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Journal of
Nanoscience and Nanotechnology
Vol. 13, 3889–3896, 2013
Temperature and Magnetic Field Effects on
Electron Transport Through DNA Molecules
in a Two-Dimensional Four-Channel System
Yong S. Joe1 3 ∗ , Sun H. Lee2 , Eric R. Hedin3 , and Young D. Kim1
1
RESEARCH ARTICLE
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University,
Seoul 130-701, Korea
2
Geophysical Institute, University of Alaska, Fairbanks, AK 99775, USA
3
Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University,
Muncie, Indiana 47306, USA
We utilize a two-dimensional four-channel DNA model, with a tight-binding (TB) Hamiltonian, and
investigate the temperature and the magnetic field dependence of the transport behavior of a short
DNA molecule. Random variation of the hopping integrals due to the thermal structural disorder,
which partially destroy phase coherence of electrons and reduce quantum interference, leads to
a reduction of the localization length and causes suppressed overall transmission. We also incorporate a variation of magnetic field flux density into the hopping integrals as a phase factor and
observe Aharonov-Bohm (AB) oscillations in the transmission. It is shown that for non-zero magnetic flux, the transmission zero leaves the real-energy axis and moves up into the complex-energy
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transmission.
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Keywords: DNA Molecule, Electron Transport, Thermal Disorder, Aharonov-Bohm Oscillations.
1. INTRODUCTION
Charge transport and electrical conduction through DNA
sequences have acquired considerable attention in recent
years. After the inter-base hybridization of -orbitals perpendicular to the planes of the stacked base-pairs in
double-stranded (ds) DNA was found by Eley and Spivey,1
it was revealed that both positive charges (holes) and electrons would propagate through -stacks of DNA bases.
Thus, the idea of using DNA as a component of future
molecular electronic devices has been reported and is still
being explored in nanotechnology and nanoelectronics.2–4
Charge transport measurements through DNA molecules
have shown controversial results. The wide range of transport behaviors can be attributed to many experimental complications, such as contact between DNA molecules and
electrodes, length and sequence of DNA, temperature, and
humidity in each experiment. In order to understand
the diverse features of the electrical transport properties of DNA molecules, many theoretical studies were
∗
Author to whom correspondence should be addressed.
J. Nanosci. Nanotechnol. 2013, Vol. 13, No. 6
devoted to this topic using various models and techniques.
For instance, one-dimensional (1D) and two-dimensional
(2D) tight-binding (TB) models5 6 and density-functional
methods7–10 have been employed. Klotsa et al.11 used two
TB models of DNA, including a one-channel fishbone
model and a two-channel ladder model, and obtained the
electronic properties in terms of localization lengths. They
showed that as backbone disorder increased, the localization lengths increased and thus, larger currents flow. The
semiconductivity of DNA, using a ladder system which has
two main chains with hopping between nearest-neighbor
sites and inter-chains between the ds-DNA was investigated by Iguchi.12 He also suggested the backbone chains
and hydrogen bonds contribute to the electronic properties
of DNA.
In particular, the temperature dependence of transport
behavior of a short DNA molecule has been studied by
Feng et al.13 taking into account Coulomb interaction of
electrons and coupling between electrons within a twolevel system in the DNA molecule. In addition, the effect
of the twist angle between neighboring base pairs due
to thermal fluctuations is considered in the theoretical
1533-4880/2013/13/3889/008
doi:10.1166/jnn.2013.7206
3889
Joe et al.
