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A review is presented of the static and dynamic magnetic properties of hole-doped cuprate superconductors measured with neutron scattering. A wide variety of experiments are described with emphasis on the monolayer…
Understanding the pseudogap phase in hole-doped high temperature cuprate superconductors remains a central challenge in condensed matter physics. From a host of recent experiments there is now compelling evidence of translational symmetry…
We report on a study of the influence of defects introduced in the CuO$_{2}$ planes of cuprates in a wide range of hole dopings n. T$_{c}$ and electrical resistivity $\rho (T)$ measurements have been performed on electron irradiated…
The (Cu)13-BEC model of high-temperature superconductivity was previously shown to account for many of the principal thermodynamic and electronic properties of the superconducting cuprates. Here I show that this model is also able to…
We discuss the interplay between electronic correlations and an underlying superlattice structure in determining the period of charge density waves (CDW's), by considering a one-dimensional Hubbard model with a repeated (non-random) pattern…
Recent STM measurements have revealed the existence of periodic charge modulations at the surface of certain cuprate superconductors. Here we show that the observed patterns are compatible with the formation of a three-dimensional crystal…
We discuss the possibility that the strain field introduced by the structural supermodulation in Bi-2212 and certain other cuprate materials may modulate the superconducting pairing interaction. We calculate the amplitude of this effect,…
We study a quasi-2D classical Landau-Ginzburg-Wilson effective field theory in the presence of quenched disorder in which incommensurate charge-density wave and superconducting orders are intertwined. The disorder precludes long-range…
The kagome metals $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) exhibit a complex interplay between charge density wave (CDW) order and superconductivity. In this study, we use ultrafast coherent phonon spectroscopy to probe the evolution of CDW order…
The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved CDW correlations are still in their infancy. We…
Kagome superconductors AV$_3$Sb$_5$ (A = K, Rb and Cs) have attracted much recent attention due to the coexistence of multiple exotic orders. Among them, the charge density wave (CDW) order has been shown to host various unconventional…
I summarize recent results, obtained with E. Demler, K. Park, A. Polkovnikov, M. Vojta, and Y. Zhang, on spin and charge correlations near a magnetic quantum phase transition in the cuprates. STM experiments on slightly overdoped BSCCO…
The recent discoveries of short-range charge-density wave fluctuations in the normal state of several hole-doped cuprate superconductors constitute a significant addition to the known intrinsic properties of these materials. Besides likely…
Superconductivity and charge density waves (CDW) are competitive, yet coexisting orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and…
We report the observation of coherent oscillations associated with charge density wave (CDW) order in the underdoped cuprate superconductor YBa2Cu3O6+x by time-resolved optical reflectivity. Oscillations with frequency 1.87 THz onset at…
The study of the interaction between superconductivity and charge ordering is helpful to resolve the pairing mechanism in high-temperature superconductors. Recently, several resistance oscillations studies trigger the speculation that a…
In order to explain the emergence of the anomalous pseudogap state and high-temperature superconductivity in the cuprates, intense research activity over three decades has focused on unravelling the connection between the various…
We show that a variety of spectral features in high-T_c cuprates can be understood from the coupling of charge carriers to some kind of dynamical order which we exemplify in terms of fluctuating charge and spin density waves. Two…
Electronic charge order is a symmetry breaking state in high-$T_\mathrm{c}$ cuprate superconductors. In scanning tunneling microscopy, the detected charge-order-induced modulation is an electronic response of the charge order. For an…
The square-lattice Hubbard and closely related $t$-$J$ models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group…