The stability of "visible"electroweak-type cosmic strings is investigated in an extension of the Standard Model by a minimal dark sector, consisting of a U(1) gauge field, broken spontaneously by a scalar. The visible and dark sectors are coupled through a Higgs-portal and a gauge-kinetic mixing term. It is found that strings whose core is "filled"with a dark scalar condensate exhibit better stability properties than their analogues in the Standard Model, when the electroweak mixing angle is close to θW=π/2. They become unstable as one lets θW approach its physical value. The instability mechanism appears to be a W-boson condensation mechanism found in previous studies on the stability of electroweak strings.

A variety of quantum systems exhibit Weyl points in their spectra where two bands cross in a point of three-dimensional parameter space with conical dispersion in the vicinity of the point. We consider theoretically the soft constraint regime where the parameters are dynamical quantum variables. We have shown that in general the soft constraints, in the quasiclassical limit, result in Weyl disks where two states are (almost) degenerate in a finite two-dimensional region of the three-dimensional parameter space. We provide concrete calculations for two setups: Weyl point in a four-terminal superconducting structure and a Weyl exciton, i.e., a bound state of Weyl electron and a massive hole.