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In this study we introduce a new class of experimental designs. In a classical randomized controlled trial (RCT), or A/B test, a randomly selected subset of a population of units (e.g., individuals, plots of land, or experiences) is assigned to a treatment (treatment A), and the remainder of the population is assigned to the control treatment (treatment B). The difference in average outcome by treatment group is an estimate of the average effect of the treatment. However, motivating our study, the setting for modern experiments is often different, with the outcomes and treatment assignments indexed by multiple populations. For example, outcomes may be indexed by buyers and sellers, by content creators and subscribers, by drivers and riders, or by travelers and airlines and travel agents, with treatments potentially varying across these indices. Spillovers or interference can arise from interactions between units across populations. For example, sellers' behavior may depend on buyers' treatment assignment, or vice versa. This can invalidate the simple comparison of means as an estimator for the average effect of the treatment in classical RCTs. We propose new experiment designs for settings in which multiple populations interact. We show how these designs allow us to study questions about interference that cannot be answered by classical randomized experiments. Finally, we develop new statistical methods for analyzing these Multiple Randomization Designs., Comment: 57 pages, 7 figures

We present neutron scattering studies of the inter-planar correlations in the high-temperature superconductor La1.88Sr0.12CuO4 (T_c=27 K). The correlations are studied both in a magnetic field applied perpendicular to the CuO2 planes, and in zero field under different cooling conditions. We find that the effect of the magnetic field is to increase the magnetic scattering signal at all values of the out-of-plane wave vector L, indicating an overall increase of the magnetic moments. In addition, weak correlations between the copper oxide planes develop in the presence of a magnetic field. This effect is not taken into account in previous reports on the field effect of magnetic scattering, since usually only L~0 is probed. Interestingly, the results of quench-cooling the sample are similar to those obtained by applying a magnetic field. Finally, a small variation of the incommensurate peak position as a function of L provides evidence that the incommensurate signal is twinned with the dominating and sub-dominant twin displaying peaks at even or odd L, respectively., Comment: 8 pages, 5 figures

We present a volume-sensitive high-energy x-ray diffraction study of the underdoped cuprate high temperature superconductor La2-xSrxCuO4 (x = 0.12, Tc=27 K) in applied magnetic field. Bulk short-range charge stripe order with propagation vector q_ch = (0.231, 0, 0.5) is demonstrated to exist below T_ch = 85(10) K and shown to compete with superconductivity. We argue that bulk charge ordering arises from fluctuating stripes that become pinned near boundaries between orthorhombic twin domains., Comment: 5 pages, 4 figures. To be submitted to Phys. Rev. Lett

We report the observation of a bulk charge modulation in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO) with a characteristic in-plane wave-vector of (0.236, $\pm \delta$), with $\delta$=0.011 r.l.u. The transverse shift of the ordering wave-vector indicates the presence of rotated charge-stripe ordering, demonstrating that the charge ordering is not pinned to the Cu-O bond direction. On cooling through the superconducting transition, we find an abrupt change in the growth of the charge correlations and a suppression of the charge order parameter indicating competition between the two orderings. Orthorhombic LSCO thus helps bridge the apparent disparities between the behavior previously observed in the tetragonal "214" cuprates and the orthorhombic yttrium and bismuth-based cuprates and thus lends strong support to the idea that there is a common motif to charge order in all cuprate families., Comment: 6 pages, 4 figues

We present high-resolution triple-axis neutron scattering studies of the high-temperature superconductor La1.88Sr0.12CuO4 (Tc=27 K). The temperature dependence of the low-energy incommensurate magnetic fluctuations reveals distinctly glassy features. The glassiness is confirmed by the difference between the ordering temperature TN ~ Tc inferred from elastic neutron scattering and the freezing temperature Tf ~ 11 K obtained from muon spin rotation studies. The magnetic field independence of the observed excitation spectrum as well as the observation of a partial suppression of magnetic spectral weight below 0.75 meV for temperatures smaller than Tf, indicate that the stripe frozen state is capable of supporting a spin anisotropy gap, of a magnitude similar to that observed in the spin and charge stripe ordered ground state of La1.875Ba0.125CuO4. The difference between TN and Tf implies that the significant enhancement in a magnetic field of nominally elastic incommensurate scattering is caused by strictly in-elastic scattering -- at least in the temperature range between Tf and Tc -- which is not resolved in the present experiment. Combining the results obtained from our study of La1.88Sr0.12CuO4 with a critical reappraisal of published neutron scattering work on samples with chemical composition close to p=0.12, where local probes indicate a sharp maximum in Tf(p), we arrive at the view that the low-energy fluctuations are strongly dependent on composition in this regime, with anisotropy gaps dominating only sufficiently close to p=0.12 and superconducting spin gaps dominating elsewhere., Comment: 8 pages, 4 figures

