  We consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH)
in the framework of two-component Ginzburg-Landau model. We have shown that
there are three types of non-Abrikosov vortices depending on chosen boundary
conditions at the core of vortices, namely, Neumann (N)-type, Dirichlet
(D)-type and Gross-Pitaevskii (GP)-type vortices. The Neumann-type vortex has a
non-vanishing condensation at the core, that is different from the ordinary
vortex, and the magnetic flux could be reversed as well in LMH. Furthermore, we
have obtained a new type of a neutral vortex which has no magnetic field. The
presence of such a vortex is related to metallic superfluid state suggested by
Babaev.
