Charge Singlets and Orbital-Selective Charge Density Wave Transitions

TL;DR

This paper investigates orbitally selective charge density wave transitions in bilayer Holstein models, revealing conditions under which charge order penetrates or remains confined, akin to orbital-selective Mott phenomena.

Contribution

It introduces a model for orbitally selective CDW transitions, analyzing charge order penetration in bilayer Holstein systems with different electron-phonon couplings.

Findings

Charge density wave order diminishes with increasing interlayer hybridization in the uniform model.

CDW order penetrates into the metallic layer at intermediate interlayer hopping in the interface model.

An orbitally selective CDW regime exists where only one layer exhibits long-range charge order.

Abstract

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 co-existence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling (EPC). 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 intermediate ratio of inter- to intra-layer hopping strengths, $1.4 \lesssim t_3/t \lesssim 3.4$. This is consistent with the occurrence of an "orbitally selective CDW" regime at weak $t_3$ in which the layer with $\lambda_{1} \neq 0$ exhibits long-range charge order, but the "metallic layer" with $\lambda_{-1}=0$, to which it is hybridized, does not.