Influence of vibrational modes on the electronic properties of DNA

We investigate the electron (hole) transport through short double-stranded DNA wires in which the electrons are strongly coupled to the specific vibrational modes (vibrons) of the DNA. We analyze the problem starting from a tight-binding model of DNA, with parameters derived from ab initio calculations, and describe the dissipative transport by equation-of-motion techniques. For homogeneous DNA sequences like poly-(guanine-cytosine), we find the transport to be quasiballistic with an effective density of states which is modified by the electron-vibron coupling. At low temperatures, the linear conductance is strongly enhanced, but above the “semiconducting” gap it is much less affected. In contrast, for inhomogeneous (“natural”) sequences, almost all states are strongly localized and transport is dominated by dissipative processes. In this case, a nonlocal electron-vibron coupling influences the conductance in a qualitative and sequence-dependent way.

Figure 1

(Color online) Density of states and transmission of poly-(GC) with 26 base pairs and the following parameters: Base pair on-site energy ${ϵ}_G=-0.35\mathrm{eV}$, Fermi energy $E_F=0\mathrm{eV}$, vibrational energy $\hslash {\omega }_0=0.01\mathrm{eV}$, cutoff $\hslash {\omega }_c=0.03\mathrm{eV}$, linewidth $\Gamma =0.1\mathrm{eV}$, and room temperature $k_{B}T=0.025\mathrm{eV}$. The strong asymmetry of the curves with respect to the band center is a consequence of the nonlocal electron-vibron coupling ${\lambda }_1$.

Figure 2

(Color online) Density of states of poly-(GC) with 26 base pairs and parameters as in Fig. 1. The solid line shows the purely electronic resonances. Inclusion of only a local electron-vibron coupling ${\lambda }_0$ reduces the weight at the original electronic resonance in favor of “vibron satellites” (dashed line). The addition of a nonlocal electron-vibron coupling ${\lambda }_1$ (dash-dotted line) introduces shifts of the resonance peaks “outside” (changing the effective bandwidth) as well as a strong asymmetry in the height of the resonances.

Figure 3

(Color online) Zero-bias conductance and $I\text{−}V$ characteristics for poly-(GC) with 26 base pairs and parameters as in Fig. 1. The inclusion of vibrons increases the zero-bias conductance at low temperatures ($k_{B}T$ roughly below $\hslash {\omega }_0$) by several orders of magnitude. At room temperature, however, the zero-bias conductance is slightly reduced. Inset: The $I\text{−}V$ characteristics show a “semiconducting” behavior at room temperature. The nonlocal electron-vibron coupling ${\lambda }_1$ increases both the nonlinear conductance in the gap and around the threshold, leading to a slightly enhanced current.

Figure 4

(Color online) Density of states of an inhomogeneous DNA with sequence ($5^{\prime }$-CAT TAA TGC TAT GCA GAA AAT CTT AG-$3^{\prime }$). We chose the following parameters: GC on-site energy ${ϵ}_G=-0.35\mathrm{eV}$, AT on-site energy ${ϵ}_A=-0.86\mathrm{eV}$, Fermi energy $E_F=0\mathrm{eV}$, vibron energy $\hslash {\omega }_0=0.01\mathrm{eV}$, cutoff $\hslash {\omega }_c=0.03\mathrm{eV}$, linewidth $\Gamma =0.1\mathrm{eV}$, and room temperature $k_{B}T=0.025\mathrm{eV}$. The density of states is fragmented into “bunches” of strongly localized states with very low elastic transmission.

Figure 5

(Color online) $I\text{−}V$ characteristics and differential conductance for an inhomogeneous DNA with sequence ($5^{\prime }$-CAT TAA TGC TAT GCA GAA AAT CTT AG-$3^{\prime }$). Parameters are the same as in Fig. 4. The inclusion of a nonlocal electron-vibron coupling ${\lambda }_1$ leads to changes in the conductance, depending on the nature of the relevant state.

Figure 6

Current at a bias of $V_b=1\mathrm{V}$ as a function of electrode-DNA coupling $\Gamma$ for the inhomogeneous DNA with sequence ($5^{\prime }$-CAT TAA TGC TAT GCA GAA AAT CTT AG-$3^{\prime }$). Other parameters are the same as in Fig. 4. The current is a nonmonotonous function of $\Gamma$ and peaks around a value ${\Gamma }_{\mathit{max}}$, where the imaginary part of the vibron self-energy ${\Sigma }_{\mathrm{vib}}$ is of the same size as $\Gamma$.