  Competing orders in condensed matter give rise to the emergence of
fascinating, new phenomena. Here, we investigate the competition between
superconductivity and charge density wave in the context of layered-metallic
compounds, transition metal dichalcogenides, in which the superconducting state
is usually suppressed by the charge density wave. We show, using real-space
self-consistent Bogoliubov-de Gennes calculations and momentum-space
calculations involving density-functional theory and dynamical mean-field
theory, that there is a surprising reappearance of superconductivity in the
presence of non-magnetic disorder fluctuations, as observed in recent
experiments.
