Electromagnetic radiation by electrons in corrugated graphene

The electromagnetic radiation of electrons in the corrugated graphene in the presence of the transport electric current in the ballistic regime is studied. Radiation of the similar nature can be observed in undulator and wiggler. We considered here an impact of the ripples in the monolayer graphene on its electromagnetic properties. The electromagnetic radiation was actually calculated with a use of the standard electromagnetic theory. Two cases, of regular and random structures are analyzed. Nonlinear relation between the random height function h(x,y) and the gauge field is shown to create the radiation frequency distribution central peak. Few mechanisms of ripples formation in monolayer graphene were considered. The ripples are considered as an incommensurate superstructure in the two-dimensional crystal, appearing as a result of forming of periodic solutions in the in-plane optical phonon subsystem. Possible instability of the flexural subsystem is discussed as well.