Upper critical magnetic field ($B_{c2}={\mu }_0{H}_{c2}={\Phi }_0/(2\pi {\xi }^2)$)

Linearize the stated model about $\psi =0$ in a uniform magnetic field. The kinetic operator has the Landau level ground energy $\hslash |q|B/(2m_{\ast })$. Its cancellation with $\alpha <0$ givesThis is the bulk orbital field scale of this model; it excludes spin-polarization limits and uses the normal-state relation $B_{c2}={\mu }_0{H}_{c2}$. For the chosen $\xi =10\mathrm{nm}$, it is about $3.29\mathrm{T}$. With $\lambda =100\mathrm{nm}$, $\kappa =10$. Counting triangular cells at $B_{c2}$ would give $a/\xi =\sqrt{4\pi /\sqrt{3}}\simeq 2.69$, but it is the linearized field equation, rather than disks of an arbitrarily chosen core radius touching, that supplied the transition criterion.