Direct observation of vortices in an electron fluid.

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance1-4, higher-than-ballistic conduction5-7, Poiseuille flow in narrow channels8-10 and violation of the Wiedemann-Franz law11. Here we provide a visualization of whirlpools in an electron fluid. By using a nanoscale scanning superconducting quantum interference device on a tip12, we image the current distribution in a circular chamber connected through a small aperture to a current-carrying strip in the high-purity type II Weyl semimetal WTe2. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that vortices are present for only small apertures, whereas the flow is laminar (non-vortical) for larger apertures. Near the vortical-to-laminar transition, we observe the single vortex in the chamber splitting into two vortices; this behaviour is expected only in the hydrodynamic regime and is not anticipated for ballistic transport. These findings suggest a new mechanism of hydrodynamic flow in thin pure crystals such that the spatial diffusion of electron momenta is enabled by small-angle scattering at the surfaces instead of the routinely invoked electron-electron scattering, which becomes extremely weak at low temperatures. This surface-induced para-hydrodynamics, which mimics many aspects of conventional hydrodynamics including vortices, opens new possibilities for exploring and using electron fluidics in high-mobility electron systems.

Unveiling Unequivocal Charge Stripe Order in a Prototypical Cuprate Superconductor.

In the cuprates, high-temperature superconductivity, spin-density-wave order, and charge-density-wave (CDW) order are intertwined, and symmetry determination is challenging due to domain formation. We investigated the CDW in the prototypical cuprate La_{1.88}Sr_{0.12}CuO_{4} via x-ray diffraction employing uniaxial pressure as a domain-selective stimulus to establish the unidirectional nature of the CDW unambiguously. A fivefold enhancement of the CDW amplitude is found when homogeneous superconductivity is partially suppressed by magnetic field. This field-induced state provides an ideal search environment for a putative pair-density-wave state.

Spatially inhomogeneous competition between superconductivity and the charge density wave in YBa2Cu3O6.67.

The charge density wave in the high-temperature superconductor YBa2Cu3O7-x (YBCO) has two different ordering tendencies differentiated by their c-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDWs in neighbouring CuO2 bilayers. This discovery has prompted several fundamental questions: how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use x-ray diffraction to study YBa2Cu3O6.67 as a function of magnetic field and temperature. We show that regions with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations impact both the superconducting and normal state properties of YBCO.

Charge-Stripe Order and Superconductivity in Ir1-xPtxTe2.

A combined resistivity and hard x-ray diffraction study of superconductivity and charge ordering in Ir Ir1-xPtxTe2, as a function of Pt substitution and externally applied hydrostatic pressure, is presented. Experiments are focused on samples near the critical composition x c ~ 0.045 where competition and switching between charge order and superconductivity is established. We show that charge order as a function of pressure in Ir0.95Pt0.05Te2 is preempted - and hence triggered - by a structural transition. Charge ordering appears uniaxially along the short crystallographic (1, 0, 1) domain axis with a (1/5, 0, 1/5) modulation. Based on these results we draw a charge-order phase diagram and discuss the relation between stripe ordering and superconductivity.

Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x.

The application of magnetic fields to layered cuprates suppresses their high-temperature superconducting behaviour and reveals competing ground states. In widely studied underdoped YBa2Cu3O6+x (YBCO), the microscopic nature of field-induced electronic and structural changes at low temperatures remains unclear. Here we report an X-ray study of the high-field charge density wave (CDW) in YBCO. For hole dopings ∼0.123, we find that a field (B∼10 T) induces additional CDW correlations along the CuO chain (b-direction) only, leading to a three-dimensional (3D) ordered state along this direction at B∼15 T. The CDW signal along the a-direction is also enhanced by field, but does not develop an additional pattern of correlations. Magnetic field modifies the coupling between the CuO2 bilayers in the YBCO structure, and causes the sudden appearance of the 3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW at low and high fields, allowing Fermi surface reconstruction, as recently suggested.

Nematicity in stripe-ordered cuprates probed via resonant x-ray scattering.

