. Finch, V. GarciaSuarez, S. Bailey,
T. Papadopoulos, I Amanatidis
The device in practice
At high
magnification the
SiO2 layer is
measured to be
8.5nm
I-V characteristics
Measurements in the
absence of molecules
(low leakage currents)
Measurements in the
presence of molecules
0.01
C u rre n t (n A )
280K
0.008
0.006
0.004
0.002
0
0
2
4
Voltage (V)
6
Molecular wires of interest
(aryleneethynylene molecular wires)
C Wang, A. Batsanov, M. Bryce and I. Sage
Org. Lett, 6(13), 2181 (2004)
General problem
H

S (H )

transport
Eg Landauer
G=2e2/h T
Electron
pumping via
Brouwer
formula
Torques and
forces
Low –
frequency
tranport
Ab initio self-consistent meanfield transport
Spin and Molecular Electronics in Atomically Generated Orbital Landscapes
Lancaster transport codes + SIESTA + nonequilibrium Greens functions (zero or finite bias; normal or
superconducting contacts; thermoelectrics; non-co-linear magnetism; NEMS)
Victor
Garcia
Modelling the gold – molecule interface
Take material specific
extended molecule
hamiltonian
add simple gold leads
Iterate process of
extending contact region
Molecule
Molecule
Molecule
Effect of a finite bias
V=0.5V
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.0
-2
-1
0
1
T(E)
1.0
0.2
0.4
0.4
0.2
0.2
0.0
0.0
2
-2
Energy (eV)
-1
0
1
-2
2
0.8
0.8
0.6
0.6
0.6
T(E)
0.8
T(E)
1.0
0.4
0.4
0.2
0.2
0.0
0.0
0.0
Energy (eV)
1
2
-2
-1
0
Energy (eV)
2
0.4
0.2
0
1
V=5V
1.0
-1
0
V=3V
1.0
-2
-1
Energy (eV)
Energy (eV)
V=1.5V
T(E)
V=1V
1.0
T(E)
T (E)
V = 0V
1
2
-2
-1
0
Energy (eV)
1
2
Example of an early SMEAGOL
calculation: molecular spin valves
‘Tunneling’
magnetoresistance
versus
‘metallic’ spin valves
Nature Materials 4 335-339
(2005)
Example:
Metallocenes
inside CNTs
Phys. Rev. Lett. 96 106804
(2006)
CoCp2@(zigzag or
chiral CNT)
Vanadocene:
VCp2@(zigzag CNT)
Control of electron
transport via geometry
Effect of ring rotations
Rotate the end benzene ring about
axis of the molecule
Reduces the magnitude of transmission
Geometry versus chemistry
Nuckolls et al., Nature 442, 904 (2006)
molecule
2
3
4
5
6
7
8
angle
0
15
30
46
52
62
88
Results for
the
conductance
Results for various
EF contacted to
hollow
Results for various
EF contacted to
adatom
Theoretical results for electron transmission
(N and S terminal atoms connected to hollow site)
Fermi level lies in the H-L gap: nice (cosine)2 dependence
Theoretical results for electron transmission
(N and S terminal atoms connected to gold adatom)
Fermi level located near sharp transport resonances: no (cosine)2 dependence
Control of electron transport via
the contact angle
CSW558
s
q
Theoretical approach


Relax geometry of the isolated molecular wire

Extend the molecule to include surface layers of gold
Vary angle theta between axis of molecule and normal to (111)
gold planes.
I. Grace, CJL, et al Nature Materials, 2006
Molecule docking on (111) gold
Three typical positions for Sulfur bonding
• Top site ~ directly above gold atom
• Hollow site ~ in the middle of 3 gold atoms
• Bridge site ~ between 2 gold atoms
Strongest bond formed on the hollow site.
In STM measurements ~ unknown contact
between molecule and tip
Hollow site
Top Site
Bridge site Does the tilt dependence depend on
docking position?
Results for conductance as a function
of tilt angle θ (with φ = 0)
• Tilting causes the resonances to
broaden and shift
• Good agreement for magnitude of
conductance
As tilt angle increases, could the
molecule be forced to rigidly rotate
about its axis?

