ac conductivity in a DNA charge transport model

We present the ac response of a DNA charge transport model, where the charge in the $\pi$-stack interacts with the base-pair opening dynamics of the double strand. The calculated ac conductivity exhibits prominent peaks at polaron normal modes with electronic character, while weaker response appears at lower frequencies in the vibrational part of the polaron normal mode spectrum. Examples of the former, strong peaks, show redshifts as the amplitude of the ac field increases.

Figure 1

(Color online) (a) Current density $J\left(t\right)$ in arbitrary units as a function of time for $\chi =0.6\mathrm{eV}∕\mathrm{\AA }$, $E_0=2\times {10}^{-6}\mathrm{V}∕\mathrm{\AA }$, and driving frequency $\omega =27\mathrm{THz}$. Continuous line (left part) corresponds to the transient behavior and dashed line (right part) to the steady state. (b) and (c) Fourier transforms of the transient and the steady state, respectively. The vertical dotted lines in (b) and (c) show positions of the polaronic normal mode frequencies. The arrow in the $x$ axis in (c) indicates the frequency of the electric field applied.

Figure 2

(Color online) (a) Real part ${\sigma }_R$ and (b) imaginary part ${\sigma }_I$ of the conductivity as a function of frequency, for $\chi =0.6\mathrm{eV}∕\mathrm{\AA }$ and $E_0=2\times {10}^{-8}\mathrm{V}∕\mathrm{\AA }$. In the insets we plot the real and imaginary parts, respectively, of the conductivity for low frequencies, i.e., in the vibrational part of the spectrum. Vertical dotted lines show the positions of normal mode frequencies of the polaron, while the shadowed stripe in the insets represents the phononic band.The dotted horizontal line in (b) indicates the zero value.

Figure 3

(Color online) Real part ${\sigma }_R$ of the conductivity as a function of frequency for (a) $\chi =1.4\mathrm{eV}∕\mathrm{\AA }$ and (b) $\chi =2\mathrm{eV}∕\mathrm{\AA }$, in the vibrational part of the spectrum. The amplitude of the ac field is $E_0=2\times {10}^{-8}\mathrm{V}∕\mathrm{\AA }$. Vertical dotted lines show the positions of discrete polaronic normal mode frequencies, while the shadowed stripe represents the phononic band of the polaronic normal mode spectrum.

Figure 4

(Color online) Variation of the frequency of the ac response with the amplitude $E_0$ of the ac field (8). (a) Redshift of the most prominent peak of $\sigma \left(\omega \right)$ for $\chi =0.6\mathrm{eV}∕\mathrm{\AA }$. (b) Absence of redshift for the weaker feature at the vibrational regime for $\chi =1.4\mathrm{eV}∕\mathrm{\AA }$. The errors $\delta \omega$ correspond to the frequency increments used in the calculations. The dotted lines are guides to the eye.