RESEARCH ARTICLE
Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules
investigations of charge transport through a model DNA
sequence with a superconducting electrode.14 In these
models, however, the possibility of electron transport along
the sugar-phosphate backbone is ignored. Hence, it is necessary to have a more sophisticated depiction of DNA
model which has four possible conduction channels for
charge carrier propagation by incorporating intra-backbone
couplings, hydrogen bonds, and a coupling between the
base-pairs and backbones. The variation of the temperature
in this advanced model induces structural disorder and ranFig. 1. A short poly(G)-poly(C) chess model for electronic transport
domizes every hopping integral in the DNA molecule, such
through a 2D four-channel DNA model. Circles and hexagons denote
nucleobases with onsite potential energies xi = 775 eV (i = 1–5, guaas intra-backbone couplings and the coupling between the
nine base), i = 887 eV (i = 6–10, cytosine base), = 85 eV (backbase-pairs and backbones. Furthermore, the effects of an
bone), and 0 = 775 eV (metallic leads). Lines denote various hopping
external magnetic field in this system should be considamplitudes: t0 = 1 eV (intra-lead coupling), tL12 = tR12 = 03 eV (couered to further examine general features of charge transport
pling between the leads and the end bases), ti i+1 Ti i+1 = 02 eV (couthrough DNA for better understanding of environmental
pling between the nearest neighbor bases), t = 03 eV (coupling between
backbone and DNA base pairs), hi (hydrogen bonds), and Ba (intraparameters.
backbone coupling).
In this article, we consider a 2D, four-channel DNA
model, which is more representative of the actual DNA
and the yellow circles are the sites of the leads. DNA base
molecule, with inhomogeneous hopping strengths between
pairs have an energy given by the ionization potentials of
base pair and backbone sites, the hydrogen bonds between
respective bases, taken as G = 775 eV and C = 887 eV.
base-pairs, and the intra-coupling along the backbone.
These are interconnected and linked to the backbone,
In this system, we study temperature-dependence of the
leads, and nearest-neighbor nucleotides by – stacking
charge transport properties. Since temperature causes therinteraction, and hydrogen bonds. Every line between sites
mal fluctuations and other structural changes of the DNA,
denotes coupling with a specified hopping amplitude.
we incorporate this effect into the TB model Hamiltonian
Hamiltonian
in a 2D four-channel chess model
through the hopping integrals
and examine
the transmisDelivered
by Publishing
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to:TB
Kyung
Hee University
can
be
written
as
sion resonances, the localization
length,
current–voltage
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characteristics, and the differential Copyright
conductanceAmerican
at vari- Scientific Publishers
(1)
HTot = HLead + HDNA + HLead-DNA
ous temperatures. In addition, we investigate the electronic
properties of a short poly(G)-poly(C) DNA molecule in the
Here, the Hamiltonian for a short poly(G)-poly(C) DNA
presence of an external magnetic field. A magnetic field
molecule is described by
with flux density penetrating the center of the 2D DNA
HDNA = i ci† ci + j di† di + a†i ai + bi† bi structure induces an Aharonov-Bohm (AB) phase differij
ence between the electron wave functions of the upper
and lower DNA strands and produces AB oscillations in
− t ci† ai + t di† bi + hi ci† d + hc
i
the transmission due to quantum interference effects. It is
shown that the periodicity of the AB oscillations is directly
− ti i+1 ci† ci+1 + Ti i+1 di† di+1
proportional to the number of loops in the DNA molecules.
i
+ Ba a†i ai+1 + Ba bi† bi+1 + hc
2. THEORETICAL MODEL AND
CALCULATIONS
We consider four possible conduction channels for charge
carrier propagation by incorporating intra-backbone couplings and hydrogen bonds, shown schematically in
Figure 1 which is called the “chess” model. Electron transport through the DNA molecule, connected between two
semi-infinite electrodes, arises through four different channels which consist of -orbital overlapping between the
nearest neighboring bases within the two main conduction chains and along the upper and lower backbones.
In Figure 1, the individual upper purple circles (lower
pink circles) represent DNA guanine (cytosine) bases,
the green hexagons are sugar-phosphate backbone sites,
3890
(2)
where ci† ci , di† di , a†i ai , and bi† bi are the creation
(annihilation) operators at the i-th G/C base and the
i-th upper and lower backbones, and ij is the onsite
potential energy of DNA G(C) base and is backbone
onsite energy. The couplings, ti i+1 Ti i+1 , are the hopping amplitudes between bases along the long axis and t
is a hopping integral between each base and backbone.
