Dynamical gauge symmetry breaking in lower-dimensional Lorentz-violating supersymmetric theory

In this work we study the dynamical generation of mass in the Lorentz-violating low-dimensional Super-Yang-Mills theory in the aether superspace coupled to a scalar matter. We also suggest that our studies can be applied for condensed matter systems, especially lower-dimensional superconductors and topological insulators. In low dimensional materials, the parameter $\Delta$ generated by presence of the aether term can be interpreted as a quantity that renormalizes the propagation velocity of the bosonic mode with respect to the Fermi velocity.