Ripples on graphene and their effect on lattice and electronic properties

A discovery of graphene, a new allotrope of carbon [1], representing the simplest, one-atom thick, membrane, opens exciting perspectives in statistical physics of two-dimensional systems in general. As expected from theory of flexible membranes [2], free suspended graphene is corrugated (rippled) due to thermal bending fluctuations, which was confirmed by experiment [3] and atomistic simulations [4]. This makes graphene strongly anharmonic crystal leading to anomalous temperature dependences of its thermal expansion, elastic moduli and other thermodynamic and mechanical properties. The ripples are also a source of pseudomagnetic gauge field [5] acting on Dirac fermions which leads to important consequences for the electronic structure such as a formation of midgap states [6,7]. Quenched ripples can be also important sources of electron scattering limiting charge-carrier mobility in graphene [8]. Possible mechanisms of this quenching are discussed. \\[3pt] [1] K.S. Novoselov et al, Science \textbf{306}, 666 (2004). \\[0pt] [2] \textit{Statistical Mechanics of Membranes and Surfaces}, ed. by D. R. Nelson, T. Piran, and S. Weinberg (World Sci, Singapore 2004). \\[0pt] [3] J.C. Meyer et al, Nature \textbf{446}, 60 (2007). \\[0pt] [4] A. Fasolino, J.H. Los, and M.I. Katsnelson, Nature Mater. \textbf{6}, 858 (2007). \\[0pt] [5] S.V. Morozov et al, Phys. Rev. Lett. \textbf{97}, 016801 (2006). \\[0pt] [6] F. Guinea, M.I. Katsnelson, and M.A.H. Vozmediano, Phys. Rev. B \textbf{77}, 075422 (2008). \\[0pt] [7] T.O. Wehling et al, Europhys. Lett. \textbf{84}, 17003 (2008). \\[0pt] [8] M.I. Katsnelson and A.K. Geim, Phil. Trans. Royal Soc. A \textbf{366}, 195 (2008).