Transport Properties of Rippled Graphene

It is common to describe graphene as ideally flat plane, however there exists both theoretical and experimental evidence that it is most usual to find it in a rippled state. The ripples can be either induced by the substrate or formed spontaneously in suspended graphene. The lateral size of such features ranges between several and tens of nanometers with the height of up to 1 nm. It has been suggested that the presence of ripples could be one of the factors ultimately limiting mobility of carriers and that it may be also responsible, by introducing an effective gauge field, for the lack of weak localization observed in certain graphene samples. In the present contribution the transport properties of the rippled graphene are studied theoretically starting with the simple case of one-dimensional modulation. Using either single-band or the full $sp^3$ tight-binding Hamiltonians we compare and discuss the importance of two ripple-related mechanisms of scattering: the variation of interatomic distances and hybridization between π and σ bands of graphene.