Critical buckling for the disappearance of superconductivity in rare-earth-doped La2-xSrxCuO4

Local inversion-symmetry breaking in a bismuthate high-Tc superconductor

The doped perovskite BaBiO₃ exhibits a maximum superconducting transition temperature (T_c) of 34 K and was the first high-T_c oxide to be discovered, yet pivotal questions regarding the nature of both the metallic and superconducting states remain unresolved. Although it is generally thought that superconductivity in the bismuthates is of the conventional s-wave type, the pairing mechanism is still debated, with strong electron-phonon coupling and bismuth valence or bond disproportionation possibly playing a role. Here we use diffuse x-ray scattering and Monte Carlo modeling to study the local structure of Ba_1-xK_xBiO₃ across its insulator-metal boundary. We find no evidence for either long- or short-range disproportionation, which resolves a major conundrum, as disproportionation and the related polaronic effects are likely not relevant for the metallic and superconducting states. Instead, we uncover nanoscale structural correlations that break inversion symmetry, with far-reaching implications for the electronic physics. This unexpected finding furthermore establishes that the bismuthates belong to the broader classes of materials with hidden spin-orbit coupling and a tendency towards inversion-breaking displacements.

Pronounced interplay between intrinsic phase-coexistence and octahedral tilt magnitude in hole-doped lanthanum cuprates

Definitive understanding of superconductivity and its interplay with structural symmetry in the hole-doped lanthanum cuprates remains elusive. The suppression of superconductivity around 1/8th doping maintains particular focus, often attributed to charge-density waves (CDWs) ordering in the low-temperature tetragonal (LTT) phase. Central to many investigations into this interplay is the thesis that La_1.875Ba_0.125CuO₄ and particularly La_1.675Eu_0.2Sr_0.125CuO₄ present model systems of purely LTT structure at low temperature. However, combining single-crystal and high-resolution powder X-ray diffraction, we find these to exhibit significant, intrinsic coexistence of LTT and low-temperature orthorhombic domains, typically associated with superconductivity, even at 10 K. Our two-phase models reveal substantially greater tilting of CuO₆ octahedra in the LTT phase, markedly buckling the CuO₂ planes. This would couple significantly to band narrowing, potentially indicating a picture of electronically driven phase segregation, reminiscent of optimally doped manganites. These results call for reassessment of many experiments seeking to elucidate structural and electronic interplay at 1/8 doping.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy

Since the discovery of stripe order in La_1.6-x Nd_0.4Sr _x CuO₄ superconductors in 1995, charge ordering in cuprate superconductors has been intensively studied by various experimental techniques. Among these studies, scanning tunneling microscope (STM) plays an irreplaceable role in determining the real space structures of charge ordering. STM imaging of different families of cuprates over a wide range of doping levels reveal similar checkerboard-like patterns, indicating that such a charge ordered state is likely a ubiquitous and intrinsic characteristic of cuprate superconductors, which may shed light on understanding the mechanism of high-temperature superconductivity. In another class of high-temperature superconductors, iron-based superconductors, STM studies reveal several charge ordered states as well, but their real-space patterns and the interplay with superconductivity are markedly different among different materials. In this paper, we present a brief review on STM studies of charge ordering in these two classes of high-temperature superconductors. Possible origins of charge ordering and its interplay with superconductivity will be discussed.

Unusual behavior of cuprates explained by heterogeneous charge localization

The discovery of high-temperature superconductivity in cuprates ranks among the major scientific milestones of the past half century, yet pivotal questions regarding the complex phase diagram of these materials remain unanswered. Generally thought of as doped charge-transfer insulators, these complex oxides exhibit pseudogap, strange-metal, superconducting, and Fermi liquid behavior with increasing hole-dopant concentration. Motivated by recent experimental observations, here we introduce a phenomenological model wherein exactly one hole per planar copper-oxygen unit is delocalized with increasing doping and temperature. The model is percolative in nature, with parameters that are highly consistent with experiments. It comprehensively captures key unconventional experimental results, including the temperature and the doping dependence of the pseudogap phenomenon, the strange-metal linear temperature dependence of the planar resistivity, and the doping dependence of the superfluid density. The success and simplicity of the model greatly demystify the cuprate phase diagram and point to a local superconducting pairing mechanism.

Data mining graphene: correlative analysis of structure and electronic degrees of freedom in graphenic monolayers with defects

The link between changes in the material crystal structure and its mechanical, electronic, magnetic and optical functionalities-known as the structure-property relationship-is the cornerstone of modern materials science research. The recent advances in scanning transmission electron and scanning probe microscopies (STEM and SPM) have opened an unprecedented path towards examining the structure-property relationships of materials at the single-impurity and atomic-configuration levels. However, there are no statistics-based approaches for cross-correlation of structure and property variables obtained from the different information channels of STEM and SPM experiments. Here we have designed an approach based on a combination of sliding window fast Fourier transform, Pearson correlation matrix and linear and kernel canonical correlation methods to study the relationship between lattice distortions and electron scattering from SPM data on graphene with defects. Our analysis revealed that the strength of coupling to strain is altered between different scattering channels, which can explain the coexistence of several quasiparticle interference patterns in nanoscale regions of interest. In addition, the application of kernel functions allowed us to extract a non-linear component of the relationship between the lattice strain and scattering intensity in graphene. The outlined approach can be further used to analyze correlations in various multi-modal imaging techniques where the information of interest is spatially distributed and generally has a complex multi-dimensional nature.

