= Lens bound on a reconstructed Fermi pocket
{title2=$A_{\max}=2k_F^2\arccos(K/k_F)-2K\sqrt{k_F^2-K^2}$}
In <rectangular-lattice Fermi-surface reconstruction>, the zero-coupling closed orbit is the overlap lens of two equal circles of radius $k_F$ with centres separated by $2K$. Two circular sectors minus their triangular portions give
$$
A_{\max}=2k_F^2\arccos\frac{K}{k_F}-2K\sqrt{k_F^2-K^2}.
$$
At fixed <chemical potential>, the upper hybridized <energy band> rises when the magnitude of the <Fourier coefficient> increases. Its occupied pocket therefore shrinks, so this lens is an upper bound in the two-wave model. It is not a universal bound for arbitrary changes of <chemical potential> or additional <energy bands>.
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