Emergent superconductivity upon disordering a charge density wave ground state

We explore the interplay of a charge density wave (CDW) order and s-wave superconductivity in a disordered system. Recent experiments on 1T-TiSe₂, where the pristine sample has a commensurate CDW order and the superconductivity appears upon copper intercalation, motivates our study. Starting with an extended Hubbard model, with parameters which yield a CDW ground state within Hartree-Fock-Bogoliubov formalism in pure systems, we show that the addition of disorder quickly wipes out the global charge order by disrupting periodic modulation of density at some (low) strength of disorder. Along with this, the subdominant superconducting order emerges in regions that spatially anticorrelate with islands of strong local CDW order. The short-range density modulations, however, continue to persist and show discernible effects up to a larger disorder strength. The local CDW puddles reduce in size with increasing disorder and they finally lose their relevance in effecting the properties of the system. Implication of our model calculations on the experimental findings of transition-metal-dichalcogenides will also be discussed.