The intra-backbone couplings are denoted as Ba and each
base-pair is coupled by the hydrogen bonds, hi .
The DNA molecule is coupled to two semi-infinite
metallic leads by the tunneling Hamiltonian
HLeads-DNA = −tL1 l0† c1 − tL2 l0† d1
− tR1 l1† cN − tR2 l1† dN + hc
(3)
J. Nanosci. Nanotechnol. 13, 3889–3896, 2013
Joe et al.
Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules
where tL12 tR12 are the contact hopping strengths
between the left (right) lead and the end DNA bases, and
li† li is the creation (annihilation) operator at the i-th site
of the leads. The leads themselves are modeled by another
TB Hamiltonian as
HLeads = 0 li† li − t0 li† li+1 + hc
(4)
t → t cos i i+1 , and hi → hi cos i i+1 . Using
cos i i+1 1 − 2 /2 1 − kB T /2I2 × i , we can
now form the final random hopping integrals as
tT i i+1 → tT i i+1 1 − kB T /2I2 × i t → t 1 − kB T /2I2 × i (5)
hi → hi 1 − kB T /2I × i where 0 is the lead onsite energy (0 = 775 eV) and
where i is a random fluctuation factor. We note here that
t0 is the intra-lead hopping amplitude. In our numerical
the
on-site energy fluctuations, which can be absorbed into
calculations, we use re-scaled parameters and the electron
the
static energy disorder, are not taken into account.
energy E, all of which are normalized with respect to the
Figure 2 shows a contour plot of the transmission
hopping integral of the leads, taken as t0 = 1 eV.
as a function of both electron energy and temperature
The TB approximation to the Schrödinger equation
and two plots of the transmission coefficient as a funcfora system, depicted in Figure 1, can be written as
tion of electron energy at T = 0 K and T = 300 K.
− Vn m m +n n = E
n . Here, the sum runs over the nearFour well-developed mini-bands with five peaks each are
est neighbors of n, E is the electron energy, and n is
merging together in Figure 2(b) due to the existence of
the site energy. The parameters Vn m are overlap integrals
intra-coupling along the backbones, the inclusion of the
(or coupling parameters) involving the overlap of the single
hydrogen bonds between the base pairs, and the coupling
site, atomic-like wave functions from sites m and n with the
between bases and backbone sites. As the temperature is
single-site potential of site n. The electron energy window
is 575 ≤ E ≤ 975, as set by the TB dispersion relation
(E = −2t0 cos ka + 0 for the uniform leads. By applying
the wave functions into the TB Schrödinger equations and
solving the matrix equation for the linearized TB Hamiltonian, we obtain the transmission amplitude as a function
of the incoming electron
energy, E.
desired transDelivered
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areMon, 06 May 2013 10:13:48
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ampli- Scientific Publishers
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tude, T = tE2 , and G = 2e2 /h T respectively.
i
i
2
3.1. Temperature Effects
Charge transport in DNA is a complex phenomenon
because the environment plays a significant role in determining the conductivity of DNA. Temperature is
one of the important factors in experiments with biomaterials, since variation of the temperature induces
structural disorder and fluctuations of the system. Here,
we apply the variation of the temperature to the hopping integrals in terms of twist-angle fluctuations, and
investigate the transport behavior for electrons through a
short poly(G)-poly(C) chess DNA molecule in order to
observe the effects of temperature. We introduce a relative
twist angle i i+1 deviated from its equilibrium value
between i and i + 1 that follows a Gaussian distribution
with average twist angle, I I+1 = 0. In the meantime, its variance is taken according to the equipartition
theorem, i2 i+1 = kB T /I2 , where I2 /kB = 250 K,
T is the temperature in kelvins, I is the reduced
moment of inertia for relative rotation of the two adjacent bases, and is the oscillator frequency of the
mode.14–17 Then, the temperature-dependent hopping integrals can be obtained as tT i i+1 → tT i i+1 cos i i+1 ,
J. Nanosci. Nanotechnol. 13, 3889–3896, 2013
Fig. 2. (a) Contour plot of the transmission versus electron energy
and temperature, and the transmission coefficient versus electron energy
for two different temperatures, (b) T = 0 K and (c) T = 300 K with
fixed parameters: hi = 05 eV, Ba = 02 eV, and random factors i =
05 −03 0 03 −05.
