Transport of charge in DNA heterostructures

2011 11th IEEE International Conference on Nanotechnology Portland Marriott August 15-18, 2011, Portland, Oregon, USA Transport of charge in DNA heterostructures Jianqing Qi, Md. Golam Rabbani, Suranga Edirisinghe and M. P. Anantram Department of Electrical Engineering, University of Washington, Seattle, WA 98195 Email: [email protected], [email protected] Abstract — We study the transmission and conductance in poly{G}(T)Npoly{G} strand, where G refers to Guanine and T refers to Thymine. We show that T plays a role as a barrier and the transmission decreases exponentially with the increasing number of Ts. We also investigate the transmission and conductance through superlattices poly{GGTT} and poly{GT}. Minibands are observed in these structures. The effect of coupling between DNA molecule and metal contacts is also explored. (iii) Conformation / distance between base pairs. It has reached a consensus that π-π stacking is the dominant element in determining the conducting behaviour of DNA. Theoretical calculations have confirmed that changes in the distance and the angle between consecutive bases can cause variability in conduction channels by influencing the hybridization between the π orbitals of adjacent bases [11]. In this paper, we consider dry single-stranded DNA heterostructures of B-configuration. The purpose is to study charge transport process in DNA by modeling the conduction in barriers and superlattices constructed of G and T bases and investigate the possible effect of the DNA molecule-metal contact coupling. The paper is organized as follows: we first describe the model and method in Section II. In this part, the Green’s function formalism is briefly reviewed. Then, we present and discuss the transmission and conductance results through poly{G}(T)Npoly{G}, poly{GT} and poly{GGTT} strands in Section III. We also study the influence of the coupling between a DNA molecule and metal contacts using a simplified model. The moleculemetal contact coupling is treated as a parameter in this study. Finally, we make some conclusions in Section IV. Index Terms – DNA, charge transport. I. INTRODUCTION The intrinsic electrical conductivity of DNA continues to be of immense interest in both biochemistry [1] and electrical engineering [2, 3]. The interest in biochemistry stems from oxidative damage of DNA while the potential to build devices and electrically sequence biomolecules poses interesting questions to electrical engineers. However, the mechanism of charge transport in DNA is still an unresolved problem. Experimental measurements of conduction in DNA cover all possible results. Researchers have found that DNA can either be an insulator [4], a semiconductor [5], an Ohmic conductor [6] or even an induced superconductor [7]. Theoretical efforts have also been devoted to this area [811]. Many factors contribute to the intrinsic conductivity of charge transport in DNA, making the study in this field a challenging problem. Mainly speaking, the intrinsic conductivity of charge through DNA is determined by: II. MODEL AND METHOD In this computational work, we generate the coordinates of atoms in B-DNA strands with nucleic acid builder (NAB) software package. Since the HOMO and LUMO levels of a nucleotide primarily lie on the bases, it is believed that the low bias transport in native DNA occurs along the base pairs and the backbone does not play a role apart from providing mechanical stability to the structure. Hence, we replace the backbones of the structures generated by NAB with hydrogen atoms. The Hamiltonian and overlap matrices are calculated with GAUSSIAN09, where the B3LYP exchangecorrelation functional and 6-31 G basis sets have been used. We consider only the interaction between nearest-neighbor bases and a block tridiagonal matrix representation of the Hamiltonian is obtained [9, 14, 15]. (i) Environment. For wet DNA the role of water molecules is critical in influencing the structure and hence the electronic properties. A-DNA usually has five to ten water molecules per base, while for B-DNA more than 13 water molecules per base are preferred [12]. At different hydration levels, different local densities of states (DOS) are obtained [8]. Besides, because the backbone of DNA is negatively charged in phosphate groups, it is believed that a DNA molecule is surrounded by cations such as Na+, K+, Mg+ and H3O+. From previous study, variations in