Transverse tunneling current through guanine traps in DNA

The current-voltage dependence of the transverse tunneling current through the electron or hole traps in DNA is investigated. The hopping of the charge between the sites of the trap and the charge-phonon coupling results in a staircase structure of the $I\text{−}V$ curve. For typical parameters of the DNA molecule, the energy characteristics of a DNA trap can be extracted from the $I\text{−}V$ dependence, viz., for a small gate voltage the phonon frequency, and for a large gate voltage the hopping integral can be found from the positions of the steps in the $I\text{−}V$ curve. Formation of the polaronic state also results in the redistribution of the tunneling current between the different sites of the traps.

Figure 1

Current vs the source-drain voltage shown for two base pairs in the trap $(N_t=2)$ and different values of phonon frequency and hole-phonon interaction strength: (a) $\gamma =0.1$, $\lambda =0.5$; (b) $\gamma =0.1$, $\lambda =1.0$; (c) $\gamma =0.2$, $\lambda =0.5$; (d) $\gamma =0.2$, $\lambda =1.0$. The solid line corresponds to $ϵ=1.3t$ while the dotted line is for $ϵ=2.7t$.

Figure 2

Current vs the source-drain voltage shown for three base pairs in the trap $(N_t=3)$ and $\gamma =0.2$, but for different tunneling points $i_0$ and different values of hole-phonon interaction strength: (a) $i_0=1$: $\lambda =0.5$ and $ϵ=1.7t$ (solid), $ϵ=3.0t$ (dashed), $\lambda =0$ and $ϵ=1.7t$ (dotted); (b) $i_0=2$: $\lambda =0.5$ and $ϵ=1.7t$ (solid), $ϵ=3.0t$ (dashed), and $\lambda =0$, $ϵ=1.7t$ (dotted); (c) $i_0=1$: $\lambda =1$ and $ϵ=1.7t$ (solid), $ϵ=3.0t$ (dashed), (d) $i_0=2$: $\lambda =1$ and $ϵ=1.7t$ (solid), $ϵ=3.0t$ (dashed).

Figure 3

(a) The average number of holes and (b) the average number of phonons for a single hole system in a $GGG$ trap are shown as a function of the base index. Dots and triangles corresponds to hole-phonon interaction strength $\lambda =1.0$ and $0.5\mathrm{eV}$, respectively.