Charge Singlets and Orbital-Selective Charge Density Wave Transitions

The possibility of "orbitally selective Mott transitions " within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion U-1 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 coexistence 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, lambda, is zero in the "metallic " layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization t(3), but decreases and eventually vanishes as t(3) 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 an intermediate ratio of inter-to intralayer hopping strengths, 1.4 (sic) t(3)/t (sic) 3.4. This is consistent with the occurrence of an "orbitally selective CDW " regime at weak t(3) in which the layer with lambda(1) &NOTEQUexpressionL; 0 exhibits long-range charge order, but the "metallic layer " with lambda(-1) = 0, to which it is hybridized, does not.