  A theoretical understanding of the experimental electronic transport
phenomena in gas sensors based on DNA functionalized graphene is presented by
quantitatively investigating the time-dependent electronic transport in these
devices using the nonequilibrium Green's function (NEGF) formalism and
tight-binding approximation. The time-dependent zeroth and first order
contributions to the current are calculated with derivations of the equation of
motion and Dyson equation. The zeroth order contribution is identified as the
time-dependent Landauer formula in terms of the slow time variable and the
first order contribution is found to be small in this experiment. The current
is explicitly calculated by deriving a formula for the transmission function
and considering a form for the hopping integral which includes the effect of
chemical vapors on the charge distribution of the carbon atoms and the
nearest-neighbor carbon-carbon distance $\rm a_{cc}$. Theoretical results are
found in agreement with the experimental results. A shift in the Fermi level
($\rm \varepsilon_f$) is calculated, which is a result of shift in the Dirac
point due to adsorption of vapors on the DNA functionalized graphene. The work
suggests that using the same values of change in $\rm a_{cc}$ due to the four
DNA bases for a specific target vapor, the theoretical values of the current
response can be predicted for different DNA sequences leading to the
application of the graphene sensors as a DNA analyser.
