Competing Unconventional Charge-Density-Wave States in Cuprate Superconductors: Spin-Fluctuation-Driven Mechanism

TL;DR

This paper develops a self-consistent theoretical framework based on the Hubbard model to explain the origin of unconventional charge-density-wave states in cuprate superconductors, emphasizing the role of spin fluctuations and vertex corrections.

Contribution

It introduces a systematic approach to analyze CDW instabilities without assuming specific q-dependence, revealing the dominance of uniform nematic and axial CDW states driven by spin fluctuations.

Findings

Uniform q=0 nematic CDW with d-form factor is the leading instability.

Axial CDW at q=Q_a becomes prominent under static uniform CDW order.

Higher-order vertex corrections, especially Aslamazov-Larkin processes, induce CDW orders at multiple q-points.

Abstract

To understand the origin of unconventional charge-density-wave (CDW) states in cuprate superconductors, we establish the self-consistent CDW equation, and analyze the CDW instabilities based on the realistic Hubbard model, without assuming any $q$-dependence and the form factor. Many higher-order many-body processes, which are called the vertex corrections, are systematically generated by solving the CDW equation. When the spin fluctuations are strong, the uniform $q=0$ nematic CDW with $d$-form factor shows the leading instability. The axial nematic CDW instability at $q = Q_a = (\delta,0)$ ($\delta \approx \pi/2$) is the second strongest, and its strength increases under the static uniform CDW order. The present theory predicts that uniform CDW transition emerges at a high temperature, and it stabilize the axial $q = Q_a$ CDW at $T = T_{CDW}$. It is confirmed that the higher-order Aslamazov-Larkin processes cause the CDW orders at both $q = 0$ and $Q_a$.