  The structure of low-energy collective states in proton-deficient N=28
isotones is analyzed using structure models based on the relativistic energy
density functional DD-PC1. The relativistic Hartree-Bogoliubov model for
triaxial nuclei is used to calculate binding energy maps in the
$\beta$-$\gamma$ plane. The evolution of neutron and proton single-particle
levels with quadrupole deformation, and the occurrence of gaps around the Fermi
surface, provide a simple microscopic interpretation of the onset of
deformation and shape coexistence. Starting from self-consistent constrained
energy surfaces calculated with the functional DD-PC1, a collective Hamiltonian
for quadrupole vibrations and rotations is employed in the analysis of
excitation spectra and transition rates of $^{46}$Ar, $^{44}$S, and $^{42}$Si.
The results are compared to available data, and previous studies based either
on the mean-field approach or large-scale shell-model calculations. The present
study is particularly focused on $^{44}$S, for which data have recently been
reported that indicate pronounced shape coexistence.
