  We study the superdeformed (SD) states and corresponding SD hypernuclei of Ar
isotopes with the multidimensionally-constrained relativistic mean field
(MDC-RMF) models which can accommodate various shape degree of freedom. %The
hyperon-nucleon $\sigma$-$\Lambda$ and $\omega$-$\Lambda $ interactions are
introduced %in the same covariant framework. We found that the density profiles
of SD states in Ar isotopes show a strong localization with a ring structure
near the surface, while the central part of the density is dilute showing a
hole structure. This localization of SD density induces an appreciable
deformation in the hyperon wave function and results in a large overlap between
the core and the hyperon in the SD hypernuclei of Ar isotopes. Then the
$\Lambda$ separation energy of SD state becomes larger than that of normally
deformed or spherical ground state. This feature is different from that found
in other nuclei such as $^{32}$S, $^{56}$Ni, and $^{60}$Zn in which the
$\Lambda$ separation energy of larger deformed state is smaller. In this
context, the measurement of the $\Lambda$ separation energy may provide an
important information on the localization of the density profile of SD states.
