full quantum vortex is merely two HQV’s of opposite spins coinciding at a same point. This means that the full quantum vortex core energy, if we ignore the cross term between two spin components in $f^{(4)}_{hom}$, is approximately twice the core energy of a HQV. If the HQV core energy is actually larger than this, that would make stabilization of the HQV more difficult, i.e., the largest allowed value for $\rho_{sp}/\rho_s$ for the HQV lattice would be smaller than what we obtain through the formalism used here.

The lattice structure can be determined by finding $(\sigma,\varsigma, {\bm \tau})$ that minimize the free energy expectation value. For this, we first set the amplitude of OP to minimize the energy for given $(\sigma,\varsigma, {\bm \tau})$ (the amplitude depends on $H_{c2}-H$), and then compare energy for different values of $(\sigma,\varsigma, {\bm
\tau})$. To determine these structures we will need to take the spatial integral of the product of four Landau level wavefunctions. We have computed these integrals in the Appendix \[app:corr\].

Lowest Landau level solution {#sec:LLL}
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In the bulk of this section we provide detailed analysis of the lowest Landau level solution for the non-chiral triplet superconductors and briefly comment on the 