f \rangle &=& -\frac{1}{c}\langle\textbf{j}\cdot\delta\textbf{A}\rangle + \beta_1 \langle |\phi_0|^4 \rangle (C^4_{\uparrow\!\uparrow} + C^4_{\downarrow\!\downarrow})/2\nonumber\\
&+& \left[\frac{2\gamma}{l^2}\!(\!\langle\!|\phi_0|^2\!|\tilde{\phi}_0|^2\!\rangle\!-\!\langle\!|\phi_0|^2\!|\tilde{\phi}_1|^2\!\rangle\!)
- \beta_2\!\langle\!|\phi_0|^2\!|\tilde{\phi}_0|^2\!\rangle\right]C^2_{\uparrow\!\uparrow} C^2_{\downarrow\!\downarrow}\nonumber\\
&+& \frac{\langle h^2_s \rangle}{8\pi} -
\frac{H^2}{8\pi}+\alpha\left[1-\frac{K+H_{c2}l^2\tilde{\kappa}}{K-H_{c2}l^2\tilde{\kappa}}\right]C_{\downarrow\!\downarrow}^2,
\label{EQ:LLLfree}\end{aligned}$$ where $\bf{j}$ is the supercurrent, $\delta\bf{A}$ is deviation of the vector potential from what we would have for the $h = H_{c2}$, and $h_s$ is the screening field of superconductor. Note that in this approximation $\bf{j}$ is calculated solely from quadratic terms, ignoring $\gamma$ terms, and by the Maxwell equation $\nabla \times \bm{h_s} = 4\pi \bm{j} /c$. More specifically $$\begin{aligned}
\bm{j}=&2eK[\Delta^*_{\uparrow\!\uparrow}(\bm{D}\Delta_{\uparrow\!\uparrow})+
\Delta^*_{\downarrow\!\downarrow}(\bm{D}\Delta_{\downarrow\!\downarrow})+c.c]\nonumber\\
&-c\tilde{\kappa}\nabla\times\hat{z}(|\Delta_{\uparrow\!\uparrow}|^2-|\Delta_{\downarrow\!\downarrow}|^2)\end{aligned}$$ Since $\nabla \times \delta \bm{A} = \bm{\hat{z}} (h_s + H - H_{c2})$ and, from Maxwell’s equations, $\nabla \times \bm{h_s} = 4\pi \bm{j} /c$, partial integration leads to [@deGenneSC] $$\begin{aligned}
\frac{1}{c}\langle\textbf{j}\cdot\delta\textbf{A}\rangle &=& \frac{1}{4\pi}
\langle \bm{h_s}\cdot (\bm{h_s} + \bm{H} - \bm{\hat{z}} H_{c2}) \rangle\nonumber\\
&=& \frac{\langle h^2_s \rangle}{4\pi} + \frac{H_{c2} - H}{4\pi}\langle h_s \rangle.\end{aligned}$$ Meanwhile, when we calculate the expectation value of $\gamma$, we set $h = H_{c2}$. This leads to the free energy of $$\begin{aligned}
\langle f \rangle &=& -\frac{H_{c2}\!-\!H}{4\pi}\langle h_s\rangle - \frac{\langle h^2_s \rangle}{8\pi} - \frac{H^2}{8\pi}\nonumber\\
&+& \alpha\left[1-\frac{K+H_{c2}l^2\tilde{\kappa}}{K-H_{c2}l^2\tilde{\kappa}}\right]C_{\downarrow\!\downarrow}^2 
+ \frac{\beta}{2} \langle |\phi_0|^4 \rangle (C^4_{\uparrow\!\uparrow} + C^4_{\downarrow\!\downarrow})\nonumber\\
&+& \left[\frac{2\gamma}{l^2}\!(\!\langle\!|\phi_0|^2\!|\tilde{\phi}_0|^2\!\rangle\!-\!\langle\!|\phi_0|^2\!|\tilde{\phi}_1|^2\!\rangle\!)
- \beta_2\!\langle\!|\phi_0|^2\!|\tilde{\phi}_0|^2\!\rangle\right]C^2_{\uparrow\!\uparrow} C^2_{\downarrow\!\downarrow}\nonumber\\
&\equiv& - \frac{H^2}{8\pi} +\langle \tilde{f} \rangle.
\label{EQ:freeExpect}\end{aligned}$$

The screening field $h_s$ can be 