In underdoped cuprate superconductors, a rich competition occurs between superconductivity and charge density wave (CDW) order. Whether rotational symmetry-breaking (nematicity) occurs intrinsically and generically or as a consequence of other orders is under debate. Here, we employ resonant x-ray scattering in stripe-ordered superconductors (La,M)2CuO4 to probe the relationship between electronic nematicity of the Cu 3d orbitals, structure of the (La,M)2O2 layers, and CDW order. We find distinct temperature dependences for the structure of the (La,M)2O2 layers and the electronic nematicity of the CuO2 planes, with only the latter being enhanced by the onset of CDW order. These results identify electronic nematicity as an order parameter that is distinct from a purely structural order parameter in underdoped striped cuprates.

Orbital symmetry of charge-density-wave order in La1.875Ba0.125CuO4 and YBa2Cu3O6.67.

Recent theories of charge-density-wave (CDW) order in high-temperature superconductors have predicted a primarily d CDW orbital symmetry. Here, we report on the orbital symmetry of CDW order in the canonical cuprate superconductors La1.875Ba0.125CuO4 (LBCO) and YBa2Cu3O6.67 (YBCO), using resonant soft X-ray scattering and a model mapped to the CDW orbital symmetry. From measurements sensitive to the O sublattice, we conclude that LBCO has predominantly s' CDW orbital symmetry, in contrast to the d orbital symmetry recently reported in other cuprates. Furthermore, we show for YBCO that the CDW orbital symmetry differs along the a and b crystal axes and that these both differ from LBCO. This work highlights CDW orbital symmetry as an additional key property that distinguishes the different cuprate families. We discuss how the CDW symmetry may be related to the '1/8-anomaly' and to static spin ordering.

The microscopic structure of charge density waves in underdoped YBa2Cu3O6.54 revealed by X-ray diffraction.

Charge density wave (CDW) order appears throughout the underdoped high-temperature cuprate superconductors, but the underlying symmetry breaking and the origin of the CDW remain unclear. We use X-ray diffraction to determine the microscopic structure of the CDWs in an archetypical cuprate YBa2Cu3O6.54 at its superconducting transition temperature ∼ 60 K. We find that the CDWs in this material break the mirror symmetry of the CuO2 bilayers. The ionic displacements in the CDWs have two components, which are perpendicular and parallel to the CuO2 planes, and are out of phase with each other. The planar oxygen atoms have the largest displacements, perpendicular to the CuO2 planes. Our results allow many electronic properties of the underdoped cuprates to be understood. For instance, the CDWs will lead to local variations in the electronic structure, giving an explicit explanation of density-wave states with broken symmetry observed in scanning tunnelling microscopy and soft X-ray measurements.

Evidence of chiral order in the charge-ordered phase of superconducting La1.875Ba0.125Cuo4 single crystals using polar Kerr-effect measurements.

High resolution polar Kerr effect measurements were performed on La1.875Ba0.125CuO4 single crystals revealing that a finite Kerr signal is measured below an onset temperature TK that coincides with the charge ordering transition temperature TCO. We further show that the sign of the Kerr signal cannot be trained with the magnetic field, is found to be the same on opposite sides of the same crystal, and is odd with respect to strain in the diagonal direction of the unit cell. These observations are consistent with a chiral "gyrotropic" order above Tc for La1.875Ba0.125CuO4; similarities to other cuprates suggest that it is a universal property in the pseudogap regime.

X-ray diffraction observations of a charge-density-wave order in superconducting ortho-II YBa2Cu3O6.54 single crystals in zero magnetic field.

X-ray diffraction measurements show that the high-temperature superconductor YBa2Cu3O6.54, with ortho-II oxygen order, has charge-density-wave order in the absence of an applied magnetic field. The dominant wave vector of the charge density wave is q(CDW)=(0,0.328(2),0.5), with the in-plane component parallel to the b axis (chain direction). It has a similar incommensurability to that observed in ortho-VIII and ortho-III samples, which have different dopings and oxygen orderings. Our results for ortho-II contrast with recent high-field NMR measurements, which suggest a commensurate wave vector along the a axis. We discuss the relationship between spin and charge correlations in YBa2Cu3O(y) and recent high-field quantum oscillation, NMR, and ultrasound experiments.

Magneto-optical measurements of a cascade of transitions in superconducting La1.875Ba0.125CuO4 single crystals.

