Nonequilibrium polaron hopping transport through DNA

We study the electronic transport through short DNA chains with various sequences of base pairs between voltage-biased leads. The strong coupling of the charge carriers to local vibrations of the base pairs leads to the formation of polarons, and in the relevant temperature range the transport is accomplished by sequential polaron hopping. We calculate the rates for these processes, extending what is known as the $P\left(E\right)$ theory of single-electron tunneling to the situation with site-specific local oscillators. The nonequilibrium charge rearrangement along the DNA leads to sequence-dependent current thresholds of the “semiconducting” current-voltage characteristics and, except for symmetric sequences, to rectifying behavior. The current is thermally activated with activation energy approaching, for voltages above the threshold, the bulk value (polaron shift or reorganization energy). Our results are consistent with some recent experiments [K. H. Yoo et al., Phys. Rev. Lett. 87, 198102 (2001)].

Figure 1

(Color online) $I\text{−}V$ characteristics for two DNA strands with sequences $5^{\prime }\text{−}\mathrm{GGGGGGGG}\text{−}{3}^{\prime }$ (dashed-dotted line) and $5^{\prime }\text{−}\mathrm{GAAAAAAG}\text{−}{3}^{\prime }$ (solid line) with the following parameters: Base pair on-site energies ${ϵ}_{\mathrm{A}}=-0.26\mathrm{eV}$, ${ϵ}_{\mathrm{G}}=+0.25\mathrm{eV}$, polaron shifts ${\Delta }_{\mathrm{A}}=0.18\mathrm{eV}$ and ${\Delta }_{\mathrm{G}}=0.47\mathrm{eV}$, Fermi energy $E_F=0\mathrm{eV}$, symmetric coupling to leads with linewidths ${\Gamma }_L={\Gamma }_R=0.01\mathrm{eV}$, vibrational energies $\hslash {\omega }_{\mathrm{A}}=11\mathrm{meV}$, $\hslash {\omega }_{\mathrm{G}}=16\mathrm{meV}$, and room temperature $k_{B}T=25\mathrm{meV}$. The inset shows the absolute value of the current on logarithmic scale. The current for the second sequence shows rectification by a factor of $\sim 200$.

Figure 2

(Color online) Differential conductance (logarithmic scale) as a function of applied bias for five different DNA sequences with parameters as in Fig. 1. For the homogeneous sequences, the threshold, i.e., the position of the maximum of the differential conductance, is set by on-site energy of the considered base pairs. For the inhomogeneous sequences, however, the threshold is not determined by the internal energy scales alone. The sequence-dependent thresholds lie in between the limits set by the homogeneous sequences. For some sequences (e.g., $5^{\prime }\text{−}\mathrm{GAAAAAAG}\text{−}{3}^{\prime }$), the peaks are broadened due to renormalized tunneling.

Figure 3

(Color online) $I\text{−}V$ curves for the two sequences $5^{\prime }\text{−}\mathrm{GAAAAAAG}\text{−}{3}^{\prime }$ (solid line) and $5^{\prime }\text{−}\mathrm{GGAAAAGG}\text{−}{3}^{\prime }$ (dashed line) (parameters see Fig. 1). Despite the very similar sequences, the $I\text{−}V$ shows clear differences. The inset shows the local chemical potential $\Phi$ for the last guanine base (at the $3^{\prime }$ end) for both sequences at various bias voltages. Equivalent behavior between local potential and $I\text{−}V$ is visible

Figure 4

(Color online) Local chemical potential $\Phi$ for all base pairs of the DNA strand with sequence $5^{\prime }\text{−}\mathrm{GAAAAAAG}\text{−}{3}^{\prime }$ (black lines) and $5^{\prime }\text{−}\mathrm{GGAAAAGG}\text{−}{3}^{\prime }$ (red lines) at various bias voltages and with parameters as in Fig. 1. The local potential differently drops for the two sequences, implying different conduction properties.

Figure 5

(Color online) Activation energy $E_a$ for polaron hopping of a homogeneous DNA with 15 G-C base pairs as a function of the polaron shift $\Delta$ for voltages $V_b=0.04\mathrm{V}$ (solid line), $V_b=0.55\mathrm{V}$ (dashed line), and $V_b=0.8\mathrm{V}$ (dashed-dotted line). All other parameters as in Fig. 1. For comparison, the dotted line shows the activation energy of polaron hopping conduction in bulk at high temperatures $(E_a=0.5\Delta )$ (Ref. 52).