Commensurate to Incommensurate Transition of Three Dimensional Charge Density Waves

TL;DR

This paper develops a diagrammatic self-consistent-field approach to study three-dimensional charge density waves in the cubic Holstein model, revealing the transition from commensurate to incommensurate phases influenced by doping and phonon frequency.

Contribution

It introduces a systematic theoretical framework for understanding CDW transitions in three dimensions, highlighting the effects of doping and phonon frequency.

Findings

Commensurate CDW locked at (π,π,π) near half-filling.

Incommensurate CDW emerges with hole doping, drifting towards (π,π,0).

Phonon frequency significantly affects transition temperatures and phase boundaries.

Abstract

Charge density wave (CDW) is a widely concerned emergent phenomenon in condensed matter physics. To establish a systematic understanding of CDW, we develop a diagrammatic self-consistent-field approach for cubic Holstein model employing fluctuation exchange approximation, and explore the emergence and transition of three-dimensional CDWs. Commensurate CDW (c-CDW) locked at $(\pi,\pi,\pi)$ is favored near half-filling, and the transition temperature is predicted around half of the nearest-neighbor hopping. Large hole doping leads to a suppression of CDW transition temperature and the emergence of incommensurate CDW (i-CDW), which is evidenced by a drifting of the ordering vector away from $(\pi,\pi,\pi)$ towards $(\pi,\pi,0)$. Phonon frequency significantly impacts the transition temperature and the phase boundary between c-CDW and i-CDW, and the optimal frequency for enlarging the CDW regime is also predicted near half of the nearest-neighbor hopping. These new theoretical results provide a systematic understanding of CDW and a fresh perspective on emergent phenomena dominated by electron-phonon interaction.