The magnetic field and temperature dependence of the electronic specific heat $C_{\rm el}$ have been systematically investigated in $\rm La_{2-{\it x}}Sr_{\it x}Cu_{1-{\it y}}Ni_{\it y}O_4$ (LSCNO) in order to study Ni-impurity effects on the superconducting (SC) gap. In LSCNO with $x$=0.15 and $y$=0.015, the value of $\gamma$ ($\equiv C_{\rm el}/T$) at $T$=0 K, $\gamma_0$, is enhanced under the magnetic field $H$ applied along the $\bm c$-axis. The increment of $\gamma_0$, $\Delta \gamma_0$, follows the Volovik relation $\Delta \gamma_0$=$A\sqrt{H}$, characteristic of the SC gap with line nodes, with prefactor $A$ similar to that of a pure sample. The $C_{\rm el}/T$ vs. $T$ curve under $H$=0 shows a d-wave-like SC anomaly with an abrupt increase at $T_{\rm c}$ and $T$-linear dependence at $T$$\ll$$T_{\rm c}$, although the $\gamma_0$-value in the $C_{\rm el}/T$ vs. $T$ curve increases with increasing Ni concentrations. Interestingly, as the SC part of $C_{\rm el}/T$, $C_{\rm el}/T$$-$$\gamma_0$$\equiv$$\gamma_{\rm s}$, decreases in LSCNO, $T_{\rm c}$ is reduced in proportion to the decrease of $\gamma_{\rm s}$. These findings can be explained phenomenologically by a simple model in which Ni impurities bring about strong pair breaking at the edges of the coherent nodal part of the Fermi surface but in the vicinity of the nodes of the SC gap. The reduction of the SC condensation energy $U_0$ in LSCNO, evaluated from $C_{\rm el}$ at $T$ {0.3em}\raisebox{0.4ex}{$<$} {-0.75em}\raisebox{-.7ex}{$\sim$} {0.3em}$T_{\rm c}$, is also understood by the same model., Comment: 7 pages, 6 figures, accepted in Phys. Rev. B

We use small angle neutron scattering to study the superconducting vortex lattice in La$_{2-x}$Sr$_x$CuO$_4$ as a function of doping and magnetic field. We show that near optimally doping the vortex lattice coordination and the superconducting coherence length $\xi$ are controlled by a van-Hove singularity crossing the Fermi level near the Brillouin zone boundary. The vortex lattice properties change dramatically as a spin-density-wave instability is approached upon underdoping. The Bragg glass paradigm provides a good description of this regime and suggests that SDW order acts as a novel source of disorder on the vortex lattice., Comment: Accepted in Phys. Rev. B

In the present work, scanning tunneling microscopy/spectroscopy (STM/STS) measurements were carried out on underdoped $\rm Bi_2Sr_{2-{\it x}}La_{\it x}CuO_{6+\delta}$ and $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$ to clarify the origin of the pseudogap, in particular, the inhomogeneous large pseudogap. The nodal part of a d-wave pairing gap, which is under no influence of the inhomogeneous large pseudogap, was also examined by relating the homogeneous bottom part of the STS gap to a nodal d-wave gap in momentum space. We report that the inhomogeneous large pseudogap in the antinodal region links to a two-dimensional electronic charge order, and that the gap size of the nodal d-wave part $\rm {\Delta}_{sc}$ scales with the superconducting critical temperature $\rm {\it T}_c$ in the pseudogap regime., Comment: 8 pages, 10 figures

Inelastic neutron-scattering experiments on the high-temperature superconductor La$_{1.855}$Sr$_{0.145}$CuO$_{4}$ reveal a magnetic excitation gap $\Delta$ that decreases continuously upon application of a magnetic field perpendicular to the CuO$_2$ planes. The gap vanishes at the critical field required to induce long-range incommensurate antiferromagnetic order, providing compelling evidence for a field-induced soft-mode driven quantum phase transition.

Angle-resolved photoemission on underdoped La$_{1.895}$Sr$_{0.105}$CuO$_4$ reveals that in the pseudogap phase, the dispersion has two branches located above and below the Fermi level with a minimum at the Fermi momentum. This is characteristic of the Bogoliubov dispersion in the superconducting state. We also observe that the superconducting and pseudogaps have the same d-wave form with the same amplitude. Our observations provide direct evidence for preformed Cooper pairs, implying that the pseudogap phase is a precursor to superconductivity.

