Nature of Spontaneous Curvature in Suspended Graphene

摘要: The nature of its intrinsic ripples is the key factor for understanding stability suspended graphene, and unraveling long-standing theoretical debate existence low-dimensional crystalline state. rippling morphology discovered also in other 2D materials, has a profound impact on electronic, mechanical chemical properties. Actually, before discovery phenomena are widely observed: example, roughing transition interface, rippled phase biomembrane, crumpling flexible sheet polymers modeled by tethered surfaces. fascinating truth that exist so many different membrane-like materials implies possible universal physical mechanism which was unclear. We consider graphene as two parts, characterizing first part spontaneous curvature k stabilizes soft ZA modes, second thermal kt caused directly height fluctuation. By choosing order parameter system, we establish Landau theory modified fluctuation wrinkling large sized graphene. find temperature rises from 0K, occurs at size dependent critical Tc, corresponds to change equilibrium configuration flat state Interestingly, stablized increases, associated with jump bond length well vanishing bending rigidity. results obtained suggest interplay between elementary excitations vital behavior materials. concepts developed here general significance least membranes.