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The extremely overdoped cuprates are generally considered to be Fermi liquid metals without exotic orders, whereas the underdoped cuprates harbor intertwined states. Contrary to this conventional wisdom, using Cu $L_3$ edge and O $K$ edge…
Understanding the interplay between charge order (CO) and other phenomena (e.g. pseudogap, antiferromagnetism, and superconductivity) is one of the central questions in the cuprate high-temperature superconductors. The discovery that…
Charge modulations are considered as a leading competitor of high-temperature superconductivity in the underdoped cuprates, and their relationship to Fermi surface reconstructions and to the pseudogap state is an important subject of…
In cuprate high-temperature superconductors, an antiferromagnetic Mott insulating state can be destabilized toward unconventional superconductivity by either hole- or electron-doping. In addition to these two electronic phases there is now…
Copper-oxide high TC superconductors possess a number of exotic orders co-existing with or proximal to superconductivity, whose quantum fluctuations may account for the unusual behaviors of the normal state, even affecting…
Identifying quantum critical points (QCPs) and their associated fluctuations may hold the key to unraveling the unusual electronic phenomena observed in cuprate superconductors. Recently, signatures of quantum fluctuations associated with…
Recent resonant x-ray scattering (RXS) experiments revealed a novel charge order in extremely overdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) [Phys. Rev. Lett. 131,116002]. The observed charge order appears around the $(\pi/3,0)$ wavevector,…
Charge-density wave order is now understood to be a widespread feature of underdoped cuprate high-temperature superconductors, although its origins remain unclear. While experiments suggest that the charge-ordering wavevector is determined…
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…
Cuprate superconductors remain central to condensed matter physics due to their technological relevance and unconventional, incompletely understood electronic behavior. While the canonical phase diagram and low-energy models have been…
One of the central issues concerning the mechanism of high temperature superconductivity in cuprates is the nature of the ubiquitous charge order and its implications to superconductivity. Here we use scanning tunneling microscopy to…
Trilayer cuprates hold the record for the highest superconducting critical temperatures ($T_{\text{c}}$), yet the underlying mechanism remains elusive. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES), we uncover a…
The high-temperature superconductivity in copper oxides emerges under strong influence of spin correlations in doped Mott insulators. Recent discoveries of charge-order (CO) correlations in Y-based hole-doped cuprates as well as in…
Signatures of superconductivity at elevated temperatures above $T_c$ in high temperature superconductors have been observed near 1/8 hole doping for photoexcitation with infrared or optical light polarized either in the CuO$_2$-plane or…
Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has…
The presence of different electronic orders other than superconductivity populating the phase diagram of cuprates suggests that they might be the key to disclose the mysteries of this class of materials. In particular charge order in the…
In the recent studies of the unconventional physics in cuprate superconductors, one of the central issues is the interplay between charge order and superconductivity. Here the mechanism of the charge-order formation in the electron-doped…
In high-temperature cuprate superconductors, superconductivity is accompanied by a "plethora of orders", and phenomena that may compete, or cooperate with superconductivity, but which certainly complicate our understanding of origins of…
Besides superconductivity, copper-oxide high temperature superconductors are susceptible to other types of ordering. We use scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of…
Charge order in underdoped and optimally doped high-$T_\mathrm{c}$ superconductors Bi$_{2}$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (Bi2201) is investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS). We have directly observed…