=90˚
Density of states
φ = 30o
φ = 70o
Determination of optimum value
of φ for each value of θ
Nature Materials 2006
Control of electron transport via Fano
resonances
Role of the fluorenone units in
aryleneethynylene molecular wires:
Introduction to Breit-Wigner resonances
4Γ1Γ 2
T
2
2
E  ε   (Γ1  Γ 2 )
Width Г
4Γ
For Γ1  Γ 2  Γ, T 
2
2
( E   )  4Γ
For E  ε, T  1
2
For E  ε, Γ1  Γ 2 , T 
4Γ1
Γ2
 1
Typical effect of varying a thiolthiolgold contact gap
Peak position ε
Breit-Wigner versus Fano resonances
side group with eigenvalue ε1
Γ1  VΦ m (1) N 0 E 
2
Γ 2  W Φ m (N) N N 1 E 
backbone state, with a resonant energy ε0
  Ψ H1 Φ
T
4Γ1Γ2
2

 
 E  ε 
  (Γ1  Γ2)2
E  ε1 

*
2
Fano resonances in 4nm and 7nm wires
4nm: 1 fluorenone unit,
2 inner phenyl rings
7nm: 3 fluorenone units,
4 inner phenyl rings
Effect of cutting the bond between
the oxygen and the fluorenone unit
Effect of replacing oxygen by a bipyridine
unit: Geometric contol of Fano
resonances by rotating the bipyridine.
Surface of constant density of states for
two energy levels of the isolated molecule.
Inverse effect: control of geometry
by electron transport: eg carbon
nanotube windmills
Alex Zettl, UC Berkley
Carbon nanotube motor
Alex Zettl,
UC Berkley
Driving a molecule via an electron
‘wind’ : carbon nanotube windmills
( PRL 100 256802 (2008))
Questions for your
amusement
1. Do the right-moving electrons of an
infinite (n,m) carbon nanotube rotate
clockwise or anti-clockwise?
2. How does the direction of rotation
depend on the energy of the electrons?
Note: Right-moving = parallel to T
Clockwise
= parallel to Ch
Chirality of right-moving currents
of a (n,m) CNT Phys. Rev. B78 233405 (2008)
(n,m)
First open channel
Second open
channel
n=m+1, m+4 etc
Anti-clockwise
Clockwise
n=m-1, m+2, m+5
etc
Clockwise
Anti-clockwise
Energy dependence
(E-E1)1/2
(E-E2)1/2
N=m+3, m+6, etc
Anti-clockwise (E2)
Clockwise
A Landauer-type approach to
angular-momentum transfer
The tangential force exerted on a
(18,0)@(6,4) nano-drill as a function
of voltage.
Black curve: The tangential force per
volt as a function of energy which
when integrated leads to fig (a).
Red curve: The flux of tangential
momentum per volt for right-moving
electrons in an infinite (6,4) CNT.
The dimensionless tangential group
velocities carried by right (red) and
left (blue) moving channels of an
infinite (6,4) CNT.
The sum of the red curves yields
the red curve of figure (b).
What is the magnetic field produced
by a current passsing through a
chiral nanotube?
B = µ0I α/|Ch|
α is the ratio of the transverse and longitudinal
group velocities, averaged over the voltage
window of injected electrons
Example: For (4,1) or (4,2) CNTs, α ~ 1
and for a current of 10-6 amps, B =10-3
Teslas,
Electron pumping by rotation
nanotubes
( submitted )
Can a rotating nanotube drive electrons from left
to right?
Brouwer: Theoretical upper bound is 1 electron
per closed loop in parameter space.
Control of electron transport
via solvation shells
Eg Oligothiophenes
HS
S
SH
n=1,2,3 and 5
n
• Length can be varied by changing the number of
central thiophene rings
• Alkane connectors reduce contact geometry
dependence
• Liverpool measure their conductance as a
function of length using I(S) and I(t) methods
• Theory uses SMEAGOL to calculate conductance
Comparison with experiment
Experiment
(blue) finds an
almost length
independent
conductance
Theory (black)
predicts an
exponential
decay with
length
41
Interaction of water with oligo thiophenes
Method: Molecular dynamics of water molecules in various
starting positions round the wire to search for energy minima
Results: There are two local energy minima
1) Side – Lowest energy
DE = -0.3 eV
2) Bottom– Higher energy
DE= -0.04 eV
42
Effect of random water beyond
first solvation shell
Results for electrical conductance
Experiment in
the presence of
water vapour
(results are
reversible)
Submitted
Nature 2008
Experiment in
vacuum or dry
argon
Blue: Measured
Green: First solvation shell (side) plus background
Red: First solvation shell (side)
Pink: First solvation shell (bottom)
Black: No Water
Summary
Chemistry versus geometry: interesting range
of geometrical effects in single-molecule
electron transport
Fano resonances dominate low-bias
conductance of aryleneethynylene molecular
wires
CNT windmills
Few
Few--molecule solvation
solvation--shell sensing