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RESEARCH ARTICLE
3. RESULTS AND DISCUSSION
RESEARCH ARTICLE
Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules
Joe et al.
increased, thermal fluctuations manifesting in the random
T ∝ exp−L/, where L is the total length of the system. Notice that the magnitude of the localization length
hopping amplitudes destroy the phase coherence of the
at T = 0 K is approximately 10 times larger than that at
electrons and reduce quantum interference. In Figure 2(c),
T = 300 K. This clearly indicates that thermal structural
the magnitude of the envelopes in the transmission specfluctuations localize the electronic wave functions, resulttrum, which initially have unit transmission, become suping in a temperature-dependent localization length.
pressed and smear out below unity due to the decrease
With the knowledge of the transmission T E, we
in the number of transmitting states, while the resonance
can evaluate the current–voltage (I–V ) characteristics by
positions are shifted due to the phase changes of the
applying the standard formalism based on the scattering
electrons.
theory of transport,25–28
A DNA double helix with disoriented base-pairs due to
the thermal fluctuations can be viewed as a 2D disordered
2e system. In this system, the disorder leads to electronic
I=
dE T EfL E − fR E
(6)
h −
localization. Hence, the thermal structural fluctuations will
considerably limit electron transport through DNA and
Here, fL/R E = 1/eE−L/R /kB T + 1 is the Fermi distrimake electron wave functions more localized. To address
bution function, where kB is a Boltzmann constant and
the effects of thermal structural fluctuations on electron
L/R stands for the electrochemical potential of the left
localization, we plot the localization length as a function
(right) metal electrodes. The difference between these is
of electron energy for two different temperatures, T =
controlled by the applied source–drain bias voltage as
0 K and T = 300 K in Figure 3. Localization length is
L − R = Vsd . Even if inelastic electron–phonon scatterinversely related to the Lyapunov coefficient N , which
ing can occur in the presence of thermal vibrations of
is widely used for a powerful proof-tool to sort out the
the DNA molecule, inelastic scattering has a minor effect
main features of complex localization patterns, and is
on the conductance because the electron–phonon coupling
calculated using transmission coefficients T E. Hence,
is very weak.29 Hence, this expression takes into account
the localization length can be written as E = N −1 ,
only the structural disorder due to thermal fluctuations and
where N = − lnT E/2N and N is the number of
the broadening of the Fermi function. The I–V characterbase-pairs.17–24 The asymptotic behavior of the localization
istics are shown in Figure 4 for two different temperatures
length indicates that theDelivered
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can partially
T =to:
0 KKyung
(solid Hee
line) University
and T = 300 K (dotted line). The
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destroy coherent charge transport
and
reduce
the
mean
nonlinear
I–V
curves
exhibit
IP: 163.180.37.28 On: Mon, 06 May 2013 10:13:48 a current gap at low applied
transmission coefficient. In other words,
high temperature
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bias, andPublishers
the voltage threshold for current onset for both
leads to the disorder of the system and a reduction of
temperatures is about the same (Vsd = 32 volts). This indithe localization length and consequently a reduction of
cates that the thermal structural disorder does not affect
the electron conductance, according to the relationship,
the voltage gap in the I–V characteristics. When Vsd >
32 volts, however, reduced current is observed at higher
temperature, since the static distortion sites due to the thermal structural vibration and twist modes increase elastic
scattering of electrons through the DNA molecule. As the
temperature increases, the linear behavior of the current
after the threshold voltage is changed to a step-like behavior, which is indicative of resonant conductance peaks in
the differential I–V curve. The differential conductance
Fig. 3. Localization lengths as a function of electron energy are plotted
for two different temperatures (a) T = 0 K and (b) T = 300 K.
