Self-dual Maxwell-Chern-Simons solitons in a parity-invariant scenario

We present a self-dual parity-invariant $U(1) \times U(1)$ Maxwell-Chern-Simons scalar $\text{QED}_3$. We show that the energy functional admits a Bogomol'nyi-type lower bound, whose saturation gives rise to first order self-duality equations. We perform a detailed analysis of this system, discussing its main features and exhibiting explicit numerical solutions corresponding to finite-energy topological vortices and non-topological solitons. The mixed Chern-Simons term plays an important role here, ensuring the main properties of the model and suggesting possible applications in condensed matter.