  Formation of topological objects during phase transitions has been discussed
extensively in literature. In all these discussions defects and anti-defects
form with equal probabilities. In contrast, many physical situations, such as
formation of baryons in relativistic heavy-ion collisions at present energies,
flux tube formation in superconductors in the presence of external magnetic
field, and formation of superfluid vortices in a rotating vessel, require a
mechanism which can bias (say) defects over anti-defects. Such a bias can
crucially affect defect-anti-defect correlations, apart from its effects on
defect density. In this paper we initiate an investigation for the basic
mechanism of biased formation of defects. For Skyrmions in 1+1 dimensions, we
show that incorporation of a chemical potential term in the effective potential
leads to a domain structure where order parameter is spatially varying. We show
that this leads to biased formation of Skyrmions.
