Shape instabilities induced by defects in free standing two-dimensional crystals

PEZZUTTI ALDO D; DANIEL A. VEGA

Cordoba

Congreso; XIII Latin American Workshop on Nonlinear Phenomena; 2013

FAMAF

During the last decades the study of low-dimensional systems has been driven by diferent technological applications, ranging from soft matter and biophysics to electronics and nanotechnology. For example, quasi-two-dimensional lms of block copolymers have been used as nanolithographic masks for pattern transfer and the synthesis of graphene, a two-dimensional crystal with unprecedented physical properties, has opened new horizons for science and technology. One of the main diculties associated with these systems for practical applications is the lack of long-range order due to the presence of topological defects that often control key material properties. For example, the non-local disorder introduced by disclinations in smectic systems reduces the applicability to several nanodevices, and the fact that graphene is actually not at but exhibits pronounced wrinkles into the third dimension was attributed to the presence of defects, like dislocations and grain boundaries. Here we study through a phase field model the coupling between the geometry and topological defects in free standing flexible membranes. To describe the dynamic of defects in a crystalline membrane we propose a minimal model that includes a Brazovskii Hamiltonian geometrically coupled to the topography of the membrane. We consider a membrane that at high temperatures is a disordered structureless deformable surface, with equilibrium properties dictated by a Helfrich-Canham Hamiltonian. The low-temperature phase is described through the Brazovskii model, where the uid membrane phase separates into a buckled crystalline state with hexagonal symmetry. We observe that the coupling between the membrane geometry and the defects is determined by the topological charge and bending stiness and surface tension. The overall dynamics and membrane conguration agrees remarkably well with recent experiments of aberration-corrected transmission electron microscopy on graphene containing arrays of dislocations [Lehtinen et al.,Nature Communications 4, 2098, 2013].