Modeling the electrical conduction in DNA nanowires: Charge transfer and lattice fluctuation theories

An analytical approach is proposed for the investigation of the conductivity properties of DNA. The charge mobility of DNA is studied based on an extended Peyrard-Bishop-Holstein model when the charge carrier is also subjected to an external electrical field. We have obtained the values of some of the system parameters, such as the electron-lattice coupling constant, by using the mean Lyapunov exponent method. On the other hand, the electrical current operator is calculated directly from the lattice operators. Also, we have studied Landauer resistance behavior with respect to the external field, which could serve as the interface between chaos theory tools and electronic concepts. We have examined the effect of two types of electrical fields (dc and ac) and variation of the field frequency on the current flowing through DNA. A study of the current-voltage $\left(I\text{−}V\right)$ characteristic diagram reveals regions with a (quasi-)Ohmic property and other regions with negative differential resistance (NDR). NDR is a phenomenon that has been observed experimentally in DNA at room temperature. We have tried to study the affected agents in charge transfer phenomena in DNA to better design nanostructures.

Figure 1

MLE vs $\chi$ ($b=0.35{\text{A}}^{-1}$).

Figure 2

MLE vs $b$ ($\chi =0.1\mathrm{eV}/\mathrm{A}$).

Figure 3

Constant external field, Landauer resistance vs the electrical field intensity in zero temperature ($\chi =0.1\mathrm{eV}/\mathrm{A},\mathrm{b}=0.35{\text{A}}^{-1}$).

Figure 4

Constant external field, MLE vs field intensity ($\chi =0.1\mathrm{eV}/\mathrm{A},\mathrm{b}=0.35{\text{A}}^{-1}$). The “red circle” and “blue diamond” lines indicate the MLE in the presence and absent of the Hoover effect, respectively.

Figure 5

Constant external field, MLE vs temperature ($E=2\mathrm{mV}/\mathrm{A},\chi =0.1\mathrm{eV}/\mathrm{A},\mathrm{b}=0.35{\text{A}}^{-1}$).

Figure 6

Constant field, current time series in (a) room temperature, (b) threshold of denaturation temperature.

Figure 7

Constant field, $I\text{−}V$ characteristic diagram. The “red circle” lines indicate the q-Ohmic lines with the slope of inverse resistance.

Figure 8

ac field, MLE vs the electrical field frequency ($E=2\mathrm{mV}/\mathrm{A}$).

Figure 9

ac field, $I\text{−}V$ characteristic diagram ($\omega =0.01\text{THz}$). The “red circle” lines indicate the q-Ohmic lines with the slope of inverse resistance.

Figure 10

ac field, $I\text{−}V$ characteristic diagram ($\omega =0.8\text{THz}$). The “red circle” lines indicate the q-Ohmic lines with the slope of inverse resistance.

Figure 11

dc field, $I\text{−}V$ characteristic diagram for different sequences. The “blue circle,” “red square,” and “black triangle” lines indicate the $I\text{−}V$ characteristic for $L60B36$ ($N=60\text{bp}$) and $CH22$ with $N=60$ and $40\text{bp}$, respectively.