3892
Fig. 4. Current as a function of source–drain voltage for T = 0 K (solid
line) and T = 300 K (dashed line). The corresponding differential conductance, dI/dV , versus applied voltage is shown in the inset.
J. Nanosci. Nanotechnol. 13, 3889–3896, 2013
Joe et al.
Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules
dI/dV , shown in the inset of Figure 4, exhibits a wide and
single resonance peak with a full-width half-maximum of
∼ 1.3 volts for T = 0 K and a triple-peak structure with
reduced amplitudes for T = 300 K. We attribute these resonant peaks in the differential conductance, arising from
the resonant tunneling through the resonant energy levels in the DNA molecule, to the re-arrangement of energy
levels due to the thermal structural fluctuations.
3.2. Magnetic Flux Effects
tT i i+1 → tT i i+1 e±i hi → hi e±i and
t → t e±i
(7)
where = 2 /N 0 denotes the total phase shift with
the number of sites N . Here, measures the total flux
through the system in units of the flux quantum, 0 h/e,
and the plus or minus signs in the exponential phase factors are applied when the electron moves in the counterclockwise or clockwise direction, respectively.
First, we study magnetic flux dependence of the electron conduction through DNA molecules in the absence of
hydrogen bonds. In Figure 5, we show contour plots of
the transmission T E as a function of magnetic flux
and electron energy for different numbers of base-pairs:
(a) one base-pair and (c) five base-pairs. For a fixed incident energy (E = 8) the transmission spectra versus magnetic flux is also depicted in (b) one base-pair and (d) five
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Fig. 5. Contour plots of the transmission as a function of electron energy (E and magnetic flux (/0 , without considering backbone effects or
hydrogen bonds (hi = 0), for different numbers of base-pairs: (a) one base-pair and (c) five base-pairs. Transmission spectra versus magnetic flux for
fixed incoming energy (E = 8) are shown for (b) one base-pair and (d) five base-pairs. As the number of base-pairs increases, the amplitude of the AB
oscillations diminishes. However, from the enlarged plot of the transmission for five base-pairs, depicted in the inset of (d), it is clearly seen that the
transmission has a small oscillatory, flux-dependent behavior with a periodicity of 0 .
J. Nanosci. Nanotechnol. 13, 3889–3896, 2013
3893
RESEARCH ARTICLE
In this section, we investigate the electronic properties of a
short poly(G)-poly(C) DNA molecule in the presence of an
external magnetic field. When a magnetic flux is present,
there exist trajectories enclosing a finite flux, which affect
the physical properties of the system. In order to focus on
the AB effects in this system, we assume that our model
in the absence of the backbone effect either has a single
loop in the ds-DNA molecule without inter-base hydrogen bonds, or multiple loops with the inclusion of interbase hydrogen bonds. [In Figs. 7(a) and (c) notice that we
color both the backbone sites and couplings between base
pairs and backbone a light gray in order to indicate lack
of consideration of the backbone effect]. A magnetic field
flux density penetrating through the center of the 2D DNA
structure induces AB phase difference between the electron wave functions of the upper and lower DNA strands
and produces AB oscillations in the transmission T E as
a function of magnetic flux.
In order to observe the quantum interference through the
double-helix DNA, the hopping integrals are modified by a
multiplication of the Peierls gauge phase factor, defined as
Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules
the on-site energy of either the upper (guanine) or lower
(cytosine) bases, giving less interaction between the two
strands. We note here that the periodicity of the AB oscillations remains the same as 0 , regardless of the size of
the loop, because there exists only a single loop in the
DNA molecule in the absence of hydrogen bonds.