We report an angle resolved photoemission study of the electronic structure of the pseudogap state in \NdLSCO ($T_c<7$ K). Two opposite dispersing Fermi arcs are the main result of this study. The several scenarios that can explain this observation are discussed., Comment: A high-resolution version can be found at http://lns.web.psi.ch/lns/download/Pockets/arXiv.pdf

We report the ultra-fast optical response of quasi-particles (QPs) in both the pseudogap (PG) and superconducting (SC) states of underdoped (UD) Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) single crystal measured with the time-resolved pump-probe technique. At a probe energy $\hbar\omega_{pr}$=1.55 eV, it is found that the reflectivity change $\Delta$R/R changes its sign at exactly $T_{c}$, which allows the direct separation of the charge dynamics of PG and SC QPs. Further systematic investigations indicate that the transient signals associated with PG and SC QPs depend on the probe beam energy and polarization. By tuning them below $T_{c}$ two distinct components can be detected simultaneously, providing evidence for the coexistence of PG and SC QPs., Comment: 4 figures. One report on the ultrast dynamics of quasiparticles in underdoped Bi2Sr2CaCu2O8

We present angle-resolved photoelectron spectroscopy data probing the electronic structure of the Nd-substituted high-$T_c$ cuprate La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_4$ (Nd-LSCO). Data have been acquired at low and high photon energies, $h\nu$ = 55 and 500 eV, respectively. Earlier comparable low-energy studies of La$_{1.4-x}$Nd$_{0.6}$Sr$_{x}$CuO$_4$ ($x = 0.10, 0.12, 0.15$) have shown strongly suppressed photoemission intensity, or absence thereof, in large parts of the Brillouin zone. Contrary to these findings we observe spectral weight at all points along the entire Fermi surface contour at low and high photon energies. No signs of strong charge modulations are found. At high photon energy, the Fermi surface shows obvious differences in shape as compared to the low-energy results presented here and in similar studies. The observed difference in shape and the high bulk-sensitivity at this photon energy suggest intrinsic electronic structure differences between the surface and bulk regions., Comment: 6 pages, 4 figures

We report the results of a combined muon spin rotation and neutron scattering study on La2-xSrxCuO4 in the vicinity of the so-called 1/8-anomaly. Application of a magnetic field drives the system towards a magnetically ordered spin-density-wave state, which is fully developed at 1/8 doping. The results are discussed in terms of competition between antiferromagnetic and superconducting order parameters., Comment: 4 pages, 4 figures

An angle-resolved photoemission study of the scattering rate in the superconducting phase of the high-temperature superconductor \LSCO\ with $x=0.145$ and $x=0.17$, as a function of binding energy and momentum, is presented. We observe that the scattering rate scales linearly with binding energy up to the high-energy scale $E_1\sim0.4$ eV. The scattering rate is found to be strongly anisotropic, with a minimum along the (0,0)-($\pi,\pi$) direction. A possible connection to a quantum-critical point is discussed., Comment: Final version published in PRB

We present angle-resolved photoemission spectroscopy (ARPES) data on moderately underdoped La$_{1.855}$Sr$_{0.145}$CuO$_4$ at temperatures below and above the superconducting transition temperature. Unlike previous studies of this material, we observe sharp spectral peaks along the entire underlying Fermi surface in the superconducting state. These peaks trace out an energy gap that follows a simple {\it d}-wave form, with a maximum superconducting gap of 14 meV. Our results are consistent with a single gap picture for the cuprates. Furthermore our data on the even more underdoped sample La$_{1.895}$Sr$_{0.105}$CuO$_4$ also show sharp spectral peaks, even at the antinode, with a maximum superconducting gap of 26 meV., Comment: Accepted by Phys. Rev. Lett

Scanning tunneling microscopy/spectroscopy is used to examine the $4a$$\times$$4a$ electronic charge order (CO) in the pseudogap (PG) state above {\it T}$_{\rm c}$ on Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$. It is demonstrated that the static CO develops markedly in the inhomogeneous PG state, while it is very weak in the homogeneous PG state. We suggest that this static CO, which is considered to be stabilized by the pinning of the dynamically fluctuating CO, will remain below {\it T}$_{\rm c}$, together with the inhomogeneous gap structure, and coexist with the superconductivity., Comment: 4 pages, 4figures, submitted to Physical Review Letters

