Higher order derivatives extension of Maxwell-Chern-Simons electrodynamics in the presence of field sources and material boundaries

In this paper we consider some new classical effects obtained for a planar electrodynamics with the presence of a higher order derivatives term. The model can be interpreted as a kind of extension for the 3d Maxwell-Chern-Simons electrodynamics with higher order derivatives. We consider setups with stationary field sources describing pointlike charges and Dirac points. We also investigate this model with the presence of a conducting line (in 3d dimensions, it is the equivalent of a conducting plate in 4d dimensions). In this case we calculate the propagator for the gauge field and the interaction force between the conducting line and a pointlike charge, as well as the force between the conducting line and a Dirac point, the source for vortex field solutions. It is shown that the image method is not valid in any case. We also compare the obtained results along the paper with the corresponding ones obtained with the standard Maxwell-Chern-Simons electrodynamics [L. H. C. Borges, Eur. Phys. J. C 80, 238 (2020)EPCFFB1434-604410.1140/epjc/s10052-020-7775-3].