Abstract—Conductivity properties of DNA molecule is investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model. This model is a tight-binding linear nanoscale chain. We have tried to study the electrical current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram. Keywords—Charge transfer in DNA, Chaos theory, Molecular electronics, Negative Differential resistance. I. INTRODUCTION N the recent decades, DNA has increasingly interested in the potential technological applications that not directly related to the coding for functional proteins that is the expressed in form of genetic information. One of the most interesting applications of DNA is related to the construction of nanostructures of high complexity, design of functional nanostructures in nanoelectronical devices, nanosensors and nanocercuits [1]-[3]. In this field, DNA is of fundamental interest to the development of DNA-based molecular technologies, as it possesses ideal structural and molecular recognition properties for use in self-assembling nanodevices with a definite molecular architecture. Also, the robust, one- dimensional flexible structure of DNA can be used to design electronic devices, serving as a wire, transistor switch, or rectifier depending on its electronic properties. In order to understand the mechanism of the charge transport along DNA sequences, numerous studies have been carried out [4]-[6]. In this regard, conductivity properties of DNA molecule could be investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model [7]. In SSH model, the non-diagonal matrix elements dependence on inter-site displacements is considered. In this approach, the coupling between the charge and lattice deformation is along the helix. This model is a tight-binding linear nanoscale chain established to describe conductivity phenomena in doped polyethylene. It is based on the assumption of a classical harmonic interaction between sites, which is linearly coupled to a tight-binding Hamiltonian. In this work, the Hamiltonian and corresponding motion equations are nonlinear and have high sensitivity to initial conditions. Then, we have tried to move toward the nonlinear dynamics and phase space analysis [8]. Nonlinear dynamics and chaos theory, regardless of any approximation, could open S. Behnia is with the Urmia University of Technology, Oroumieh, Iran, (Fax: +98-4433554184; email: s.behnia@sci.uut.ac.ir) S. Fathizadeh is with the University of Technology, Oroumieh, Iran, (e- mail: s.fathizadeh@sci.uut.ac.ir). new horizons to understand the conductivity mechanism in DNA. For a detailed study, we have tried to study the current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram. II. ANALYSIS OF THE MODEL We have considered DNA charge transfer model via a single, simple, flexible and chemically specific model Hamiltonian. As the isolated bases in DNA are planar and the inter-base tight-binding matrix elements are small, the separation approximately holds and theories of the chemical bond appropriate to systems can be applied. In the field of conductivity phenomena in systems, the SSH model has shown a remarkable track of success for conducting polymers such as polyacetylene. Then, the DNA Hamiltonian in the presence of external field has the following form: . field ph e ph SSH H H H H H + + + = − (1) The SSH model is used to simulate the electronic and lattice parts of system as following [9]: ]. [ )] ( [ ) ( 2 2 1 1 1 1 0 0 2 1 2 + + + + + + + + − − − + − + = ∑ ∑ ∑ ∑ n n n n n n n n n n n n n s n n SSH c c c c x x t c c x x k x m H α ε  (2) where m is the base pair mass and n x is the position of n-th base-pair. The energy 0 ε represents the onsite energy, + n c and n c are creation and annihilation operators of an electron. 0 t denotes the hopping integral, α is the electron-lattice coupling constant and s k is the harmonic potential constant. The next two terms in Hamiltonian represent the vibrational mode of external phonon bath at frequency 0 ω and the local external ph e − interaction term, respectively. ∑ ∑ + + = + + + + − n n n n n n n n ph e ph b b c c b b H H . ) ( 0 0 γ ω (3) where + n b and n b are creation and annihilation operators of an phonon at the site n and 0 γ is the ph e − coupling constant. The external electrical field along DNA is characterized from ∑ + = n n n field c ndc eE H . (4) DNA Nanowires: A Charge Transfer Approach S. Behnia, S. Fathizadeh I World Academy of Science, Engineering and Technology International Journal of Electronics and Communication Engineering Vol:9, No:6, 2015 623 International Scholarly and Scientific Research & Innovation 9(6) 2015 ISNI:0000000091950263 Open Science Index, Electronics and Communication Engineering Vol:9, No:6, 2015 publications.waset.org/10002253/pdf