Non-equilibrium electron
transport in dry DNA
C D Pemmaraju, I Rungger and S Sanvito
School of Physics and CRANN, Trinity College, Dublin
http://www.spincomp.com
QuantSim09, Warwick, UK
Outline
Motivation
Electronic structure
Spatial distribution of electronic wavefunctions
Energy spectrum and level alignment
Zero Bias results
Dependence on geometry
Effect of solvation layers
Finite bias results
Incoherent contributions
Conclusions
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Intro to DNA
A-DNA
B-DNA
Z-DNA
5'
3'
So can DNA be used as a current carrying wire?
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Earlier experiments
Insulator (12 eV)
Nature 391, 775 (1998)
Metal
Nature 398, 407 (1999)
PRL 85, 4992 (2000)
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Superconductor
Science 291, 280 (2001)
Earlier experiments
Rev.Mod.Phys, 76, 195 (2004)
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Recent Experiments
PNAS, 102, 11589 (2005)
26-bp long ds-DNA of a complex sequence
Deposited on Au-111 and connected to Au nano particle
Semi-conducting behaviour with a voltage gap of ~2 eV is observed
Large currents of ~220 nA at 2.0 V
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Recent Experiments
Appl. Phys. Lett. 87, 083902 (2005)
SAM of 12 bp poly(GC)-poly(GC) DNA on Au(111)
●Voltage gap of ~2 V
●Current in the range of ~1 nA
●
poly(G)-poly(C) DNA deposited flat on Au(111)
Voltage gap of ~2.0 V is observed
Current ~ 1nA above 2.0 V
Nat.Mat, 7, 68 (2008)
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Why study dry poly(G)-poly(C) DNA?
poly(G)-poly(C) is possibly the best case scenario for high
conductance.
Has the same base sequence (C or G) on each strand.
Formation of extended states more likely.
Has the smallest band gap
Guanine has the lowest I.P
Cytosine has the highest E.A
Degree of solvation in STM set-ups is unclear
Dry conditions are easier to handle ab-initio
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Computational approach
●
●
The DFT+NEGF formalism is used
Calculations carried out using the SMEAGOL
code
www.smeagol.tcd.ie
–
–
two terminal device setup
LDA+Approximate self interaction
correction scheme (ASIC)
Phys. Rev. B 75, 045101 (2007)
●
poly(G)-poly(C) DNA with alkyl-thiol connectors
on Au(111) leads
●
System size: ~ 6000 orbitals
●
Complex plane integration points: 128
●
●
Real energy points to integrate non-equilibrium
contribution to DM: 1000-5000
Parallelized over 256-512 compute nodes
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SMEAGOL: NEGF + DFT
Green's function:
−1
G  E =[ E i −H eff ]
L
R
Coupling matrices:
†
 L=i   L− L 
L = F 
eV
2
H eff = H M   L R
†
 R =i  R − R 
R =F −
eV
2
SMEAGOL (NEGF): A. R. Rocha et al., PRB 73, 085414 (2006); Nature Materials 4, 335 (2005);
http://www.smeagol.tcd.ie
SIESTA (DFT): J. Soler et al., J. Phys.: Condens. Matter 14, 2745 (2002)
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Electronic structure
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periodic poly(G)-poly(C) A-DNA
Back bone
Cytosine
Guanine derived HOMO band has a very small band-width ~60 meV
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Finite fragments of DNA?
Guanine band splits into discrete levels.
Levels spread over a much wider energy range ~0.6 eV
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Localization of electronic states
HOMO localized at 5' end of the Guanine chain
Energy is lowered moving from the 5' to 3' end
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Localization of electronic states
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Localization of electronic states
Periodic
5'
G
G
G
G
G
G
G
G
G
G
G
3'
3'
C
C
C
C
C
C
C
C
C
C
C
5'
Finite
5'
G
G
G
G
G
G
G
G
G
G
G
3'
3'
C
C
C
C
C
C
C
C
C
C
C
5'
Surface dipole leads to localization of electronic wavefunctions
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Effect of a solvation layer
Energy levels are rearranged as water layer screens the dipole
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Energy level alignment
We need quasi-particle energies i.e I.P and E.A
Semi-local DFT functionals perform poorly
Self-interaction corrections + Correlation effects are needed
Guanine
Expt (eV) -EHOMO/ELUMO
ΔSCF
GGA
ASIC
GGA
Ionization Potential (I.P) 8.2
5.2
8.8
7.9
Electron Affinity (E.A)
1.4
4.04
-1.2
3.8
4.76
>7.9
NA
Band Gap
Cytosine
Expt (eV) -EHOMO/ELUMO
ΔSCF
GGA
ASIC
GGA
Ionization Potential (I.P) 8.9
5.6
9.7
8.54
Electron Affinity (E.A)
0.2
2.1
4.8
-0.7
Band Gap
8.7
3.5
4.9
>8.54
ΔSCF Energies provide the best estimates of removal/addition energies
I.P(ΔSCF)=E(N)-E(N-1), E.A(ΔSCF)=E(N+1)-E(N)
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Energy level alignment
For short chains, I.P decreases with increasing chain length
Hybrid-DFT gives higher I.P compared to ordinary GGA.
