Induced current and transmission through the barrier in the four-fermion model in 2 + 1 dimensions

A three-dimensional theoretical model with compactification of the third dimension in the presence of a four-fermion interaction under the A ₃ external gauge field, where the mass was generated in a two-dimensional brane, has been considered. In the framework of this model the appearance of an induced current was predicted. The induced current was obtained as the function of the flux of Aharonov-Bohm field. The resulting expression oscillates with frequency, depending on the value of the flux. In the absence of compactification, the transmission coefficient through the delta-shaped barrier that was formed by the four-fermion interaction was obtained.