High-resolution neutron inelastic scattering experiments in applied magnetic fields have been performed on La$_{1.895}$Sr$_{0.105}$CuO$_{4}$ (LSCO). In zero field, the temperature dependence of the low-energy peak intensity at the incommensurate momentum-transfer $\mathbf{Q}^{\ }_{\mathrm{IC}}=(0.5,0.5\pm\delta,0),(0.5\pm\delta,0.5,0)$ exhibits an anomaly at the superconducting $T^{\}_{c}$ which broadens and shifts to lower temperature upon the application of a magnetic field along the c-axis. A field-induced enhancement of the spectral weight is observed, but only at finite energy transfers and in an intermediate temperature range. These observations establish the opening of a strongly downward renormalized spin gap in the underdoped regime of LSCO. This behavior contrasts with the observed doping dependence of most electronic energy features., Comment: accepted for publication in Phys. Rev. Lett

The existence of coherent quasiparticles near the Fermi energy in the low temperature state of high-temperature superconductors has been well established by angle-resolved photoemission spectroscopy (ARPES). This technique directly probes the momentum-resolved electronic excitation spectrum of the CuO$_2$ planes. We present a study of close to optimally doped La$_{1.83}$Sr$_{0.17}$CuO$_4$ in the superconducting state and report an abrupt change in the quasiparticle spectral function, as we follow the dispersion of the ARPES signal from the Fermi energy up to 0.6 eV. The interruption in the quasiparticle dispersion separates coherent quasiparticle peaks at low energies from broad incoherent excitations at high energies. We find that the boundary between these low-energy and high-energy features exhibits a cosine-shaped momentum dependence, reminiscent of the superconducting d-wave gap. Further intriguing similarities between characteristics of the incoherent excitations and quasiparticle properties (lifetime, Fermi arcs) suggest a close relation between the electronic response at high and low energies in cuprate superconductors.

Using polarized neutron scattering we establish that the magnetic order in La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_4$ is either (i) one dimensionally modulated and collinear, consistent with the stripe model or (ii) two dimensionally modulated with a novel noncollinear structure. The measurements rule out a number of alternative models characterized by 2D electronic order or 1D helical spin order. The low-energy spin excitations are found to be primarily transversely polarized relative to the stripe ordered state, consistent with conventional spin waves., Comment: 4 pages, 4 figures. Final version, published in Phys. Rev. Lett

We performed STM/STS measurements on underdoped Bi2212 crystals with doping levels p ~ 0.11, ~ 0.13 and ~ 0.14 to examine the nature of the nondispersive 4a X 4a charge order in the superconducting state at T << Tc. The charge order appears conspicuously within the pairing gap, and low doping tends to favor the charge order. We point out the possibility that the 4a X 4a charge order will be dynamical in itself, and pinned down over regions with effective pinning centers. The pinned 4a X 4a charge order is closely related to the spatially inhomogeneous pairing gap structure, which has often been reported in STS measurements on high-Tc cuprates., Comment: 12 pages, 16 figures, to be published in Phys. Rev. B

We performed low-bias STM measurements on underdoped Bi2212 crystals, and confirmed that a two-dimensional (2D) superstructure with a periodicity of four lattice constants (4a) is formed within the Cu-O plane at T

To examine the so-called small pseudogap and the superconducting (SC) condensation energy U(0), the electronic specific heat Cel was measured on La_{2-x}Sr_{x}CuO_{4} up to ~120K. In samples with doping level p (=x) less than ~0.2, small pseudogap behavior appears in the \gamma (=Cel/T) vs. T curve around the mean-field critical temperature for a d-wave superconductor Tco (=2*\Delta_{0}/(4~5)k_B), where \Delta_{0} is the maximum gap at T<

Our inelastic neutron scattering experiments of the spin excitations in the slightly overdoped La{1.83}Sr{0.17}CuO{4} compound show that, under the application of a magnetic field of 5 Tesla, the low-temperature susceptibility undergoes a weight redistribution centered at the spin-gap energy. Furthermore, by comparing the temperature dependence of the neutron data with ac-susceptibility and magnetization measurements, we conclude that the filling in of the spin gap tracks the irreversibility/melting temperature rather than Tc2, which indicates an unusual interplay between the magnetic vortices and the spin excitations even in the slightly overdoped regime of high-temperature superconductors., Comment: 7 pages, including 5 figures

On the basis of the tunneling spectra of Bi2212, we report that there exist two kinds of pseudogaps; one with a characteristic energy comparable to the superconducting (SC) gap and another one that is 3 to 4 times larger. The smaller energy-scale pseudogap (SPG) develops progressively below temperature T*, which nearly scales with the SC gap amplitude D0, in addition to the larger energy-scale pseudogap (LPG). The SPG smoothly develops into the SC-state gap with no tendency to close at Tc., Comment: 7 pages, 6 figures, reference for figures: http://mary.sci.hokudai.ac.jp/LABS/kouatsu/egefigure/index.html