cations’ type [9] and position [8] can bring different highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels. There have been experimental efforts to engineer the environment of DNA to mitigate its role on transport by chemically modifying the backbone [13]. The transmission through the molecule is computed using the Green’s function approach [16]. In this approach, we calculate the retarded Green’s function, defined by Gr (E)  (ii) Sequence. It has been shown that each of the four bases in DNA, Guanine (G), Adenine (A), Cytosine (C) and Thymine (T), has a different ionization potential (IP) [10]. As a result, the intrinsic conductance depends on the sequence. 978-1-4577-1515-0/11/$26.00 ©2011 IEEE 1 ES  H   ( E )   rR ( E ) r L (1) for each energy point E. Here H is the device Hamiltonian matrix, S the overlap matrix and ΣrL(R) the lead (contact) selfenergy (L (R) stands for left (right)). The self-energies represent connection of the device (here, one unit cell of 487 We show transmission through poly{G}(T)Npoly{G} at the energy points around the HOMO levels in terms of different numbers of Ts in Fig. 1. We find the width of the conduction channel around HOMO is about 370meV (inset plot) which agrees with our earlier work. We plot the transmission versus N at energy E=-5.44eV (red stars and blue curve). We see that the values of transmission decrease exponentially with the increasing number of Ts. Thus we conclude T to be a large barrier. From the fitting equation at the energy point E=-5.44eV, log10(Transmission)=-1.86N0.24, we find that the addition of each T can cause a reduction in transmission by approximately 72 times. This can be understood by considering the difference in HOMO levels of G and T. In our calculation, the HOMO level of an isolated G base without the backbone is about -5.69eV, while the HOMO level of an isolated T base without the backbone is about -6.63eV. This indicates that for hole transport T represents a barrier. As the valence band offset between G and T is approximately 1eV (comparison of IPs leads to a similar conclusion), we test the possibility of modeling the transmission through the poly{G}(T)Npoly{G} by a simple square potential barrier, poly{G}(g)Npoly{G}, where g refers to the modified G whose on-site potential has been decreased by 1eV. The resulting transmission is significantly higher and the agreement with the square potential barrier is poor (magenta circles and green curve in Fig. 1). DNA structure) to the leads, which are assumed to be semiinfinite in extent and are repetitions of the same unit cell (for each lead). The lead unit cell can be the same as the device DNA unit cell, or it can be unit cell of a metal, such as gold. In this work, we first focus on the first case and then present some results for the latter case by roughly approximating the connection between the DNA molecule and the metal contacts as a constant value. The self-energies are calculated using the following equation rL ( R ) ( E )  H D L ( R ) g Lr ( R ) ( E ) H L ( R ) D (2) is the retarded surface Green’s function of the where left (right) lead, HD-L(R) is the coupling between the device and the left (right) lead and HL(R)-D=H+D-L(R). We use an iterative approach to calculate grL(R). Details of this calculation can be found in [16]. Next, we calculated the lead broadening functions given by grL(R)  L ( R ) ( E )  2 Im  rL ( R ) ( E )  , (3) where Im(x) represents the imaginary part of x. For the calculation of Gr, we use the fast recursive Green’s function (RGF) algorithm and calculate only the diagonal, first upper and first lower diagonal blocks of Gr, which are sufficient for calculating transmission, conductance and density of states (DOS), the quantities that we are interested in. The transmission T(E) through the DNA molecule is found from T ( E )  tr   L ( E )G r ( E ) R ( E )G a ( E )  (4) where the advanced Green’s function Ga is given by Ga=Gr+. The linear response conductance G(Ef) is given by, G( E f )  f ( E  E f ) 2e2 dET ( E )  E h Once the magnitude of T as a barrier was ascertained, we considered the transmission in the following superlattices: (i) poly{GT} and (ii) poly{GGTT}, with the aim of observing minibands in these structures. Minibands are expected because G serves as a quantum dot for holes while T is a barrier connecting the quantum dots, akin to that seen in semiconductor superlattices [17]. In Fig. 2, we present the transmission through