Quantum transport in DNA wires:
Influence of a dissipative environment
Rafael Gutierrez Laliga
In cooperation with S. Mandal and G. Cuniberti
Molecular Computing Group
University of Regensburg
Outline
• Why DNA ?
• Electronic transport in DNA: a bird’s eye view
• DNA wire in water: a Hamiltonian model
• Formalism and approximations
• Strong dissipative limit
• Conclusions
Why DNA ?
• Groundbreaking : repair of oxidative damage
; ET over long distances (∼ 40 Å)
(C. J. Murphy et al., Science (1993))
• Molecular electronics ⇒ potential applications
as template (self-recognition and assembling)
as molecular wire (M-DNA, poly(GC))
M. Hazani et al. , Chem. Phys. Lett. (2004)
Electronic transport in DNA: a bird’s eye view
• Experiments: DNA is insulator, metal, semiconductor
; sample preparation and experimental conditions are crucial
(dry vs. aqueous environment, metal-molecule contacts, single molecules vs. bundles · · ·)
• Theory: Variety of factors modifying charge propagation:
static disorder, dynamical disorder, environment (hydration shell, counterions)
see: D. Porath, G. Cuniberti, and R. Di Felice,
Charge Transport in DNA-Based Devices
Top. Curr. Chem. (2004)
Transport in
single
Poly(GC) oligomers in
water
B. Xu et al. Nanoletters 4, 1105 (2004)
metallic behaviour !
large currents !
Transport in
single
Poly(GC) oligomers in
water
Ab initio (H. Wang et al. PRL (2004)): dry Poly(GC) ; e−γ L, γ ∼ 1.5 Å−1
Algebraic behaviour induced by the environment !?
DNA wire in water: a Hamiltonian model
• ab initio calculations (e.g. E. Artacho et al. , Mol. Phys. (2003)) ;
(i) decoupled HOMO/LUMO channels
(ii) backbones non conducting
H =
X
j
†
bj bj bj − t||
X



†

bi bj + H.c.
<i,j>
{z
}
HC

X d †
X  †
+ j dj dj − t⊥ bj dj + H.c.
j {z
j
|
}
|
{z
}
Hd
HC−d


X
X
† 
†
†
+ α Ω α B α B α + λα d j d j B α + B α 
α,j
|
{z
}
|
{z
}
HB
HF−B
|
+ Hleads
Formalism and approximations
• Green function techniques
• Phonon bath ; continuous frequency spectrum J(ω) ∼ ( ωωc )s
• neglect nonequilibrium effects (eV→0)
el
=E
• no inelastic electron tunneling, Eel
out
in
; Landauer-like expression :
†
t(E) = T r[GW (E)ΓR GW (E) ΓL]
t(E) includes full interaction with the
bath ; decoherence
Low-bias, strong dissipative limit
New kBT-dependent electronic manifold around EF=0
Bath-selfenergy ΣB(E):
Re ΣB(E) ; renormalization and/or new states (polaron band)
Im ΣB(E) (“friction”) ; decoherence, strong suppression of the polaron band
; incoherent polaronic band ; pseudo-gap opening
Transmission t(E) and low-bias current I(V)
Dissipation ≠ 0
Dissipation=0
1
1
T=10 K
T=300 K
0.6
t(E)
t(E)
0.8
0.4
-0.1
0
10
-18
0.4
0
0.1
E (eV)
-0.02
0
-0.1
-0.05
0
-0.2
-0.1
0
0.02
0
0.05
0.1
0.1
0.2
E (eV)
50
I(V) (nA)
I(V) (nA)
0.6
T=10 K
T=300
-12
0.2
100
-100
10
E(eV)
0.2
0
0.8
0
-50
-0.2
-0.15
-0.1
-0.05
V (Volts)
0
0.05
V (Volts)
• pseudo-gap increases with temperature
• incoherent DOS also increases with temperature
• I(V ) displays “metallic” behaviour at high kBT
0.1
0.15
0.2
Temperature dependence of t(EF ) (Arrhenius plot)
10
10
-24
-36
-48
10
10
t/t||=0.4
t/t||=0.6
t/t||=0.9
-12
10
t(EF)
Yoo et al. PRL 87, 198102 (2001)
t(EF)
10
J0/ωc=8
J0/ωc=20
-8
-12
0
20
40
60
3
80
-1
10 /T (K )
Activated behaviour
; phonon assisted hopping
100
Scaling of t(EF ) with the chain length L = N abp
-1
10
J0/ωc=2 γ=0.28 Å
-2
10
-1
J0/ωc=8 γ=0.14 Å
0.08
-5
J0/ωc=10
J0/ωc=13
linear fit
linear fit
10
t(EF)
10
-9
10
t(EF)
t(EF)
0.06
-7
-3
0.04
10
-4
-5
10
-12
10 0
2
NA-T
4
0.02
6
-1
J0/ωc=8 γ=0.28 Å , ∆E=1.4 eV
8
10
12
14
16
0.07
0.08
N
0.09
0.1
0.11
1/N
• Increasing coupling to the bath
exponential tF ∼ e−γL =⇒ algebraic tF ∼ L−α dependence
• Exponential dependence is related to virtual tunneling through pseudo-gap (γ 1 Å−1)
• Introduction of a barrier ; (AT)n pairs, enforces exp-dependence
0.12
Structural base-pair fluctuations
Random on-site energies drawn from Gaussian distribution P () =
2
2
√ 1 e− /2σ
2πσ
1
σ0= 0
σ0 = 0.1 eV
σ0= 0.8 eV
0.8
No Disorder
σ=0.05 eV
σ=0.6 eV
-5
t(E)
ln t(EF)
0.6
0.4
γ=0.191
γ=0.193
γ=0.2
-10
0.2
0
-1
-0.8
-0.6
-0.4
-0.2
0
E/t||
0.2
0.4
0.6
0.8
1
-15
5
10
15
20
N
“Thermal” disorder does not appreciably affect the pseudo-gap formation
Conclusions
Perspectives
• Environment drastically affects charge transport
• parameter estimation
• Strong coupling regime:
• Sequence dependence
(i) bath-induced pseudo-gap
(ii) finite kBT-dependent DOS near EF
; activated behaviour
; weak exponential or algebraic L−dep.
• Contact to Xue et al. (2004) experiments
(i) (too ?) large currents ∼ 50 − 200 nA
(ii) (bath-induced) algebraic L-dependence
(Klotsa et al. ICPS27 (2004), Roche et al. PRL (2003)
• Nondiagonal EPI