elementary flux quanta of hc/(Ne) and the core energy of a $hc/e$ vortex

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$Z_2$ superconductor is known to have an elementary flux quanta of $hc/2e$ (of vortex).

In the following Refs,

S. Sachdev, Phys. Rev. B 45, 389 (1992).
[S. Sachdev, Science 288, 475 (2000)](http://arxiv.org/abs/cond-mat/0009456)
T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000).

some of them argue that to have deconfined phases, superconducting states in their vicinity allow low energy vortex excitations with quantized magnetic ﬂux equal to $hc/e$. The elementary ﬂux quantum is always $hc/(2e)$, but it can be argued quite generally that core energy of a $hc/e$ vortex is lower than twice that
of a $hc/(2e)$ vortex.

Question: How can we have a consistent and complete physical understanding of the above picture? Why quantized magnetic ﬂux of $hc/e$ is favored (at a the core of vortex?), and why does it sense the deconfined phase?

Question 2: For $Z_N$ superconductor, I suppose we have, the elementary ﬂux quantum is always $\frac{hc}{Ne}$, but it can be argued quite generally that core energy of a $\frac{hc}{e}$ vortex is lower than N times that
of a $\frac{hc}{Ne}$ vortex???

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