  We study properties of Abrikosov-Nielsen-Olesen (ANO) strings with the
Coleman-Weinberg (CW) potential, which we call CW-ANO strings. While the
scale-invariant scalar potential has a topologically trivial vacuum admitting
no strings at the classical level, quantum correction allows topologically
nontrivial vacua and stable string solutions. We find that the system of the CW
potential exhibits significant difference from that of the conventional
Abelian-Higgs model with the quadratic-quartic potential. While a
single-winding string is qualitatively similar in both systems, and the static
intervortex force between two strings at large distance is attractive/repulsive
in the type-I/II regime for both, that between two CW-ANO strings exhibits a
nontrivial structure. It develops an energy barrier between them at
intermediate distance, implying that the string with winding number $n > 1$ can
constitute a metastable bound state even in the type-II regime. We name such a
superconductor type-$\overline{1.5}$. We also discuss implications to
high-energy physics and cosmology.