Doping-dependent charge order correlations in electron-doped cuprates

Understanding the interplay between charge order (CO) and other phenomena (for example, pseudogap, antiferromagnetism, and superconductivity) is one of the central questions in the cuprate high-temperature superconductors. The discovery that similar forms of CO exist in both hole- and electron-doped cuprates opened a path to determine what subset of the CO phenomenology is universal to all the cuprates. We use resonant x-ray scattering to measure the CO correlations in electron-doped cuprates (La2-x Ce x CuO4 and Nd2-x Ce x CuO4) and their relationship to antiferromagnetism, pseudogap, and superconductivity. Detailed measurements of Nd2-x Ce x CuO4 show that CO is present in the x = 0.059 to 0.166 range and that its doping-dependent wave vector is consistent with the separation between straight segments of the Fermi surface. The CO onset temperature is highest between x = 0.106 and 0.166 but decreases at lower doping levels, indicating that it is not tied to the appearance of antiferromagnetic correlations or the pseudogap. Near optimal doping, where the CO wave vector is also consistent with a previously observed phonon anomaly, measurements of the CO below and above the superconducting transition temperature, or in a magnetic field, show that the CO is insensitive to superconductivity. Overall, these findings indicate that, although verified in the electron-doped cuprates, material-dependent details determine whether the CO correlations acquire sufficient strength to compete for the ground state of the cuprates.

Core-level photoemission spectra of Mo0.3Cu0.7Sr2ErCu2Oy, a superconducting perovskite derivative. Unconventional structure–property relationships

The correlation between the critical temperature, T_c, and the apical oxygen distance, the buckling angle and the charge transfer energy (Δ) with the oxidation, in the family of materials: Mo_0.3Cu_0.7Sr₂ErCu₂O_y.

Controlling coherence via tuning of the population imbalance in a bipartite optical lattice

The control of transport properties is a key tool at the basis of many technologically relevant effects in condensed matter. The clean and precisely controlled environment of ultracold atoms in optical lattices allows one to prepare simplified but instructive models, which can help to better understand the underlying physical mechanisms. Here we show that by tuning a structural deformation of the unit cell in a bipartite optical lattice, one can induce a phase transition from a superfluid into various Mott insulating phases forming a shell structure in the superimposed harmonic trap. The Mott shells are identified via characteristic features in the visibility of Bragg maxima in momentum spectra. The experimental findings are explained by Gutzwiller mean-field and quantum Monte Carlo calculations. Our system bears similarities with the loss of coherence in cuprate superconductors, known to be associated with the doping-induced buckling of the oxygen octahedra surrounding the copper sites.

Negative oxygen isotope effect on the static spin stripe order in superconducting La(2-x)Ba(x)CuO(4) (x=1/8) observed by muon-spin rotation

Large negative oxygen-isotope (^{16}O and ^{18}O) effects (OIEs) on the static spin-stripe-ordering temperature T_{so} and the magnetic volume fraction V_{m} were observed in La_{2-x}Ba_{x}CuO_{4}(x=1/8) by means of muon-spin-rotation experiments. The corresponding OIE exponents were found to be α_{T_{so}}=-0.57(6) and α_{V_{m}}=-0.71(9), which are sign reversed to α_{T_{c}}=0.46(6) measured for the superconducting transition temperature T_{c}. This indicates that the electron-lattice interaction is involved in the stripe formation and plays an important role in the competition between bulk superconductivity and static stripe order in the cuprates.

Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O(8+x). Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.

Resonant elastic soft x-ray scattering

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site and valence specific probe to study spatial modulations of charge, spin and orbital degrees of freedom in solids on the nanoscopic length scale. It is not only used to investigate single-crystalline materials. This method also enables one to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces.

Mean-field pairing theory for the charge-stripe phase of high-temperature cuprate superconductors

Striped high-T(c) superconductors such as La(2-y-x)Nd(y)Sr(x)CuO(4) and La(2-x)Ba(x)CuO(4) near x = 1/8 show a fascinating competition between spin and charge order and superconductivity. A theory for these systems therefore has to capture both the spin correlations of an antiferromagnet and the pair correlations of a superconductor. For this purpose we present here an effective Hartree-Fock theory incorporating both electron pairing with finite center-of-mass momentum and antiferromagnetism. We show that this theory reproduces the key experimental features such as the formation of the antiferromagnetic stripe patterns at 7/8 band filling or the quasi-one-dimensional electronic structure observed by photoemission spectroscopy.

