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Copper oxide high temperature superconductors universally exhibit multiple forms of electronically ordered phases that break the native translational symmetry of the CuO2 planes. The interplay between these orders and the superconducting…
Charge stripe order has recently been established as an important ingredient of the physics of cuprate high-T$_c$ superconductors. However, due to the complex interplay between competing phases and the influence of disorder, it is unclear…
Electron interactions are pivotal for defining the electronic structure of quantum materials. In particular, the strong electron Coulomb repulsion is considered the keystone for describing the emergence of exotic and/or ordered phases of…
During the last decade, translational and rotational symmetry-breaking phases -- density wave order and electronic nematicity -- have been established as generic and distinct features of many correlated electron systems, including pnictide…
The cuprates exhibit anomalous momentum-space structure with antinodal gap and nodal arc in the underdoped regime, which evolves into a complete hole-type Fermi surface with a large Luttinger volume in the overdoped regime. The real-space…
Within the framework of the kinetic energy driven d-wave superconductivity, the electronic structure of the electron doped cuprate superconductors is studied. It is shown that although there is an electron-hole asymmetry in the phase…
In correlated electrons system, quantum melting of electronic crystalline phase often gives rise to many novel electronic phases. In cuprates superconductors, melting the Mott insulating phase with carrier doping leads to a quantum version…
Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…
The experimentally measured phase diagram of cuprate superconductors in the temperature-applied magnetic field plane illuminates key issues in understanding the physics of these materials. At low temperature, the superconducting state gives…
In many quantum materials, strong electron correlations lead to the emergence of new states of matter. In particular, the study in the last decades of the complex phase diagram of high temperature superconducting cuprates highlighted…
Electronic phases with symmetry properties matching those of conventional liquid crystals have recently been discovered in transport experiments on semiconductor heterostructures and metal oxides at milli-Kelvin temperatures. We report the…
Understanding the electron pairing in hole-doped cuprate superconductors has been a challenge, in particular because the "normal" state from which it evolves is unprecedented. Now, after three and a half decades of research, involving a…
We propose a theory for the underdoped hole-doped cuprates, focusing on the "nodal-anti-nodal dichotomy" observed in recent experiments. Our theory begins with an ordered antiferromagnetic Fermi liquid with electron and hole pockets. We…
In the search for mechanisms of high-temperature superconductivity it is critical to know the electronic spectrum in the pseudogap phase from which superconductivity evolves. The lack of angle-resolved photoemission data for every cuprate…
The existence of electronic symmetry breaking in the underdoped cuprates, and its disappearance with increased hole-density $p$, are now widely reported. However, the relationship between this transition and the momentum space…
The electronic nematic order characterized by broken rotational symmetry has been suggested to play an important role in the phase diagram of the high temperature cuprates. We study the interplay between the electronic nematic order and a…
Do charge modulations compete with electron pairing in high-temperature copper-oxide superconductors? We investigated this question by suppressing superconductivity in a stripe-ordered cuprate compound at low temperature with high magnetic…
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar-sometimes identical-ordering temperatures even…
Correlation effects in CuO$_2$ layers give rise to a complicated landscape of collective excitations in high-T$_{\rm c}$ cuprates. Their description requires an accurate account for electronic fluctuations at a very broad energy range and…
Although the vast majority of high-$T_c$ cuprate superconductors are hole-doped, a small family of electron-doped compounds exists. Under investigated until recently, there has been tremendous recent progress in their characterization. A…