Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules in a Two-Dimensional Four-Channel System

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1 Copyright 2013 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Nanoscience and Nanotechnology Vol. 13, , 2013 Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules in a Two-Dimensional Four-Channel System Yong S. Joe 1 3, Sun H. Lee 2, Eric R. Hedin 3, and Young D. Kim 1 1 Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul , 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 plane. We also Delivered point out by thatpublishing the hydrogentechnology bonds between to: the Kyung base Hee pair with University flux variations play a role to determine the IP: periodicity of AB oscillations On: Mon, in 06 the May transmission :13:48 Copyright American Scientific Publishers 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. devoted to this topic using various models and techniques. For instance, one-dimensional (1D) and two-dimensional (2D) tight-binding (TB) models 5 6 and density-functional methods 7 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 J. Nanosci. Nanotechnol. 2013, Vol. 13, No /2013/13/3889/008 doi: /jnn

2 Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules Joeetal. 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 randomizes every hopping integral in the DNA molecule, such through a 2D four-channel DNA model. Circles and hexagons denote Fig. 1. A short poly(g)-poly(c) chess model for electronic transport as intra-backbone couplings and the coupling between the nucleobases with onsite potential energies x i = 7 75 ev (i = 1 5, guanine base-pairs and backbones. Furthermore, the effects of an base), i = 8 87 ev (i = 6 10, cytosine base), = 8 5 ev (back- bone), and external magnetic field in this system should be considered to further examine general features of charge transport 0 = 7 75 ev (metallic leads). Lines denote various hopping amplitudes: t 0 = 1 ev (intra-lead coupling), t L1 2 = t R1 2 = 0 3 ev (coupling between the leads and the end bases), t i i+1 T i i+1 = 0 2 ev (coupling between the nearest neighbor bases), t = 0 3 ev (coupling between through DNA for better understanding of environmental parameters. backbone and DNA base pairs), h i (hydrogen bonds), and B a (intrabackbone In this article, we consider a 2D, four-channel DNA coupling). model, which is more representative of the actual DNA molecule, with inhomogeneous hopping strengths between and the yellow circles are the sites of the leads. DNA base base pair and backbone sites, the hydrogen bonds between pairs have an energy given by the ionization potentials of base-pairs, and the intra-coupling along the backbone. respective bases, taken as G = 7 75 ev and C = 8 87 ev. In this system, we study temperature-dependence of the These are interconnected and linked to the backbone, charge transport properties. Since temperature causes thermal leads, and nearest-neighbor nucleotides by stacking fluctuations and other structural changes of the DNA, interaction, and hydrogen bonds. Every line between sites we incorporate this effect into the TB model Hamiltonian denotes coupling with a specified hopping amplitude. through the hopping integrals Delivered and examine by Publishing the transmission resonances, the localization IP: length, current voltage On: Mon, can 06 be May written 2013 as10:13:48 Technology The to: TB Kyung Hamiltonian Hee University in a 2D four-channel chess model characteristics, and the differential Copyright conductanceamerican at vari- Scientific Publishers H Tot = H Lead + H DNA + H Lead-DNA (1) ous temperatures. In addition, we investigate the electronic properties of a short poly(g)-poly(c) DNA molecule in the presence of an external magnetic field. A magnetic field with flux density penetrating the center of the 2D DNA structure induces an Aharonov-Bohm (AB) phase difference between the electron wave functions of the upper and lower DNA strands and produces AB oscillations in the transmission due to quantum interference effects. It is shown that the periodicity of the AB oscillations is directly proportional to the number of loops in the DNA molecules. 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, Here, the Hamiltonian for a short poly(g)-poly(c) DNA molecule is described by H DNA = i c i c i + j d i d i + a i a i + b i b i i j t c i a i + t d i b i + h i c i d + h c i t i i+1 c i c i+1 + T i i+1 d i d i+1 i + B a a i a i+1 + B a b i b i+1 + h c (2) where c i c i, d i d i, a i a i, and b i b i are the creation (annihilation) operators at the i-th G/C base and the i-th upper and lower backbones, and i j is the onsite potential energy of DNA G(C) base and is backbone onsite energy. The couplings, t i i+1 T i 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 B a and each base-pair is coupled by the hydrogen bonds, h i. The DNA molecule is coupled to two semi-infinite metallic leads by the tunneling Hamiltonian H Leads-DNA = t L1 l 0 c 1 t L2 l 0 d 1 t R1 l 1 c N t R2 l 1 d N + h c (3) 3890 J. Nanosci. Nanotechnol. 13, , 2013

