Charge Singlets and Orbital Selective Charge Density Wave Transitions

The possibility of 'orbitally selective Mott transitions' within a multi-band Hubbard model, in which one orbital with large on-site electron-electron repulsion U₁ is insulating and another orbital, to which it is hybridized, with small U_-1, is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the co-existence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling. To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a 'Holstein-Metal interface' where the electron-phonon coupling (EPC) λ is zero in the 'metal' layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization t₃, but decreases and eventually vanishes as t₃ grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at intermediate ratio of inter- to intra-layer hopping strengths 1.4 ≤ t₃/t ≤ 3.4. This is consistent with the occurrence of an 'orbitally selective CDW' regime at weak t₃ in which the layer with λ₁≠0 exhibits long range charge order, but the 'metallic layer' with λ_-1=0, to which it is hybridized, does not.