poly{GT} at the energy close to the HOMO level. A miniband with a width of approximately 40meV is predicted. Compared to the width of 370meV in poly{G}, the role of T as a barrier for hole transport is very obvious. It is worth noting that the four dips in the blue solid curve are not real gaps. We have confirmed that the occurrence of these dips is due to the variations in the eigenvalues of the Hamiltonian for the bases. In the ideal situation, the eigenvalues for all G bases and all T bases should be identical. However, when we construct the DNA structures, small numerical errors may exist in parameters such as the distance and the angle between adjacent bases, which may cause variations in the eigenvalues of bases. By constructing the structure with Hamiltonians of identical eigenvalues, the dips will disappear. We also show the DOS for poly{GT} in Fig. 3. For clarity, we only show the DOS at the first four bases in the molecular device. DOS at other bases provides similar information. DOS indicates the number of states per energy interval at each energy level that can be occupied in various spatial regions. The transmission at a given energy depends on the availability of delocalized state at that energy. The transmission in Fig. 2 corresponds to the DOS in Fig. 3. In Fig. 4, we show the transmission (5) where G0=2e2/h≈77 μS is the conductance quantum, T(E) is the transmission as defined above, f is the Fermi function and Ef is the Fermi level in the contacts. Finally the density of states D(E) is calculated from D( E )    Im G ( E)    1 r (6) where the summation is performed over all the atomic orbitals  in a DNA strand. III. RESULTS Conduction behavior involves either electron transport in conduction bands or hole transport in valence bands. Here we consider the latter situation. We first model the transmission through a barrier for holes constructed from the sequence poly{G}(T)Npoly{G}, where N is the number of Ts, varying from 0 to 8. We treat the 10 bases in the middle as the device part and construct the two semi-infinite contacts by repeating the 10 bases in a unit cell of G. Then we calculate the surface Green’s function as mentioned above. A similar method is applied to poly{GT} and poly{GGTT}. For poly{GT} and poly{GGTT}, we construct the contact leads by repeating the 10 bases in a unit cell of poly{GT} and the 20 bases in a unit cell of poly{GGTT} (10 G bases and 10 T bases) respectively. 488 through poly{GGTT} at energy points that are close to the HOMO level. In the case of poly{GGTT}, the width of the miniband is only 3µeV, which is about thirteen thousand times smaller than the bandwidth of poly{GT}. This narrow width is rationalized by noting that the transmission through poly{G}TTpoly{G} is 72 times weaker than the transmission through poly{G}Tpoly{G} (Fig. 1). The DOS for poly{GGTT} is also calculated, as shown in Fig. 5. coupling between the molecule and the metal contacts. To get an initial feeling of how the molecule-metal contact coupling influences the transport, we consider a unit cell of poly{GT} connected to two metal contacts and study the transmission at energy around HOMO level by treating the coupling with various strengths, ranging from weak-coupling limit to strong-coupling limit. The transmission results at ΓL=ΓR=10meV, 50meV, 100meV, 300 meV and 500 meV are presented in Fig. 8. We see that when the coupling increases from 10meV to 50meV and then to 100meV, the magnitude of the transmission keeps increasing. When the coupling is increased further, to 300meV and 500meV, the magnitude of the transmission decreases. This is expectable because the transmission is determined by the product of the DOS and the coupling. As the coupling is increasing, DOS in the molecule is broadened. When the coupling is not too strong, the broadening is small; hence the DOS doesn’t change much. As the coupling increases from the weak limit, the transmission increases. However, when the coupling is strong enough, the DOS will broaden significantly and its value is very small, causing a reduction in the transmission. The transmission results under different coupling strengths can be used to compare with the experimental results. We also model the conductance through these sequences. When the size of a conductor is much shorter than the mean free path, the conductance can not be given by the traditional equation in terms of the conductivity, the area and the length of the conductor any