Quantum transport at the Dirac point: Mapping out the minimum conductivity from pristine to disordered graphene

The phase space for graphene's minimum conductivity $\sigma_\mathrm{min}$ is mapped out using Landauer theory modified for scattering using Fermi's Golden Rule, as well as the Non-Equilibrium Green's Function (NEGF) simulation with a Monte Carlo sampling over impurity distributions. The resulting `fan diagram' spans the range from ballistic to diffusive over varying aspect ratios ($W/L$), and bears several surprises. {The device aspect ratio determines how much tunneling (between contacts) is allowed and becomes the dominant factor for the evolution of $\sigma_{min}$ from ballistic to diffusive regime. We find an increasing (for $W/L>1$) or decreasing ($W/L<1$) trend in $\sigma_{min}$ vs. impurity density, all converging around $128q^2/\pi^3h\sim 4q^2/h$ at the dirty limit}. In the diffusive limit, the {conductivity} quasi-saturates due to the precise cancellation between the increase in conducting modes from charge puddles vs the reduction in average transmission from scattering at the Dirac Point. In the clean ballistic limit, the calculated conductivity of the lowest mode shows a surprising absence of Fabry-P\'{e}rot oscillations, unlike other materials including bilayer graphene. We argue that the lack of oscillations even at low temperature is a signature of Klein tunneling

Neutral Current induced π0\pi^0 production and neutrino magnetic moment

We have studied the total cross section, $Q^2$, momentum and angular distributions for pions in the $\nu$($\bar \nu$) induced $\pi^0$ production from nucleons. The calculations have been done for the weak production induced by the neutral current in the standard model and the electromagnetic production induced by neutrino magnetic moment. It has been found that with the present experimental limits on the muon neutrino magnetic moment $\mu_{\nu_\mu}$, the electromagnetic contribution to the cross section for the $\pi^0$ production is small. The neutrino induced neutral current production of $\pi^{0}$, while giving an alternative method to study the magnetic moment of neutrino $\mu_{\nu_\mu}$, does not provide any improvement over the present experimental limit on $\mu_{\nu_\mu}$ from the observation of this process in future experiments at T2K and NO$\nu$A.Comment: 6 pages, 5 figure

The preliminary study of urbanization, fossil fuels consumptions and CO2 emission in Karachi

According to population, Karachi is the first largest city of Pakistan and 9th largest in the world. During last three decades, it has faced mass urbanization, huge population growth, many fold increase in vehicles and industrial development. As a result the demand of more energy in form of fossil fuels increased for domestic, industrial and transportation purpose. In this research the maximum available data of Karachi about urbanization, population and vehicles growth, industrialization, energy consumption and CO2 emissions are analyzed. Time periods considered for this work are according to the availability of the data. The results show that during 1947 to 2008, both urban population and urban area increased to 1500%. During 1990 to 2008, the percentage growth in vehicles is double than that of population growth during this time period. During 1980 to 2007 the consumption of oil and petrol, natural gas and coal increased to 219%, 365% and 287%, respectively. The emission of CO2 jumped from 39 million metric tons in 1980 to 151 million metric tons in 2007