Effect of disorder outside the CuO2 planes on Tc of copper oxide superconductors

The effect of disorder on the superconducting transition temperature T(c) of cuprate superconductors is examined. Disorder is introduced into the cation sites in the plane adjacent to the CuO2 planes of two single-layer systems, Bi(2.0)Sr(1.6)Ln(0.4)CuO(6+delta) and La(1.85-y)Nd(y)Sr0.15CuO4. Disorder is controlled by changing rare earth (Ln) ions with a different ionic radius in the former, and by varying the Nd content in the latter with the doped carrier density kept constant. We show that this type of disorder works as weak scatterers in contrast to the in-plane disorder produced by Zn, but remarkably reduces T(c), suggesting novel effects of disorder on high-T(c) superconductivity.

New Materials Derived from Ybco: CrSr2RECu2O8 (RE = La, Pr, Nd, Eu, Gd, Tb, Dy, Y, Ho, Er, Lu)

Eleven new oxides, derived from yttrium barium copper oxide by replacing the square-planar copper [Cu-O4] of the basal plane of the triple perovskite-based structure with octahedral Cr(IV), have been prepared at high pressure and temperature. Their crystal structures have been determined, and their complex microstructure has been established by means of high-resolution electron microscopy and electron diffraction. The materials have a general formula of CrSr2RECu2O8 (RE = La, Pr, Nd, Eu, Gd, Tb, Dy, Y, Ho, Er, and Lu); they are tetragonal, show the symmetry of space group P4/mmm, and do not appear to be superconducting.

Soft fermi surfaces and breakdown of Fermi-liquid behavior

Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.

Magnon heat transport in doped La2CuO4

We present results of the thermal conductivity of La2CuO4 and La(1.8)Eu(0.2)CuO4 single crystals which represent model systems for the two-dimensional spin-1/2 Heisenberg antiferromagnet on a square lattice. We find large anisotropies of the thermal conductivity which are explained in terms of two-dimensional heat conduction by magnons within the CuO2 planes. Nonmagnetic Zn substituted for Cu gradually suppresses this magnon thermal conductivity kappa(mag). A semiclassical analysis of kappa(mag) is shown to yield a magnon mean free path which scales linearly with the reciprocal concentration of Zn ions.

Competition of static stripe and superconducting phases in La(1.48)Nd(0.4)Sr(0.12)CuO(4) controlled by pressure

We have investigated the pressure effect on T(c) and the Hall coefficient in the static stripe-ordered phase of La(1.48)Nd(0.4)Sr(0.12)CuO(4) crystal under hydrostatic pressure. We found a dramatic change of the Hall coefficient and an abrupt increase of T(c) at low pressure of about 0.1 GPa. The results are indicative of a transition from one- to two-dimensional charge transport, associated with the suppression of low-temperature-tetragonal (LTT) phase. From the uniaxial pressure measurements it turns out that the observed critical change is induced primarily due to the in-plane compression of the CuO(2) planes which would make the pinning potential of the LTT lattice distortions weaker.

From antiferromagnetic order to static magnetic stripes: the phase diagram of (La,Eu)2-xSrxCuO4

The magnetic order of (La,Eu)2-xSrxCuO4 ( x</=0.2) has been investigated with &mgr;SR techniques. In this system a low temperature tetragonal (LTT) structure is present in the entire range of doping and it is possible to follow the evolution from the long range antiferromagnetic state at x = 0 to the static magnetic stripes. We find a nonmonotonic change of the Neel temperature with increasing x and the obtained magnetic phase diagram of the LTT phase resembles the generic phase diagram of the cuprates where the superconductivity is replaced by a second antiferromagnetic phase.

Local magnetic order vs superconductivity in a layered cuprate

We report on the phase diagram for charge-stripe order in La1.6-xNd0. 4SrxCuO4, determined by neutron and x-ray scattering studies and resistivity measurements. From an analysis of the in-plane resistivity motivated by recent nuclear-quadrupole-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 approximately 1 / 8. This result is consistent with theories in which superconductivity depends on the existence of charge-stripe correlations.

Cu NQR study of the stripe phase local structure in the lanthanum cuprates

Using Cu nuclear quadrupole resonance (NQR) in Eu-doped La2-xSrxCuO4 we find the evidence of the pinned stripe phase at 1.3 K for 0. 08</=x</=0.18. The pinned fraction increases by 1 order of magnitude near hole doping x = 1/8. The NQR line shape reveals three inequivalent Cu positions: (i) sites in the charged stripe, (ii) nonmagnetic sites outside the stripes, and (iii) sites with a magnetic moment of 0.29&mgr;(B) in the antiferromagnetically correlated regions. A dramatic change of the NQR signal for x>0.18 correlating with the onset of bulk superconductivity corresponds to the depinning of the stripe phase.

Nearly singular magnetic fluctuations in the normal state of a high-Tc cuprate superconductor

Polarized and unpolarized neutron scattering was used to measure the wave vector- and frequency-dependent magnetic fluctuations in the normal state (from the superconducting transition temperature, Tc = 35 kelvin, up to 350 kelvin) of single crystals of La1.86Sr0.14CuO4. The peaks that dominate the fluctuations have amplitudes that decrease as T-2 and widths that increase in proportion to the thermal energy, kBT (where kB is Boltzmann's constant), and energy transfer added in quadrature. The nearly singular fluctuations are consistent with a nearby quantum critical point.