more. It has to be calculated by considering the interface effect between the conductor and the contacts. Here we focus on the low bias limit and evaluate the linear response conductance at 300 K. The Fermi level Ef in the contacts together with the molecular energy levels is critical in understanding the flow of charge through the molecule. Experimentally, it is difficult to determine the position of Ef because of the complicated details of the molecule-contact coupling. Here, we explore the conductance when the Fermi level is in the HOMO vicinity. The conductance through poly{G}(T)Npoly{G} at energy points around the HOMO level in terms of the number of Ts is shown in Fig. 6 (inset). Again, we see that with the increasing number of Ts, the conductance keeps decreasing. Similar to the case for transmission in poly{G}(T)Npoly{G}, we also choose an energy point at Ef =-5.44eV and plot the conductance versus the number of Ts. From the fitting equation, we again see that barrier effect of T: with the addition of one T the conductance decreases approximately by 72 times. Experimental results show an exponentially decreasing relation between the conductance through a G-C rich DNA molecule and the number of A-T base pairs [11]. In Fig. 7, We present the conductance versus Fermi energy in the HOMO vicinity through poly{GT} and poly{GGTT}. Compared to the conduction through poly{G} the maximum value for poly{GT} decreases about 3 times, while for poly{GGTT} the conductance we obtain is on the order of 10-5G0, which is reasonable because of the strong barrier effect of T. Finally, we explore the role of the coupling between the molecular device and a metal contact in influencing the transmission. The strength of the coupling between the molecular device and the contacts is important in determining the flow of current. In the previous part, we construct the two contacts with repetitions of the unit cell of the DNA molecule, either with the unit cell being the same as that of the device such as in poly{G}, poly{GT} and poly{GGTT}, or with the unit cell different from the device unit such as in poly{G}(T)Npoly{G} (when N ≠ 0). In both cases, the couplings between the device and the contacts are chosen to be perfect, producing a transmission with the maximum value almost equal to 1. However, in an experiment, usually a molecular device is connected to two metal contacts. Experimentally, it is difficult to control the IV. CONCLUSION We have carried out density functional theory calculation of dry single DNA strands, poly{G}(T)Npoly{G}, poly{GT} and poly{GGTT}. By studying the transmission and conductance through poly{G}(T)Npoly{G}, we confirmed that T is a barrier for hole transport, which has been observed experimentally. The transmission and conductance decrease exponentially when the number of Ts is increasing. By calculating the fitting equation at energy point when E=-5.44eV, we find one more T can cause 72 times reduction in transmission and conductance. For superlattices poly{GT} and poly{GGTT}, we find minibands with width of about 40meV and 3μeV respectively. Compared to the bandwidth in poly{G}, which is around 370meV, the narrow bandwidths in poly{GT} and poly{GGTT} are attributed to the large barrier effect of T. We also investigate the influence of coupling between DNA molecule and the metal contacts. By modeling the transmission through a unit cell of poly{GT} connected to metals contacts at different coupling strengths, we show that when the coupling increases from the weak limit, the magnitude of transmission also increases. When the coupling increases further into the strong limit, the transmission begins to decrease. This is because the transmission is determined by the product of the DOS and the coupling. At small coupling the DOS does not broaden a lot and the coupling dominates, while at strong coupling the value of DOS is very small because of the large broadening and therefore the transmission decreases. ACKNOWLEDGMENT We acknowledge financial support from NSF grant number 1027812. 489 poly{G}(T)Npoly{G}. The width of the conduction channel is about 370meV. With the increasing number of Ts, the magnitude of transmission decreases. From top to bottom, N = 0 (black solid), 1 (red points), 2 (blue solid), 3 (magenta stars), 4 (green x), 5 (yellow circles), 6 (black dots), 7 (cyan plus), 8 (blue dashdot). REFERENCES [1] J. C. Genereux, A. K. Boal and J. K. Barton, “DNA-Mediated Charge Transport in Redox Sensing and Signaling,” J. Am. Chem. Soc., vol. 132, no. 3, pp 891-905, 2010. [2] H. Mehrez and M. P. Anantram, “Interbase electronic coupling for transport through DNA,” Phys. Rev. 