3 Joeetal. Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules where t L1 2 t R1 2 are the contact hopping strengths between the left (right) lead and the end DNA bases, and l i l i is the creation (annihilation) operator at the i-th site of the leads. The leads themselves are modeled by another TB Hamiltonian as H Leads = 0 l i l i t 0 l i l i+1 + h c (4) t t cos i i+1, and h i h i cos i i+1. Using cos i i /2 1 k B T / 2I 2 i, we can now form the final random hopping integrals as t T i i+1 t T i i+1 1 k B T/2I 2 i t t 1 k B T/2I 2 i (5) i i h i h i 1 k B T/2I 2 i where 0 is the lead onsite energy ( 0 = 7 75 ev) and t 0 is the intra-lead hopping amplitude. In our numerical where i is a random fluctuation factor. We note here that calculations, we use re-scaled parameters and the electron the on-site energy fluctuations, which can be absorbed into energy E, all of which are normalized with respect to the the static energy disorder, are not taken into account. hopping integral of the leads, taken as t 0 = 1eV. Figure 2 shows a contour plot of the transmission The TB approximation to the Schrödinger equation as a function of both electron energy and temperature for a system, depicted in Figure 1, can be written as and two plots of the transmission coefficient as a function of electron energy at T = 0 K and T = 300 K. V n m m + n n = E n. Here, the sum runs over the nearest neighbors of n, E is the electron energy, and n is Four well-developed mini-bands with five peaks each are the site energy. The parameters V n m are overlap integrals merging together in Figure 2(b) due to the existence of (or coupling parameters) involving the overlap of the single intra-coupling along the backbones, the inclusion of the site, atomic-like wave functions from sites m and n with the hydrogen bonds between the base pairs, and the coupling single-site potential of site n. The electron energy window between bases and backbone sites. As the temperature is is 5 75 E 9 75, as set by the TB dispersion relation (E = 2t 0 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 Delivered energy, E. by The Publishing desired transmission coefficient and the corresponding IP: conductance On: aremon, 06 May :13:48 Technology to: Kyung Hee University obtained by taking the square of thecopyright transmission American amplitude, T = t E 2, and G = 2e 2 /h T Scientific Publishers respectively. 3. RESULTS AND DISCUSSION 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, i i+1 2 =k BT/I 2, where I 2 /k B = 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 Then, the temperature-dependent hopping integrals can be obtained as t T i i+1 t T i i+1 cos i i+1, 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: h i = 0 5 ev,b a = 0 2 ev, and random factors i = J. Nanosci. Nanotechnol. 13, ,

4 Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules Joeetal. increased, thermal fluctuations manifesting in the random T exp L/, where L is the total length of the system. hopping amplitudes destroy the phase coherence of the Notice that the magnitude of the localization length electrons and reduce quantum interference. In Figure 2(c), at T = 0 K is approximately 10 times larger than that at the magnitude of the envelopes in the transmission spectrum, T = 300 K. This clearly indicates that thermal structural which initially have unit transmission, become sup- fluctuations localize the electronic wave functions, result- pressed and smear out below unity due to the decrease ing in a temperature-dependent localization length. in the number of transmitting states, while the resonance With the knowledge of the transmission T E, we positions are shifted due to the phase changes of the can evaluate the current voltage (I V ) characteristics by electrons. applying the standard formalism based on the scattering A DNA double helix with disoriented base-pairs due to theory of transport, the thermal fluctuations can be viewed as a 2D disordered system. In this system, the disorder leads to electronic I = 2e de T E f localization. Hence, the thermal structural fluctuations will h L E f R E (6) considerably limit electron transport through DNA and Here, f L/R E = 1/ e E L/R /k B T + 1 is the Fermi distribution make electron wave functions more localized. To address function, where k B 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 = V sd. Even if inelastic electron phonon scattering inversely related to the Lyapunov coefficient N, which 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 = ln T E / 2N and N is the number of the broadening of the Fermi function. The I V characteristics base-pairs The asymptotic behavior of the localization are shown in Figure 4 for two different temperatures length indicates that thedelivered thermal fluctuations by Publishing can partially Technology T = to: 0 K Kyung (solid Hee line) University and T = 300 K (dotted line). The destroy coherent charge transport IP: and reduce theon: mean Mon, nonlinear 06 May I V 2013 curves 10:13:48 exhibit a current gap at low applied transmission coefficient. In other words, Copyright high temperature American Scientific bias, andpublishers the voltage threshold for current onset for both leads to the disorder of the system and a reduction of the localization length and consequently a reduction of the electron conductance, according to the relationship, temperatures is about the same (V sd = 3 2 volts). This indicates that the thermal structural disorder does not affect the voltage gap in the I V characteristics. When V sd > 3 2 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. 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, , 2013

5 Joeetal. 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 Magnetic Flux Effects 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 t T i i+1 t T i i+1 e ±i h i h i e ±i and t t e ±i (7) 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 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 Delivered by Publishing Technology to: Kyung Hee University IP: On: Mon, 06 May :13:48 Copyright American Scientific Publishers 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 (h i = 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, ,