Next, we examine the transmission characteristics as a
function of electron energy for a fixed value of magnetic
flux for two different numbers of base-pairs. In Figure 6,
we show transmission resonances as a function of electron energy (left column) and contour plots of transmission in the complex-energy plane (right column) for
different values of the magnetic flux and different number
of base-pairs. In the case of one base-pair and /0 = 1
RESEARCH ARTICLE
base-pairs in Figure 5. For a single base pair, AB oscillations with flux variation arising from quantum interference
have a period of 0 and a noticeable amplitude of 0.4.
In the case with five base-pairs, the amplitude of the AB
oscillations in the transmission is shown to be negligible
in Figure 5(d). However, from the enlarged plot depicted
in the inset of (d), it is clearly seen that the transmission has a small oscillatory, flux-dependent transmission,
in which the AB resonance oscillations are out of phase
by 180 in comparison with Figure 5(b) [The locations
of peaks are shifted by 0 /2]. The reduced amplitude of
the AB oscillations in the case with 5 base-pairs is due
to the transmission being restricted more to only one or
the other strand at electron energy values in proximity to
Joe et al.
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Fig. 6. Transmission resonances as a function of electron energy: (a) /0 = 1, (c) /0 = 03 for one base-pair, and (e) /0 = 03 for five
base-pairs. Contour plots of the transmission in the complex-energy plane: (b) /0 = 1, (d) /0 = 03 for one base-pair, and (f) /0 = 03 for
five base-pairs. Two distinct BW resonances appear as peaks and poles at E ≈ 7.75 and E ≈ 8.87 in (a)–(d), but the transmission zero leaves the
real-energy axis and moves up into the complex-energy plane in (d).
3894
J. Nanosci. Nanotechnol. 13, 3889–3896, 2013
Joe et al.
Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules
the two transmission bands have almost no overlap, which
severely mitigates the amplitude of the AB oscillations,
as noted in Figure 5(d). The five well-defined resonance
peaks within each band are shown in Figure 6(f) as five
distinct resonance poles in the complex-energy plane.
Finally, we investigate the electron phase shift through
a short DNA molecule with the inclusion of hydrogen
bonds between the base pairs. The existence of hydrogen
bonds generates many sub-rings, each enclosing magnetic
flux. As the number of base-pairs in the DNA molecule
changes, the number of loops within the DNA varies. For
instance, a single base-pair generates two enclosed paths
(2 loops) and five base-pairs produces six enclosed paths
(6 loops) due to the hydrogen bonds hi i = 1 5 connecting bases across the long axis of DNA [see Figs. 7(a)
and (c)]. The total transmission T E versus magnetic flux
(/0 for one base-pair (2 loops) with hi = 05 and
E = 75 is displayed in Figure 7(b) showing periodic AB
oscillations with 20 periodicity. A contour plot of T as a
function of E and /0 for five base-pairs with hi = 05 is
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Fig. 7. Schematics of DNA molecules with magnetic flux for (a) one base-pair with 2 loops and (c) five base-pairs with 6 loops. (b) Transmission
versus flux for one base-pair with hi = 05 and E = 75. In the case of five base-pairs, a contour plot of the transmission as a function of E and /0
is shown in (d), and the transmission versus flux for (e) hi = 05 and (f) hi = 09 with fixed E = 75. The periodicity of AB oscillations in terms of
0 is the same as the number of loops through the DNA.
J. Nanosci. Nanotechnol. 13, 3889–3896, 2013
3895
RESEARCH ARTICLE
(or = l 0 , where l = 0 1 2 ), two distinct BreitWigner (BW) resonances appear at E ≈ 7.75 and E ≈ 8.87
which correspond to the onsite energy values of guanine
and cytosine, respectively [Fig. 6(a)]. When /0 = 03,
the transmission minimum at E ≈ 8.3 is slightly shifted
to higher energy, E ≈ 8.4, and no longer reaches to zero
[Tmin E = 02 in Fig. 6(c)]; the two peak positions of
the BW resonances remain the same, however. In other
words, the transmission zero [ReE = 0 and ImE = 0
in Fig. 6(b)] leaves the real-energy axis and moves progressively up into the complex-energy plane as the magnitude of the flux increases from 0.0 to 0.5 [ReE = 0 and
ImE = 08 for /0 = 03 in Fig. 6(d)]. For values of
flux greater than 0.5, the transmission zero jumps to the
negative half of the complex-energy plane and returns to
the real-energy axis from below as /0 → 10.
