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.
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 wide range of e
xperimental characterizations, it is possible to delineate a clear and consistent cuprate story. It starts with doping holes into a charge-transfer insulator, resulting in in-gap states. These states exhibit a pseudogap resulting from the competition between antiferromagnetic superexchange $J$ between nearest-neighbor Cu atoms (a real-space interaction) and the kinetic energy of the doped holes, which, in the absence of interactions, would lead to extended Bloch-wave states whose occupancy is characterized in reciprocal space. To develop some degree of coherence on cooling, the spin and charge correlations must self-organize in a cooperative fashion. A specific example of resulting emergent order is that of spin and charge stripes, as observed in La$_{2-x}$Ba$_x$CuO$_4$. While stripe order frustrates bulk superconductivity, it nevertheless develops pairing and superconducting order of an unusual character. The antiphase order of the spin stripes decouples them from the charge stripes, which can be viewed as hole-doped, two-leg, spin-$frac12$ ladders. To achieve superconducting order, the pair correlations in neighboring ladders must develop phase order. In the presence of spin stripe order, antiphase Josephson coupling can lead to pair-density-wave superconductivity. Alternatively, in-phase superconductivity requires that the spin stripes have an energy gap, which empirically limits the coherent superconducting gap. Hence, superconducting order in the cuprates involves a compromise between the pairing scale, which is maximized at $xsimfrac18$, and phase coherence, which is optimized at $xsim0.2$.
Both Zn-doping and $c$-axis magnetic fields have been observed to increase the spin stripe order in La$_{2-x}$Ba$_x$CuO$_4$ with $x$ close to 1/8. For $x=0.095$, the applied magnetic field also causes superconducting layers to decouple, presumably by
favoring pair-density-wave order that consequently frustrates interlayer Josephson coupling. Here we show that introducing 1% Zn also leads to an initial onset of two-dimensional (2D) superconductivity, followed by 3D superconductivity at lower temperatures, even in zero field. We infer that the Zn pins pair-density-wave order locally, establishing the generality of such behavior.
Neutron scattering has played a significant role in characterizing magnetic and structural correlations in Fe$_{1+y}$Te$_{1-x}$Se$_x$ and their connections with superconductivity. Here we review several key aspects of the physics of iron chalcogenide
superconductors where neutron studies played a key role. These topics include the phase diagram of Fe$_{1+y}$Te$_{1-x}$Se$_{x}$, where the doping-dependence of structural transitions can be understood from a mapping to the anisotropic random field Ising model. We then discuss orbital-selective Mott physics in the Fe chalcogenide series, where temperature-dependent magnetism in the parent material provided one of the earliest cases for orbital-selective correlation effects in a Hunds metal. Finally, we elaborate on the character of local magnetic correlations revealed by neutron scattering, its dependence on temperature and composition, and the connections to nematicity and superconductivity.
Superconductivity in cuprates is achieved by doping holes into a correlated charge-transfer insulator. While the correlated character of the parent insulator is now understood, there is no accepted theory for the normal state of the doped insulator.
I present a mostly empirical analysis of a large range of experimental characterizations, making the case for two pseudogaps: (1) a large pseudogap resulting from the competition between the energy of superexchange-coupled local Cu moments and the kinetic energy of doped holes; (2) a small pseudogap that results from dopant disorder and consequent variations in local charge density, leading to a distribution of local superconducting onset temperatures. The large pseudogap closes as hole kinetic energy dominates at higher doping and the dynamic antiferromagnetic correlations become overdamped. Establishing spatially-homogeneous $d$-wave superconductivity is limited by those regions with the weakest superconducting phase coherence, which tends to be limited by low-energy spin fluctuations. The magnitude of the small pseudogap is correlated with the doping-dependent energy $E_{rm cross}$ associated with the neck of the hour-glass dispersion of spin excitations. The consequences of this picture are discussed.
We discuss various methods to obtain the resolution volume for neutron scattering experiments, in order to perform absolute normalization on inelastic magnetic neutron scattering data. Examples from previous experiments are given. We also try to prov
ide clear definitions of a number of physical quantities which are commonly used to describe neutron magnetic scattering results, including the dynamic spin correlation function and the imaginary part of the dynamic susceptibility. Formulas that can be used for general purposes are provided and the advantages of the different normalization processes are discussed.
On the basis of negative transport coefficients, it has been argued that the quantum oscillations observed in underdoped YBa(2)Cu(3)O(6+x) in high magnetic fields must be due to antinodal electron pockets. We point out a counter example in which elec
tron-like transport in a hole-doped cuprate is associated with Fermi-arc states. We also present evidence that the antinodal gap in YBa(2)Cu(3)O(6+x) is robust to modest applied magnetic fields. We suggest that these observations should be taken into account when interpreting the results of the quantum oscillation experiments.
Magnetic excitations in the energy range up to 100 meV are studied for over-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.25$ and 0.30, using time-of-flight neutron spectroscopy. Comparison of spectra integrated over the width of an antiferromagnetic B
rillouin zone demonstrates that the magnetic scattering at intermediate energies, $20 lesssim omega lesssim 100$ meV, progressively decreases with over-doping. This strongly suggests that the magnetism is not related to Fermi surface nesting, but rather is associated with a decreasing volume fraction of (probably fluctuating) antiferromagnetic bubbles.
We report a detailed study of the temperature and magnetic-field dependence of the spin susceptibility for a single crystal of La(1.875)Ba(0.125)CuO(4). From a quantitative analysis, we find that the temperature-dependent anisotropy of the suscepti
bility, observed in both the paramagnetic and stripe-ordered phases, directly indicates that localized Cu moments dominate the magnetic response. A field-induced spin-flop transition provides further corroboration for the role of local moments. Contrary to previous analyses of data from polycrystalline samples, we find that a commonly-assumed isotropic and temperature-independent contribution from free carriers, if present, must be quite small. Our conclusion is strengthened by extending the quantitative analysis to include crystals of La(2-x)Ba(x)CuO(4) with x=0.095 and 0.155. On the basis of our results, we present a revised interpretation of the temperature and doping dependence of the spin susceptibility in La(2-x)(Sr,Ba)(x)CuO(4).
We report on the phase diagram for charge-stripe order in La(1.6-x)Nd(0.4)Sr(x)CuO(4), determined by neutron and x-ray scattering studies and resistivity measurements. From an analysis of the in-plane resistivity motivated by recent nuclear-quadrupol
e-resonance studies, we conclude that the transition temperature for local charge ordering decreases monotonically with x, and hence that local antiferromagnetic order is uniquely correlated with the anomalous depression of superconductivity at x = 1/8. This result is consistent with theories in which superconductivity depends on the existence of charge-stripe correlations.
