We present both numerical and analytical study of graphene roughness with a crystal structure including $500 \times 500$ atoms. The roughness can effectively result in a random gauge field and has important consequences for its electronic structure. Our results show that its height fluctuations in small scales have scaling behavior with a temperature dependent roughness exponent in the interval of $ 0.6 < \chi < 0.7 $. The correlation function of height fluctuations depends upon temperature with characteristic length scale of $ \approx 90 {\AA}$ (at room temperature). We show that the correlation function of the induced gauge field has a short-range nature with correlation length of about $\simeq 2-3 {\AA}$. We also treat the problem analytically by using the Martin-Siggia-Rose method. The renormalization group flows did not yield any delocalized-localized transition arising from the graphene roughness. Our results are in good agreement with recent experimental observations.Comment: 5 Pages, 5 figure

We investigate the structure and electronic properties of phosphatidylcholine (PC) under different degrees of hydration at the single-molecule and monolayer type level by linear scaling ab initio calculations. Upon hydration, the phospholipid undergoes drastic long-range conformational rearrangements which lead to a sickle-like ground-state shape. The structural unit of the tilted gel-phase PC appears to be a water-bridged PC dimer. We find that hydration dramatically alters the surface potential, dipole and quadrupole moments of the lipids and consequently guides the interactions of the lipids with other molecules and the communication between cells.

It has been argued that the electron-hole puddles formed on graphene are mostly due to substrate-induced charged impurities [