Recent experiments on the original cuprate high-temperature superconductor, La(2-x)Ba(x)CuO4, revealed a remarkable sequence of phase transitions. Here we investigate such crystals with the polar Kerr effect, which is sensitive to time-reversal-symmetry breaking. Concurrent birefringence measurements accurately locate the structural phase transitions from high-temperature tetragonal to low-temperature orthorhombic, and then to lower-temperature tetragonal, at which temperature strong Kerr signal onsets. Hysteretic behavior of the Kerr signal suggests that time-reversal symmetry is already broken well above room temperature, an effect that was previously observed in high quality YBa2Cu3O(6+x) crystals.

Spontaneous symmetry breaking by charge stripes in the high pressure phase of superconducting La1.875Ba0.125CuO4.

In those cases where charge-stripe order has been observed in cuprates, the crystal structure is such that the average rotational symmetry of the CuO2 planes is reduced from fourfold to twofold. As a result, one could argue that the reduced lattice symmetry is essential to the existence of stripe order. We use pressure to restore the average fourfold symmetry in a single crystal of La1.875Ba0.125CuO4, and show by x-ray diffraction that charge-stripe order still occurs. Thus, electronically driven stripe order can spontaneously break the lattice symmetry.

A clamp-type pressure cell for high energy x-ray diffraction.

We present a clamp-type pressure cell for high energy x-ray diffraction. The pressure cell was specifically designed for studies of weak superstructure reflections at low temperatures in transition metal oxides, resulting from, e.g., charge density modulations. Using a photon energy of E=100 keV, the bulk properties of single crystals with a volume of typically 2-5 mm3 can be studied in transmission geometry. To demonstrate the performance of the pressure cell, we present data on the charge stripe order in the high-temperature superconductor La1.875Ba0.125CuO4.

Two-dimensional superconducting fluctuations in stripe-ordered La1.875Ba0.125CuO4.

Recent spectroscopic observations of a d-wave-like gap in stripe-ordered La(2-x)Ba(x)CuO(4) with x=1/8 have led us to critically analyze the anisotropic transport and magnetization properties of this material. The data suggest that concomitant with the spin ordering is an electronic decoupling of the CuO(2) planes. We observe a transition (or crossover) to a state of two-dimensional (2D) fluctuating superconductivity, which eventually reaches a 2D superconducting state below a Berezinskii-Kosterlitz-Thouless transition. Thus, it appears that the stripe order in La(2-x)Ba(x)CuO(4) frustrates three-dimensional superconducting phase order, but is fully compatible with 2D superconductivity and an enhanced T(c).

Nuclear-magnetic-resonance evidence for charge inhomogeneity in stripe ordered La(1.8-x)Eu0.2Sr(x)CuO4.

We report 17O nuclear-magnetic-resonance (NMR) results in the stripe ordered La(1.8-x)Eu0.2Sr(x)CuO4 system. Below a temperature T(q) approximately 80 K, the local electric field gradient and the absolute intensity of the NMR signal of the planar O site exhibit a dramatic decrease. We interpret these results as microscopic evidence for a spatially inhomogeneous charge distribution, where the NMR signal from O sites in the domain walls of the spin density modulation are wiped out due to large hyperfine fields, and the remaining signal arises from the intervening Mott insulating regions.

Magnon-hole scattering and charge order in Sr14-xCaxCu24O41.

The magnon thermal conductivity kappa(mag) of the hole-doped spin ladders in Sr14-xCaxCu24O41 has been investigated at low doping levels x. The analysis of kappa(mag) reveals a strong doping and temperature dependence of the magnon mean free path l(mag), which is a local probe for the interaction of magnons with the doped holes in the ladders. In particular, this novel approach to studying charge degrees of freedom via spin excitations shows that charge ordering of the holes in the ladders leads to a freezing out of magnon-hole scattering processes.

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

The magnetic order of (La,Eu)2-xSrxCuO4 ( x

Inhomogeneous low frequency spin dynamics in La(1.65)Eu(0.2)Sr(0.15)CuO(4).

We report Cu and La nuclear magnetic resonance measurements in the title compound that reveal an inhomogeneous glassy behavior of the spin dynamics. A low temperature peak in the La spin lattice relaxation rate and the "wipeout" of Cu intensity both arise from these slow electronic spin fluctuations that reveal a distribution of activation energies. Inhomogeneous slowing of spin fluctuations appears to be a general feature of doped lanthanum cuprate.