Impurity induced phase competition and supersolidity

TL;DR

This paper investigates how impurities in the attractive Hubbard model induce charge order and can lead to a supersolid phase through impurity interactions, with implications for cuprates and CDW materials.

Contribution

It demonstrates impurity-induced charge order and supersolidity in the attractive Hubbard model, highlighting the role of impurity correlations and RKKY-like interactions.

Findings

Single impurities induce charge-ordered textures.

Correlated impurities can form a supersolid phase.

Random impurities do not produce coherent charge order.

Abstract

Several material families show competition between superconductivity and other orders. When such competition is driven by doping, it invariably involves spatial inhomogeneities which can seed competing orders. We study impurity-induced charge order in the attractive Hubbard model, a prototypical model for competition between superconductivity and charge density wave order. We show that a single impurity induces a charge-ordered texture over a length scale set by the energy cost of the competing phase. Our results are consistent with a strong-coupling field theory proposed earlier in which superconducting and charge order parameters form components of an $SO(3)$ vector field. To discuss the effects of multiple impurities, we focus on two cases: correlated and random distributions. In the correlated case, the CDW puddles around each impurity overlap coherently leading to a `supersolid' phase with coexisting pairing and charge order. In contrast, a random distribution of impurities does not lead to coherent CDW formation. We argue that the energy lowering from coherent ordering can have a feedback effect, driving correlations between impurities. This can be understood as arising from an RKKY-like interaction, mediated by impurity textures. We discuss implications for charge order in the cuprates and doped CDW materials such as NbSe$_2$.