CP-Violating Solitons in the Minimal Supersymmetric Standard Model

We study non-topological and CP-violating static wall solutions in the framework of the Minimal Supersymmetric Standard Model. We show that such membranes, characterized by a non-trivial winding of the relative $U(1)$ phase of the two Higgs fields in the direction orthogonal to the wall, exist for small values of the mass of the CP-odd Higgs boson when loop corrections to the Higgs potential are included. Although their present-day existence is excluded by experimental bounds, we argue why they may have existed in the early universe with important cosmological consequences.