Evolution of the electronic excitation spectrum with strongly diminishing hole-density in superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}

A complete knowledge of its excitation spectrum could greatly benefit efforts to understand the unusual form of superconductivity occurring in the lightly hole-doped copper-oxides. Here we use tunnelling spectroscopy to measure the T\to 0 spectrum of electronic excitations N(E) over a wide range of hole-density p in superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+/delta}. We introduce a parameterization for N(E) based upon an anisotropic energy-gap /Delta (\vec k)=/Delta_{1}(Cos(k_{x})-Cos(k_{y}))/2 plus an effective scattering rate which varies linearly with energy /Gamma_{2}(E) . We demonstrate that this form of N(E) allows successful fitting of differential tunnelling conductance spectra throughout much of the Bi_{2}Sr_{2}CaCu_{2}O_{8+/delta} phase diagram. The resulting average /Delta_{1} values rise with falling p along the familiar trajectory of excitations to the 'pseudogap' energy, while the key scattering rate /Gamma_{2}^{*}=/Gamma_{2}(E=/Delta_{1}) increases from below ~1meV to a value approaching 25meV as the system is underdoped from p~16% to p<10%. Thus, a single, particle-hole symmetric, anisotropic energy-gap, in combination with a strongly energy and doping dependent effective scattering rate, can describe the spectra without recourse to another ordered state. Nevertheless we also observe two distinct and diverging energy scales in the system: the energy-gap maximum /Delta_{1} and a lower energy scale /Delta_{0} separating the spatially homogeneous and heterogeneous electronic structures.Comment: High resolution version available at: http://people.ccmr.cornell.edu/~jcdavis/files/Alldredge-condmat08010087-highres.pd

Effect of large strain on dielectric and ferroelectric properties of Ba0.5Sr0.5TiO3 thin films

BaxSr1−xTiO3 is ideally suited as a tunable medium for radio frequency passive component. In this context we have studied the effect of biaxial strain on the dielectric and ferroelectricproperties of Ba0.5Sr0.5TiO3thin filmsgrown epitaxially on SrTiO3 (001) substrates. The lattice parameters of the films determined by high-resolution x-ray diffraction with the thickness varying from 160 to 1000 nm indicated large biaxial compressive strain which decreased from 2.54% to 1.14% with increasing film thickness. Temperature-dependent measurements of the dielectric constant in our strained Ba0.5Sr0.5TiO3thin films revealed a significant increase in the Curie temperature as the film thickness is below 500 nm. Enhanced ferroelectric behavior was observed for highly strained films with a remanent polarization of 15 μC/cm2 in the 160-nm-thick layer. However, the thick films(≥500 nm) exhibited weak temperature dependence of the dielectric constant without any pronounced peak corresponding to the Curie temperature, which may suggest inhomogeneous strain distribution in the thick films

Coagulation and fragmentation dynamics of inertial particles

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process in time-periodic incompressible flows. We find that this process approaches an asymptotic, dynamical steady state where the average number of particles of each size is roughly constant. We compare the steady-state size distributions corresponding to two fragmentation mechanisms and for different flows and find that the steady state is mostly independent of the coagulation process. While collision rates determine the transient behavior, fragmentation determines the steady state. For example, for fragmentation due to shear, flows that have very different local particle concentrations can result in similar particle size distributions if the temporal or spatial variation of shear forces is similar.Comment: 8 pages, 7 figure

A momentum-dependent perspective on quasiparticle interference in Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}

Angle Resolved Photoemission Spectroscopy (ARPES) probes the momentum-space electronic structure of materials, and provides invaluable information about the high-temperature superconducting cuprates. Likewise, the cuprate real-space, inhomogeneous electronic structure is elucidated by Scanning Tunneling Spectroscopy (STS). Recently, STS has exploited quasiparticle interference (QPI) - wave-like electrons scattering off impurities to produce periodic interference patterns - to infer properties of the QP in momentum-space. Surprisingly, some interference peaks in Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} (Bi-2212) are absent beyond the antiferromagnetic (AF) zone boundary, implying the dominance of particular scattering process. Here, we show that ARPES sees no evidence of quasiparticle (QP) extinction: QP-like peaks are measured everywhere on the Fermi surface, evolving smoothly across the AF zone boundary. This apparent contradiction stems from different natures of single-particle (ARPES) and two-particle (STS) processes underlying these probes. Using a simple model, we demonstrate extinction of QPI without implying the loss of QP beyond the AF zone boundary

Spectroscopic scanning tunneling microscopy insights into Fe-based superconductors

In the first three years since the discovery of Fe-based high Tc superconductors, scanning tunneling microscopy (STM) and spectroscopy have shed light on three important questions. First, STM has demonstrated the complexity of the pairing symmetry in Fe-based materials. Phase-sensitive quasiparticle interference (QPI) imaging and low temperature spectroscopy have shown that the pairing order parameter varies from nodal to nodeless s\pm within a single family, FeTe1-xSex. Second, STM has imaged C4 -> C2 symmetry breaking in the electronic states of both parent and superconducting materials. As a local probe, STM is in a strong position to understand the interactions between these broken symmetry states and superconductivity. Finally, STM has been used to image the vortex state, giving insights into the technical problem of vortex pinning, and the fundamental problem of the competing states introduced when superconductivity is locally quenched by a magnetic field. Here we give a pedagogical introduction to STM and QPI imaging, discuss the specific challenges associated with extracting bulk properties from the study of surfaces, and report on progress made in understanding Fe-based superconductors using STM techniques.Comment: 36 pages, 23 figures, 229 reference

Mechanistic origins of variability in phytoplankton dynamics. Part II: analysis of mesocosm blooms under climate change scenarios

Driving factors of phytoplankton spring blooms have been discussed since long, but rarely analyzed quantitatively. Here, we use a mechanistic size-based ecosystem model to reconstruct observations made during the Kiel mesocosm experiments (2005–2006). The model accurately hindcasts highly variable bloom developments including community shifts in cell size. Under low light, phytoplankton dynamics was mostly controlled by selective mesozooplankton grazing. Selective grazing also explains initial dominance of large diatoms under high light conditions. All blooms were mainly terminated by aggregation and sedimentation. Allometries in nutrient uptake capabilities led to a delayed, post-bloom dominance of small species. In general, biomass and trait dynamics revealed many mutual dependencies, while growth factors decoupled from the respective selective forces. A size shift induced by one factor often changed the growth dependency on other factors. Within climate change scenarios, these indirect effects produced large sensitivities of ecosystem fluxes to the size distribution of winter phytoplankton. These sensitivities exceeded those found for changes in vertical mixing, whereas temperature changes only had minimal impacts

How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+d

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the enigmatic 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles -- the excitations resulting from the breaking of Cooper pairs -- should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi2Sr2CaCu2O8+d in r-space and k-space simultaneously. We find that although the low energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy independent fashion. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.Comment: This is author's version. See the Nature website for the published versio

Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states

In the high-transition-temperature (high-Tc) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced1. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within CuO2 unit cell. We analyze spectroscopic-imaging scanning tunneling microscope images of the intra-unit-cell states in underdoped Bi2Sr2CaCu2O8+{\delta} and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90o -rotational symmetry within every CuO2 unit cell.Comment: See the Nature website for the published version. High-resolution version of figures, supplementary information and supplementary movies are available at http://eunahkim.ccmr.cornell.edu/KimGroup/highlights.htm