Proximity-induced charge density wave in a metallic system

Nonlocal quasiparticles in correlated quantum materials can exhibit the proximity effect. For instance, in metal superconductor hybrid systems, the leaking of Cooper pairs to the metallic region induces superconducting correlations in a standard metal. This paper explores the proximity effects of charge density wave (CDW) on metal using the attractive Hubbard model, which harbors CDW state at half filling. Our fully self-consistent calculations demonstrate that periodic charge modulations develop in a metal due to the tunneling of finite momentum particle-hole pairs from the CDW region. Upon doping the normal region, the commensurate CDW changes to an incommensurate one by incorporating regular phase shifts. Furthermore, the induced CDW produces a soft gap in the density of states and thus can be detected in tunneling experiments. We discuss our results in light of recent reports of such proximity-induced charge order in different two-dimensional heterostructures.