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キーワード:
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要旨:
Even in the absence of Coulomb interactions, phase fluctuations induced
by quantum size effects become increasingly important in superconducting
nanostructures as the mean level spacing becomes comparable with the
bulk superconducting gap. Here we study the role of these fluctuations,
termed "quantum capacitance," in the phase diagram of a one-dimensional
ring of ultrasmall Josephson junctions at zero temperature by using
path-integral techniques. Our analysis also includes dissipation due to
quasiparticle tunneling and Coulomb interactions through a finite mutual
and self-capacitance. The resulting phase diagram has several
interesting features: A finite quantum capacitance can stabilize
superconductivity even in the limit of only a finite mutual-capacitance
energy, which classically leads to breaking of phase coherence. In the
case of vanishing charging effects, relevant in cold-atom settings where
Coulomb interactions are absent, we show analytically that superfluidity
is robust to small quantum finite-size fluctuations and identify the
minimum grain size for phase coherence to exist in the array. We have
also found that the renormalization group results are in some cases very
sensitive to relatively small changes of the instanton fugacity. For
instance, a certain combination of capacitances could lead to a
nonmonotonic dependence of the superconductor-insulator transition on
the Josephson coupling.
