366
T. Simon et al.
Fig. 20.2 Three types of DNA sequences. Each sequence is represented by a tight binding
model Hamiltonian, with on-site hole energies and hopping matrix elements (in eV), taken from
Refs. [23–25]. In each sequence only one of the strands (upper) is coupled to the two electrodes
Table 20.1 Calculated currents (nA)
No correlation
Base-pair correlation
Strand correlation
- -CGCG- -
19.5
7.8
9.0
GCGC
- -ATAT- -
47.7
43.7
23.9
TATA
- -CATG- -
50.8
40.7
10.4
GTAC
where N m =
2N
n=1 δ n m ,1 is the hole occupation number at the mth eigenstate. Notice that the infinite time limit assures that the entire frequency band of the dynamical fluctuations is accounted for in the current calculation [21].
20.5 Results
Steady state currents were calculated for hole chemical potentials, μ L = μ 0 + eΦ/2,
μ R = μ 0 − eΦ/2. The values μ 0 = 7 eV and eΦ = 4.5 eV were chosen to assure
that the entire “band” of molecular orbitals is within the Fermi conductance window [15]. The metallic nature of the electrodes was captured using a semi-elliptic
band model [33], J J (E) = 2π
j J
ξ 2
j J
δ(E − ε j J ) ∼ =
ξ 2
J
γ 2
J
4γ 2
j J
− (E − μ J ) 2 , with
a band width parameter, γ J = 5 eV, and a molecule-electrode coupling parameter, ξ J = 0.02 eV. For the nuclear baths an Ohmic model was invoked, where,
J n b (ω) =
2πη 2
n b
ω 2
C,n b
ωe
−ω/ω C,n b for ω > 0, and zero otherwise. To account for the net
effect of bath correlations, the different baths were all associated with the same
spectral density, η n b ≡ η = 0.1 and ω C,n b ≡ ω C = 0.25 eV for n b = 1, 2, . . . , M.
The temperature of the system was set to zero (using a numerical value 10 −6 K).
This choice fixes the direction of energy flow from the system into the bath. Energy flow into the molecular system, following thermal activation of low frequency
modes (ω K B T ), is therefore explicitly blocked.
The calculated currents for three different sequences (Fig. 20.2) are presented
in Table 20.1 for three different types of bath correlations (see Fig. 20.1). Notice
T. Simon et al.
Fig. 20.2 Three types of DNA sequences. Each sequence is represented by a tight binding
model Hamiltonian, with on-site hole energies and hopping matrix elements (in eV), taken from
Refs. [23–25]. In each sequence only one of the strands (upper) is coupled to the two electrodes
Table 20.1 Calculated currents (nA)
No correlation
Base-pair correlation
Strand correlation
- -CGCG- -
19.5
7.8
9.0
GCGC
- -ATAT- -
47.7
43.7
23.9
TATA
- -CATG- -
50.8
40.7
10.4
GTAC
where N m =
2N
n=1 δ n m ,1 is the hole occupation number at the mth eigenstate. Notice that the infinite time limit assures that the entire frequency band of the dynamical fluctuations is accounted for in the current calculation [21].
20.5 Results
Steady state currents were calculated for hole chemical potentials, μ L = μ 0 + eΦ/2,
μ R = μ 0 − eΦ/2. The values μ 0 = 7 eV and eΦ = 4.5 eV were chosen to assure
that the entire “band” of molecular orbitals is within the Fermi conductance window [15]. The metallic nature of the electrodes was captured using a semi-elliptic
band model [33], J J (E) = 2π
j J
ξ 2
j J
δ(E − ε j J ) ∼ =
ξ 2
J
γ 2
J
4γ 2
j J
− (E − μ J ) 2 , with
a band width parameter, γ J = 5 eV, and a molecule-electrode coupling parameter, ξ J = 0.02 eV. For the nuclear baths an Ohmic model was invoked, where,
J n b (ω) =
2πη 2
n b
ω 2
C,n b
ωe
−ω/ω C,n b for ω > 0, and zero otherwise. To account for the net
effect of bath correlations, the different baths were all associated with the same
spectral density, η n b ≡ η = 0.1 and ω C,n b ≡ ω C = 0.25 eV for n b = 1, 2, . . . , M.
The temperature of the system was set to zero (using a numerical value 10 −6 K).
This choice fixes the direction of energy flow from the system into the bath. Energy flow into the molecular system, following thermal activation of low frequency
modes (ω K B T ), is therefore explicitly blocked.
The calculated currents for three different sequences (Fig. 20.2) are presented
in Table 20.1 for three different types of bath correlations (see Fig. 20.1). Notice