Coulomb interactions of massless Dirac fermions in graphene; pair-distribution functions and exchange-driven spin-polarized phases

The quasi-2D electrons in graphene behave as massless fermions obeying a Dirac-Weyl equation in the low-energy regime near the two Fermi points. The stability of spin-polarized phases (SPP) in graphene is considered. The exchange energy is evaluated from the analytic pair-distribution functions, and the correlation energies are estimated via a closely similar four-component 2D electron fluid which has been investigated previously. SPPs appear for sufficiently high doping, when the exchange energy alone is considered. However, the inclusion of correlations is found to {\it suppress} the spin-phase transition in ideal graphene.Comment: 5 pages, 3 figures, Revte

The Classical-Map Hyper-Netted-Chain (CHNC) technique for inhomogeneous electron systems. Application to quantum dots

The Classical-map Hyper-Netted-Chain (CHNC) technique is a simple method of calculating quantum pair-distribution functions, spin-dependent energies, etc., of strongly-interacting {\it uniform} systems. We present CHNC calculations of charge densities and energies of {\it non-uniform} systems, viz., quantum dots, and compare with quantum Monte Carlo and density -functional results. Results for up to 210 electrons are reported.Comment: Latex manuscript and one figure (colour online). New calculations extending to 210 electrons are include

Chronic Kidney Disease of Unknown aetiology (CKDu) and multiple-ion interactions in drinking water

Recent experimental work on the nephrotoxicity of contaminants in drinking water using laboratory mice, motivated by the need to understand the origin of chronic kidney disease of unknown aetiology is examined within our understanding of the hydration of ions and proteins. Qualitative considerations based on Hofmeister-type action of these ions, as well as quantitative electrochemical models for the Gibbs free-energy change for ion-pair formation are used to explain why Cd$^{2+}$ in the presence of F$^-$ and water hardness due to Mg$^{2+}$ ions (but not Ca$^{2+}$) can be expected to be more nephrotoxic, while AsO$_3^{3-}$ in the presence of F$^-$ and hardness may be expected to be less nephrotoxic. The analysis is applied to a variety of ionic species typically found in water to predict their likely combined electro-chemical action. These results clarify the origins of chronic kidney disease in the north-central province of Sri Lanka. The conclusion is further strengthened by a study of the dietary load of Cd and As, where the dietary loads are found to be safe, especially when the mitigating effects of micronutrient ionic forms of Zn and Se, as well as corrections for bio-availability are taken in to account. The resulting aetiological picture supports the views that F$^-$, Cd$^{2+}$ (to a lesser extent), and Mg$^{2+}$ ions found in stagnant household well water act together with enhanced toxicity, becoming the most likely causative factor of the disease. Similar incidence of CKDu found in other tropical climates may have similar geological origins.Comment: 14 pages, one figur

Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers

The exchange and correlation $E_{xc}$ of strongly correlated electrons in 2D layers of finite width are studied as a function of the density parameter $r_s$, spin-polarization $\zeta$ and the temperature $T$. We explicitly treat strong-correlation effects via pair-distribution functions, and introduce an equivalent constant-density approximation (CDA) applicable to all the inhomogeneous densities encountered here. The width $w$ defined via the CDA provides a length scale defining the $z$-extension of the quasi-2D layer resident in the $x$-$y$ plane. The correlation energy $E_c$ of the quasi-2D system is presented as an interpolation between a 1D gas of electron-rods (for $w/r_s>1$) coupled via a log(r) interaction, and a 3D Coulomb fluid closely approximated from the known {\it three-dimensional} correlation energy when $w/r_s$ is small. Results for the $E_{xc}(r_s,\zeta,T)$, the transition to a spin-polarized phase, the effective mass $m^*$, the Land\'e $g$-factor etc., are reported here.Comment: Revtex manuscript, 9 postscript figure