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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., Comment: 34 pages, 8 figures and 4 Tables more...

We investigate the time-dependent electronic transport in single-walled carbon nanotubes (SWCNTs) functionalized with Au clusters on CO gas exposure. Using a tight-binding Hamiltonian and the nonequilibrium Green's function (NEGF) formalism the time-dependent zeroth and first order contributions to the current are calculated. The zeroth order contribution is identified as the time-dependent Landauer formula in terms of the slow time variable, whereas the first order contribution is found to be small. The Green's function for the SWCNT is derived using the equation of motion and Dyson equation technique. The conductance is explicitly evaluated by considering a form for the hopping integral which accounts for the effect of dopants on the charge distribution of the carbon atoms and the nearest-neighbor distance. The effect of dopants is also studied in terms of fluctuations by calculating the autocorrelation function for the experimental and theoretical data. These calculations allow direct comparison with the experiment and demonstrate how the presence of dopants modifies the conductance of the SWCNT measured experimentally and provide the only study of fluctuations in the sensor response in terms of the autocorrelation function., Comment: 20 pages, 5 figures more...

We calculate the two-time current correlation function using the experimental data of the current-time characteristics of the Gas-DNA-decorated carbon nanotube field effect transistor. The pattern of the correlation function is a measure of the sensitivity and selectivity of the sensors and suggest that these gas flow sensors may also be used as DNA sequence detectors. The system is modelled by a one-dimensional tight-binding Hamiltonian and we present analytical calculations of quantum electronic transport for the system using the time-dependent nonequilibrium Green's function formalism and the adiabatic expansion. The zeroth and first order contributions to the current $I^{(0)}(\bar{t})$ and $I^{(1)}(\bar{t})$ are calculated, where $I^{(0)} (\bar{t})$ is the Landauer formula. The formula for the time-dependent current is then used to compare the theoretical results with the experiment., Comment: 14 pages, 5 figures and 2 tables more...

The Chiral Random Matrix Model or the Gaussian Penner Model (generalized Laguerre ensemble) is re-examined in the light of the results which have been found in double well matrix models [D97,BD99] and subtleties discovered in the single well matrix models [BH99]. The orthogonal polynomial method is used to extend the universality to include non-polynomial potentials. The new asymptotic ansatz is derived (different from Szego's result) using saddle point techniques. The density-density correlators are the same as that found for the double well models ref. [BD99] (there the results have been derived for arbitrary potentials). In the smoothed large N limit they are sensitive to odd and even N where N is the size of the matrix [BD99]. This is a more realistic random matrix model of mesoscopic systems with density of eigenvalues with gaps. The eigenvalues see a brick-wall potential at the origin. This would correspond to sharp edges in a real mesoscopic system or a reflecting boundary. Hence the results for the two-point density-density correlation function may be useful in finding one eigenvalue effects in experiments in mesoscopic systems or small metallic grains. These results may also be relevant for studies of structural glasses as described in ref. [D02]., Comment: 17 pages, 3 figures more...

This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The density-density correlators of these models depend on whether N, where N is the size of the matrix, takes even or odd values. The fact that this dependence persists in the large N thermodynamic limit is an unusual property and may have consequences in the study of one electron effects in mesoscopic systems. Secondly, we study the parametric and cross correlators of the Harish Chandra-Itzykson-Zuber matrix model. The analytic expressions determine how the correlators change as a parameter (e.g. the strength of a perturbation in the hamiltonian of the chaotic system or external magnetic field on a sample of material) is varied. The results are relevant for the conductance fluctuations in disordered mesoscopic systems., Comment: 12 pages, Latex, 2 Figures more...