In the case of five base-pairs and /0 = 03, the transmission T of the structure exhibits weakly split groups
of transmission resonances in each mini-band due to the
inter-base-pair tunneling [Fig. 6(e)]. With five base-pairs,
RESEARCH ARTICLE
Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules
shown in Figure 7(d), where pronounced oscillatory behavior as a function of flux variation is observed in the two
transmission mini-bands centered within 72 < E < 80
and 87 < E < 94. We also plot the transmission versus flux for two different hydrogen bonds, hi = 05 and
hi = 09 with a fixed E = 75 in Figures 7(e) and (f),
respectively. In both cases (five base-pairs with 6 loops),
the periodicity increases to 60 . For hi = 09, we observe
a series of Fano-like resonance (a pair combination of a
full transmission and a full reflection) in the transmission
as a function of the modulated magnetic flux threading the
DNA molecule. This indicates that careful fine-tuning of
the magnetic flux allows for selective switching application in molecular electronic devices. It should be noted
from Figure 7 that the periodicity of the AB oscillations is
directly proportional to the number of loops in the DNA
molecules. In other word, one base-pair with 2 loops has
a periodicity of 20 and the case with five base-pairs and
6 loops has a periodicity of 60 in the transmission versus
flux. In general, the periodicity of AB oscillations in the
transmission is (q + 10 , where q is the number of base
pair in DNA. Therefore, the length of DNA molecule plays
a crucial role in determining the periodicity and patterns
of AB oscillations in the transmission.
Joe et al.
pair in DNA. By examining the transmission resonance
with a constant magnetic flux in the case of a single basepair system, we demonstrate that the transmission zero
leaves the real-energy axis and moves up or down into the
complex-energy plane for values of the magnetic flux not
equal to an integer multiple of the flux quantum.
Acknowledgment: One of the authors (Y. S. Joe)
acknowledges support from both the International Scholar
Program at Kyung Hee University and the Korea Research
Foundation and Korean Federation of Science and Technology Societies Grant, funded by the Korean Government
(MOEHRD, Basic Research Promotion Fund).
References and Notes
1. D. D. Eley and D. I. Spivey, Trans. Faraday Soc. 58, 441 (1962).
2. H. Tabata, L.-T. Cai, J.-H. Gu, S. Tanaka, Y. Otsuka, Y. Sacho,
M. Taniguchi, and T. Kawai, Synth. Metals 133, 469 (2003).
3. H.-A. Wagenknecht, Chemie in Unserer Zeit 36, 318 (2002).
4. A. Csaki, G. Maubach, D. Born, J. Reichert, and W. Fritzsche, Single
Mol. 3, 275 (2002).
5. G. Cuniberti, L. Craco, D. Porath, and C. Dekker, Phys. Rev. B
65, 241314 (2002).
6. P. Carpena, P. Bernaola-Galvan, P. Ch. Ivanov, and H. E. Stanley,
Nature London 418, 955 (2002).
7. H. Wang, J. P. Lewis, and O. F. Sankey, Phys. Rev. Lett. 93, 016401
(2004).
4. CONCLUSIONS
8. Ch.
Walch,
and M. P. Anantram, Phys. Rev. B
Delivered by Publishing Technology
to: Adessi,
KyungS.Hee
University
67,
081405(R)
(2003).
In summary, we have investigated
the
temperature
and
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Received: 12 September 2012. Accepted: 11 January 2013.
3896
J. Nanosci. Nanotechnol. 13, 3889–3896, 2013