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Anantram, “Influence of counter-ion-induced disorder in DNA conduction,” Appl. Phys. Lett., vol. 82, no. 14, pp. 2353, 2003. [10] S. P. Walch, “Model calculations of the electron affinities and ionization potentials of DNA,” Chem. Phys. Lett., vol. 374, pp. 496500, 2003. [11] C. Adessi, S. Walch and M. P. Anantram, “Environment and structure influence on DNA conduction,” Phys. Rev. B, vol. 67, pp. 081405, 2003. [12] R. G. Endres, D. L. Cox and R. R. P. Singh, “Colloquiumμ The quest for high-conductance DNA,” Rev. Mod. Phys., vol. 76, no. 1, 2004. [13] A. K. Mahapatro, K. J. Jeong, G. U. Lee and D. B. Janes, “Sequence specific electronic conduction through polyion-stabilized doublestranded DNA in nanoscale break junctions,” Nanotechnology, vol. 18, no. 19, pp. 195202, 2007. [14] B. Gazdy, M. Seel, and J. Ladik, “The role of self-consistency in quantum-mechanical studies of disordered quasi-one-dimensional systems,” Chem. Phys, vol. 86, pp. 41-48, 1984 [15] Y.-J. Ye and Y. Jiang, “Electronic structures and long-range electron transfer through DNA molecules,” Int. J. Quantum Chem, Vol. 78, pp. 112, 2000. [16] M. P. Anantram, M. S. Lundstrom and D. E. Nikonov, “Modeling of nanoscale devices,” Proceedings of the IEEE, vol 96, No. 9, 2008. [17] C. Weisbuch, B. Vinter, Quantum Semiconductor Structures: Fundamentals and Applications, Academic Press, 1993. Fig. 2 Transmission versus energy for poly{GT}. The width of the conduction channel is about 40meV. The blue solid curve represents the calculated transmission result, while the red dashed curve shows the ideal conduction channel. The four dips in the blue curve are due to the variations in eigenvalues of the Hamiltonian for the bases. The dips will disappear if we construct the structure with Hamiltonians of identical eigenvalues. Fig. 3 DOS for poly{GT} at the first four bases in the molecular deivce. DOS indicates the number of states per energy interval at energy levels that can be occupied. Upper, DOS for the first two G bases in the molecular device; lower, DOS for the first two T bases in the molecular device. Again, for ideal situation, the variations along the miniband will disappear. Fig. 1 Common logarithm of transmission versus N for poly{G}(T)Npoly{G} (red stars) and poly{G}(g)Npoly{G} (magenta circles) when E=-5.44eV. The fitting relation for Ts is log10(Transmission)=-1.86N0.24 (blue line), indicating that with the addition of each T the transmission decreases about 72 times. The fitting relation for modified Gs is log10(Transmission)=-1.69N+0.44 (green line). The poor agreement between the blue line and green line is because of the weak coupling between G and T. Inset, the transmission versus energy (in unit of eV) for Fig. 4 Transmission versus energy for poly{GGTT}. The width of the miniband is only 3 eV because of the strong barrier effect of T. 490 Fig. 8 Transmission versus Fermi energy through poly{GT} when the strength of coupling between DNA molecule and the contact varies from 10meV, 50meV, 100meV, 300meV and 500meV. The magnitude of transmission first increases and then decreases when the strength of the coupling increases from weak limit to strong limit. Fig. 5 DOS for poly{GGTT} at the first eight bases in the molecular device. Upper, DOS for the first four G bases in the molecular deivce; lower, DOS for the first four T bases in the molecular device. Fig. 6 Common logarithm of conductance versus N through poly{G}(T)Npoly{G} when E=-5.44eV (red stars). The fitting relations are log10(Conductance) =-1.86N-0.32 (blue line). Inset, conductance versus Fermi energy (in unit of eV) for poly{G}(T)Npoly{G} at low bias limit. With the increasing number of Ts, the conductance decreases. From top to bottom, N = 0 (black solid), 1 (red points), 2 (blue solid), 3 (magenta stars), 4 (green x), 5 (yellow circles), 6 (black dots), 7 (cyan plus), 8 (blue dashdot). Fig. 7 Conductance versus Fermi energy through poly{GT} (upper) and poly{GGTT} (lower). Compared to poly{G}, the maximum value of conductance in poly{GT} decreases about 3 times, while the magnitude of conductance through poly{GGTT} is only on the order of 10-5G0. The reason is the large barrier effect of T. 491 View publication stats