I.P value converges at around 6 base pairs
GGA HOMO eigenvalue much too high
An approximate Self-Interaction correction is applied to “tune” the HOMO eigenvalue to
match the ΔSCF I.P
ΔSCF band-gap > 3.8 eV
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Energy level alignment
GGA HOMO is pinned at EF leading to a sharp DOS
The same feature is seen in the transmission
coefficient
The correct HOMO-EF distance is restored with ASIC
ASIC LUMO states are roughly 1.5 eV too low as they
do not correspond directly to E.A
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Zero Bias Results
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Adaptive mesh
1 meV
Refinement:
Start with uniform mesh and broadened GF
Resolve peaks
Add mesh points where needed and
decrease broadening
Iterate until true width of resonances is
reached.
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4.0 10-7 eV
Zero bias properties
HOMO
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Effect of alkyl-thiol connections
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Effect of a solvation layer
HOMO
HOMO
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Finite bias Results
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Voltage gap vs. transmission gap
Vg
LUMO
ELUMO
EFL
EHOMO
EFR
HOMO
1)LUMO and HOMO do not move with bias: Vg=4*Min(EHOMO,ELUMO)
●
2)LUMO and HOMO move with one of the two leads (asymmetric
coupling, STM): Vg=ELUMO+EHOMO
●
3)LUMO and HOMO avoid the bias window: Vg=4*Max(EHOMO,ELUMO)
●
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Finite bias setup: G3'C3' arrangement
The 3' ends of a 6 base pair DNA are connected to Au via thiol groups.
Coupling of localized states expected to be asymmetric
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G3'C3' geometry: PDOS and LDOS
HOMO is localized at
the G5' end
LUMO is localized at
the C5' end
HOMO
LUMO
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G3'C3' geometry: I-V
Vgap ~ 2 eV
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G3'C3' setup: Bias dependent transmission
HOMO peak conducts first for both positive and negative bias
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G3'G5' geometry
Both the 5' and 3' ends of the Guanine chain are connected.
Cytosine chain is left unconnected
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G3'G5' geometry: PDOS and LDOS
HOMO is localized at G5'
LUMO is localized at C5'
Coupling of HOMO to leads
expected to be even more
asymmetric.
LUMO
HOMO
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G3'G5' arrangement: I-V
Vgap ~ 2.2 eV
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G3'G5' geometry: Bias dependent transmission
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Incoherent contributions
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Incoherent contributions: floating probes
To obtain a basic approximation for incoherent contributions to the current
•We apply the idea of M. Büttiker [PRB 33, 3020 (1986)] and add a set of additional
fictitious leads to the system, so that all states are coupled to at least one of the leads
•The Fermi energy of each of the additional leads is set by the condition that no current
can flow into these.
−1
G  E =[ E − H M− L− R −∑  n ]
L
R
1
Current conservation:
I n =∫ dE T nm  f n − f m =0
⇒
†
3
occupied
empty
EF,n
T nm=Tr [ n G  m G ]
EF ,L
EF ,2
EF ,1
Total current:
I =∫ dE T LR  f L− f R ∑n ∫ dE T Ln  f L− f n 
coherent
2
incoherent
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EF ,3
EF ,R
Incoherent contributions:System setup
1
2
linker
4
6
8
10
G
G
G
G
linker
11
C
C
C
C
3
5
7
9
12
The system is partitioned into 12 units each with its own floating lead and local
Fermi level
The coupling strength (broadening) is controlled by a parameter δ
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Incoherent contributions
1
2
linker
4
6
8
10
G
G
G
G
linker
11
C
C
C
C
3
5
7
9
VB=0.2 V
12
The local Fermi level seems
to follow the potential drop
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Incoherent contributions
VB=0.2 eV
Current without the incoherent contributions is rather small.
At a given bias, increasing the strength of δ increases the current
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Incoherent contributions
TnR exhibits a position dependence
Electrons from probe “n” tunneling into the
right lead “R”, only “see” electronic states
localized to the right of “n”.
5'
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1
2
3
4
G
G
G
G
C
C
C
C
1
2
3
4
Conclusions
Electronic states on DNA fragments are strongly localized.
The Fermi level of Au is expected to lie within the HOMO-LUMO gap of DNA.
Most of the states on DNA are expected to couple asymmetrically to the leads
in SAM geometries
A voltage gap of ~ 2 eV is expected for coherent tunneling conduction.
The size of the voltage gap is most likely determined by Guanine HOMO
levels as the empty Cytosine states are too high.
Currents obtained from a purely coherent tunneling mechanism are several
orders of magnitude smaller than those experimentally observed.
Incoherent contributions may be treated in a qualitative way by introducing an
additional broadening through local fictitious leads
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Acknowledgements
Ivan Rungger
Alexandre Rocha
Stefano Sanvito
Computational resources
TCHPC
Funding
Thank You
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Weakly coupled states
generalized bound state : Re n  E W = E W
L , 
R , 

and
 L ,  =    L  
∣Im n  E W ∣
†
 R ,  =    R  †
1
Im   = − L ,  R ,  
2
L ,  f L ,  R , f R , 
occupation =
 L ,  R , 
2 e L ,  R , 
I =
h  L ,  R , 
•Mapping from DFT to single level tight-binding-like parameters
•For a true bound state ɣLα=ɣRα = 0, so that Iα =0; the occupation however is undefined for states in the
bias window (fLα ≄ fRα ).
© CRANN
www.crann.tcd.ie
Some definitions
γL
εα
γR
ΣL
ΣR
γ α determ ines the broadening of trans m is s ion peaks
rα is a m eas ure of coupling as y m m etry
T α → 1 as rα → 0 (ev en coupling )
rα → + 1 if s tate is s trong ly coupled to the left lead
rα → -1 if s tate is s trong ly coupled to the rig ht lead
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Localization in 2 base pair DNA
G
C
C
HOMO
LUMO
HOMO-1
LUMO-1
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G