Theory of interaction-induced charge order in CrSBr

TL;DR

This paper develops ab initio models to understand charge density wave states in CrSBr, revealing how Coulomb interactions and doping influence charge order patterns, consistent with experimental findings.

Contribution

It introduces a comprehensive ab initio framework combining density functional theory and many-body techniques to study charge order in CrSBr, highlighting the role of Coulomb interactions.

Findings

Charge density wave states with cosine-like modulations are predicted.

Periodicities of charge order match experimental doping levels.

Short-range Coulomb interactions favor stripe-like localized states.

Abstract

CrSBr is a layered van der Waals insulator with a quasi one-dimensional electronic structure and in-plane ferromagnetic order. Recent experimental work on Li-doped CrSBr reveals quasi-1D charge modulated states. In this study, we develop ab initio effective models for CrSBr to investigate these states and solve them using mean-field theory and density matrix embedding theory. The models are parametrized using density functional theory, the constrained random phase approximation, and the Rytova-Keldysh form of the long-range Coulomb interaction. Our simulations indicate the emergence of a charge density wave state characterized by cosine-like intra-chain density modulations and inter-chain phase shifts that minimize the Coulomb repulsion. Notably, at a doping level corresponding to $1/n$ electron per CrSBr unit, the most stable pattern exhibits a periodicity of $n$ cells, in agreement with experimental observations and Peierls' instability arguments. Moreover, we demonstrate that the inter-chain order is sensitive to the range of Coulomb interactions. If the interaction is hard-truncated to a short-ranged form, some localized stripe-like states are computationally favored. This work provides an ab initio framework for understanding the interplay of competing electronic and magnetic phases in CrSBr and related materials.