Loop super-Virasoro Lie conformal superalgebra

The loop super-Virasoro conformal superalgebra $mathfrak{cls}$ associated with the loop super-Virasoro algebra is constructed in the present paper. The conformal superderivation algebra of $mathfrak{cls}$ is completely determined, which is shown to consist of inner superderivations. And nontrivial free and free $mathbb{Z}$-graded $mathfrak{cls}$-modules of rank two are classified. We also give a classification of irreducible free $mathfrak{cls}$-modules of rank two and all irreducible submodules of each free $mathbb{Z}$-graded $mathfrak{cls}$-module of rank two.