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

Abstract

Studies on the interplay between the charge order and the $d$-wave superconductivity in the copper-oxide high $T_{\mathrm{c}}$ 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.

arXiv comment11 pages, 12 figures, special topics in J. Phys. Soc. Jpn. (2021)

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Cited by in corpus (11)

• A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice
• $Ab$ $initio$ low-energy effective Hamiltonians for high-temperature superconducting cuprates Bi${}_2$Sr${}_2$CuO${}_6$, Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$, HgBa${}_2$CuO${}_4$ and CaCuO${}_2$
• Mott Quantum Critical Points at finite doping
• Superconductivity studied by solving ab initio low-energy effective Hamiltonians for carrier doped CaCuO${}_2$, Bi${}_2$Sr${}_2$CuO${}_6$, Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$, and HgBa${}_2$CuO${}_4$
• Testing for pair-density-wave order in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$
• Exciton dynamics uncovering electron fractionalization in superconducting cuprates
• Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons
• Pseudogap in electron-doped cuprates: Strong correlation leading to band splitting
• Quantum criticality of bandwidth-controlled Mott transition
• Influence of oxygen-coordination number on the electronic structure of single-layer La-based cuprates
• Fermi Machine -- Quantum Many-Body Solver Derived from Correspondence between Noninteracting and Strongly Correlated Fermions