  We study a three-orbital Hubbard model with negative Hund coupling in
infinite dimensions, combining dynamical mean-field theory with continuous time
quantum Monte Carlo simulations. This model, which is relevant for the
description of alkali-doped fullerides, has previously been shown to exhibit a
spontaneous orbital selective Mott phase in the vicinity of the superconducting
phase. Calculating the pair potential and double occupancy in each orbital, we
study the competition between different homogeneous ordered states and
determine the corresponding finite temperature phase diagram of the model. We
identify two distinct types of spontaneous orbital-selective Mott states and
show that an orbital-selective $s$-wave superconducting state with one
superconducting and two metallic orbitals is spontaneously realized between the
conventional $s$-wave superconducting phase and these two kinds of
spontaneously orbital-selective Mott states.
