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

PEZZUTTI A; DA VEGA

Córdoba

Workshop; XIII LATIN AMERICAN WORKSHOP ON NONLINEAR PHENOMENA; 2013

LAWNP

During the last decades the study of low-dimensional systems has been driven by dierenttechnological applications, ranging from soft matter and biophysics to electronics and nanotechnology.For example, quasi-two-dimensional lms of block copolymers have been used asnanolithographic masks for pattern transfer and the synthesis of graphene, a two-dimensionalcrystal with unprecedented physical properties, has opened new horizons for science and technology.One of the main diculties associated with these systems for practical applicationsis the lack of long-range order due to the presence of topological defects that often controlkey material properties. For example, the non-local disorder introduced by disclinations insmectic systems reduces the applicability to several nanodevices, and the fact that grapheneis actually not at but exhibits pronounced wrinkles into the third dimension was attributedto the presence of defects, like dislocations and grain boundaries. Here we study through aphase eld model the coupling between the geometry and topological defects in free standingexible membranes. To describe the dynamic of defects in a crystalline membrane we proposea minimal model that includes a Brazovskii Hamiltonian geometrically coupled to the topographyof the membrane. We consider a membrane that at high temperatures is a disorderedstructureless deformable surface, with equilibrium properties dictated by a Helfrich-CanhamHamiltonian. The low-temperature phase is described through the Brazovskii model, wherethe 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 determinedby the topological charge and bending stiness and surface tension. The overall dynamics andmembrane conguration agrees remarkably well with recent experiments of aberration-correctedtransmission electron microscopy on graphene containing arrays of dislocations [Lehtinen et al.,Nature Communications 4, 2098, 2013].