6 Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules Joeetal. 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 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 Delivered by Publishing Technology to: Kyung Hee University IP: On: Mon, 06 May :13:48 Copyright American Scientific Publishers Fig. 6. Transmission resonances as a function of electron energy: (a) / 0 = 1, (c) / 0 = 0 3 for one base-pair, and (e) / 0 = 0 3 for five base-pairs. Contour plots of the transmission in the complex-energy plane: (b) / 0 = 1, (d) / 0 = 0 3 for one base-pair, and (f) / 0 = 0 3 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) J. Nanosci. Nanotechnol. 13, , 2013

7 Joeetal. Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules (or = l 0, where l = ), two distinct Breit- Wigner (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 = 0 3, the transmission minimum at E 8.3 is slightly shifted to higher energy, E 8.4, and no longer reaches to zero [T min E = 0 2 in Fig. 6(c)]; the two peak positions of the BW resonances remain the same, however. In other words, the transmission zero [Re E = 0 and Im E = 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 [Re E = 0 and Im E = 0 8 for / 0 = 0 3 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 / In the case of five base-pairs and / 0 = 0 3, 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, 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 h i 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 h i = 0 5 and E = 7 5 is displayed in Figure 7(b) showing periodic AB oscillations with 2 0 periodicity. A contour plot of T as a function of E and / 0 for five base-pairs with h i = 0 5is Delivered by Publishing Technology to: Kyung Hee University IP: On: Mon, 06 May :13:48 Copyright American Scientific Publishers 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 h i = 0 5 and E = 7 5. 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) h i = 0 5 and (f) h i = 0 9 with fixed E = 7 5. The periodicity of AB oscillations in terms of 0 is the same as the number of loops through the DNA. J. Nanosci. Nanotechnol. 13, ,

8 Temperature and Magnetic Field Effects on Electron Transport Through DNA Molecules Joeetal. 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 7 2 <E<8 0 and 8 7 <E<9 4. We also plot the transmission versus flux for two different hydrogen bonds, h i = 0 5 and h i = 0 9 with a fixed E = 7 5 in Figures 7(e) and (f), respectively. In both cases (five base-pairs with 6 loops), the periodicity increases to 6 0.Forh i = 0 9, 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 2 0 and the case with five base-pairs and 6 loops has a periodicity of 6 0 in the transmission versus flux. In general, the periodicity of AB oscillations in the transmission is (q + 1 0, 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. 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, (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, (2004). 8. Ch. Adessi, S. Walch, and M. P. Anantram, Phys. Rev. B 4. CONCLUSIONS Delivered by Publishing Technology to: Kyung Hee University In summary, we have investigated IP: the temperature On: and Mon, 0667, May (R) 2013 (2003). 10:13:48 magnetic field dependence of the transport Copyright behavior American of a Scientific Publishers short DNA molecule in a 2D four-channel DNA model, using a TB Hamiltonian. First, the structural disorder and fluctuations induced by the variation of temperature are incorporated into the random variation of hopping strengths. Since the random hopping amplitudes destroy phase coherence of the electrons and reduce quantum interference, the transmission resonances are smeared out and suppressed below unity. This structural disorder of the DNA molecule leads to a reduction of the localization length due to the decrease in the overlap of the electronic wave functions on adjacent sites, and changes the linear behavior of the current voltage characteristics to a steplike behavior of the current after the threshold voltage. Second, the presence of magnetic flux through the DNA molecule induces a phase shift between the electron waves of the upper and lower DNA strands and produces AB oscillations in the transmission. In the absence of hydrogen bonds, variation of the magnetic field flux density, which is incorporated into hopping integrals as a phase factor, produces AB oscillations in the transmission whose periodicity is the elementary flux quantum, 0, regardless of the length of DNA molecule. In the presence of hydrogen bonds, on the other hand, the periodicity of the AB oscillations is (q + 1 0, where q is the number of base 9. E. Artacho, M. Machado, D. Sanchez-Portal, P. Ordejon, and J. M. Soler, Molecular Phys. 101, 1587 (2003). 10. J. X. Zhong, Nanotech. 2, 105 (2003). 11. D. Klotsa, R. A. Romer, and M. S. Turner, Biophys. J. 89, 2187 (2005). 12. K. Iguchi, J. Phys. Soc. Jpn. 70, 593 (2001). 13. J. F. Feng, X. S. Wu, S. J. Xiong, and S. S. Jiang, Solid State Communications 139, 452 (2006). 14. W. 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Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, New York, 2005). 29. M. Hjort and S. Stafstrom, Phys. Rev. Lett. 87, (2001). Received: 12 September Accepted: 11 January J. Nanosci. Nanotechnol. 13, , 2013