Charge Order and Superconductivity as Competing Brothers in Cuprate High-$T_{\rm c}$ Superconductors

TL;DR

This paper reviews how charge order and d-wave superconductivity in cuprates are interconnected phenomena arising from electron fractionalization, with a focus on their competition and experimental signatures in strongly correlated systems.

Contribution

It introduces the concept of electron fractionalization as a unifying framework to understand the competition between charge order and superconductivity in cuprates, supported by high-accuracy quantum many-body solutions.

Findings

Charge inhomogeneity and superconductivity originate from carrier attraction near Mott insulators.

Severe competition between charge order and superconductivity is revealed by quantum many-body solvers.

Experimental spectroscopic signatures support the fractionalization-based mechanism.

Abstract

Studies on the interplay between the charge order and the $d$-wave superconductivity in the copper-oxide high $T_{\rm c}$ superconductors are reviewed with a special emphasis on the exploration based on the unconventional concept of the electron fractionalization and its consequences supported by solutions of high-accuracy quantum many-body solvers. Severe competitions between the superconducting states and the charge inhomogeneity including the charge/spin striped states revealed by the quantum many-body solvers are first addressed for the Hubbard models and then for the {\it ab initio} Hamiltonians of the cuprates derived without adjustable parameters to represent the low-energy physics of the cuprates. The charge inhomogeneity and superconductivity are born out of the same mother, namely, the carrier attraction arising from the strong Coulomb repulsion near the Mott insulator (Mottness) and accompanied electron fractionalization. The same mother makes the severe competition of the two brothers inevitable. The electron fractionalization has a remarkable consequences on the mechanism of the superconductivity. Recent explorations motivated by the concept of the fractionalization and their consequences on experimental observations in energy-momentum resolved spectroscopic measurements including the angle resolved photoemission spectroscopy (ARPES) and the resonant inelastic X-ray spectroscopy (RIXS) are overviewed, with future vision for the integrated spectroscopy to challenge the long-standing difficulties in the cuprates as well as in other strongly correlated matter in general.