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Superconductivity in layered cuprates is induced by doping holes into a parent antiferromagnetic insulator. It is now recognized that another common emergent order involves charge stripes, and our understanding of the relationship been charge stripes and superconductivity has been evolving. Here we review studies of 214 cuprate families obtained by doping La$_2$CuO$_4$. Charge-stripe order tends to compete with bulk superconductivity; nevertheless, there is plentiful evidence that it coexists with two-dimensional superconductivity. This has been interpreted in terms of pair-density-wave superconductivity, and the perspective has shifted from competing to intertwined orders. In fact, a new picture of superconductivity based on pairing within charge stripes has been proposed, as we discuss.
Superconductivity in the vicinity of a competing electronic order often manifests itself with a superconducting dome, centred at a presumed quantum critical point in the phase diagram. This common feature, found in many unconventional superconductors
We investigate in underdoped cuprates possible coexistence of the superconducting (SC) order at zero momentum and pair density wave (PDW) at momentum ${bf Q}=(pi, pi)$ in the presence of a Neel order. By symmetry, the $d$-wave uniform singlet pairing
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 similar forms 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 ordering
One of the central questions in the cuprate research is the nature of the normal state which develops into high temperature superconductivity (HTSC). In the normal state of hole-doped cuprates, the existence of charge density wave (CDW) is expected t