Inelastic quantum transport in a ladder model: Implications for DNA conduction and comparison to experiments on suspended DNA oligomers

We investigate quantum transport characteristics of a ladder model, which effectively mimics the topology of a double-stranded DNA molecule. We consider the interaction of tunneling charges with a selected internal vibrational degree of freedom and discuss its influence on the structure of the current-voltage characteristics. Further, molecule-electrode contact effects are shown to dramatically affect the orders of magnitude of the current. Recent electrical transport measurements on suspended DNA oligomers with a complex base-pair sequence, revealing strikingly high currents, are also presented and used as a reference point for the theoretical modeling. A semiquantitative description of the measured $I-V$ curves is achieved, suggesting that the coupling to vibrational excitations plays an important role in DNA conduction.

Figure 1

(Color online) (a) Scheme (not drawn to scale) of the experimental setup showing dithiolated dsDNA (thicker lines for clarity) chemically bonded to two metal electrodes (upper, GNP; lower, gold surface), supported by a monolayer of thiolated ssDNA. (b) AFM topography image showing top view of the sample. Several GNPs are clearly seen on the background of the ssDNA monolayer. The GNPs mark the position of the hybridized dsDNA. The inset is a height profile of the GNP lying on the ssDNA surface. (c) Collection of $I\text{−}V$ curves from different samples. In some other cases we measured smaller or no voltage gap. Note that several curves show saturation of the current amplifier at $220\mathrm{nA}$. (d) A $F\text{−}Z$ curve of one of the curves in (c), (green, forward; red, backward) demonstrating the tip-GNP adhesion (red line) without pressing the GNP through the monolayer. The $I\text{−}V$ curve is recorded at the closest point of the tip to the GNP without pressing it through the ssDNA monolayer.

Figure 2

(Color online)Upper panel: Schematic representation of the double-strand DNA with the experimentally relevant base-pair sequence (Ref. 11). The ${\left(\mathrm{C}{\mathrm{H}}_2\right)}_3\text{−}\mathrm{S}\mathrm{H}$ linker groups are omitted for simplicity (see the text for details). Lower panel: Two-leg ladder used to mimic the double-strand structure of a DNA molecule. $L$ and $R$ refer to left and right electrodes, respectively. The coupling terms to the electrodes ${\Gamma }_{\alpha ,\ell },\ell =X,\overline{X}$, $\alpha =L,R$, are assumed to be energy-independent constants (wideband limit; see the text for details).

Figure 3

(Color online) (a) Tight-binding electronic band structure of an infinite DNA system, obtained by a periodic repetition of the 26-base sequence of Ref. 11. Notice the strongly fragmented band structure with very flat bands. The open (yellow) rectangles indicate for reference the approximate position of the bands for a periodic poly(GC) oligomer. (b)–(d) Spectral density $A(E,V=0)$, which at zero voltage coincides with the projected density of states onto the molecular region, for the finite-size DNA chain contacted in different ways by left and right electrodes (see Fig. 2): (b) ${\Gamma }_{L,X}={\Gamma }_{R,\overline{X}}=0,{\Gamma }_{L,\overline{X}}={\Gamma }_{R,X}=250\mathrm{meV}$, (c) ${\Gamma }_{L,X}={\Gamma }_{R,\overline{X}}=250\mathrm{meV}$, ${\Gamma }_{L,\overline{X}}={\Gamma }_{R,X}=0\mathrm{meV}$, (d) ${\Gamma }_{L,X}={\Gamma }_{R,\overline{X}}={\Gamma }_{L,\overline{X}}={\Gamma }_{R,X}=250\mathrm{meV}$. The onsite energies were set at the LUMO values reported in Ref. 23 and the hopping parameters were set to $t_X=t_{\overline{X}}=t=0.27\mathrm{eV}$, $t_{X\overline{X}}=0.25\mathrm{eV}$. (e) $I\text{−}V$ characteristics for two different temperatures and the contact situation (b). (f) Corresponding transmission function $t\left(E\right)$. (g) Differential conductance $g\left(V\right)$.

Figure 4

(Color online) $I\text{−}V$ characteristics for different values of the reduced interstrand hopping $t_{X\overline{X}}∕t$ in ${\mathrm{DNA}}_{26}$ for a fixed electron-vibron coupling strength $g=1$. Upper and lower panels correspond to two different (asymmetric) ways of coupling the ladder to the electrodes: (a) ${\Gamma }_{L,X}={\Gamma }_{R,\overline{X}}=0,{\Gamma }_{L,\overline{X}}={\Gamma }_{R,X}=250\mathrm{meV}$ and (b) ${\Gamma }_{L,\overline{X}}={\Gamma }_{R,X}=0,{\Gamma }_{L,X}={\Gamma }_{R,\overline{X}}=250\mathrm{meV}$. Notice the strong variation in the current when going from case (a) to case (b).

Figure 5

(Color online) Dependence of the current on the effective electron-vibron coupling strength $g=\lambda ∕\Omega$ at $T=300\mathrm{K}$ and for $t_{X\overline{X}}=0.71t$. The vibron frequency was fixed at $20\mathrm{meV}$. With increasing coupling the total current is reduced and the zero-current gap is enhanced. The lower panels show the spectral density at $V\sim 1.5\mathrm{V}$ for the three values of $g$. Despite the increased number of vibron satellites with increasing coupling, the total intensity is reduced.

Figure 6

(Color online) Dependence of the elastic $(n=0)$ and inelastic $(n\ne 0)$ components of the current at a fixed voltage on the electron-vibron coupling strength $\lambda$ and the mode frequency $\Omega$. A more detailed analysis of the behavior is presented in the text. The dashed lines correspond to the total current (sum of elastic and inelastic components).

Figure 7

(Color online) Theoretical curves (solid lines) compared with two different $I\text{−}V$ curves as obtained on suspended double-strand DNA oligomers contacted by a GNP (Ref. 11) In both cases the temperature and the coupling to the electrodes were kept fixed at $T=300\mathrm{K}$ and ${\Gamma }_{L,X}={\Gamma }_{R,\overline{X}}=250\mathrm{meV}$, ${\Gamma }_{R,X}={\Gamma }_{L,\overline{X}}=0$, respectively.