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Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing which can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here we use SJTM to visualize the interplay of PDW and DSC states in Bi2Sr2CaCu2O8+x at a carrier density where the charge density wave (CDW) modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed (Lozano et al, PHYSICAL REVIEW B 103, L020502 (2021)). Taken in combination, these data indicate that the PDW in Bi2Sr2CaCu2O8+x is a vestigial nematic pair density wave state (J. Wardh and M. Granath arXiv:2203.08250v1)., Comment: 15 pages, 4 figures

One of the most widely discussed features of the cuprate high Tc superconductors is the presence of a pseudogap in the normal state. Recent transport and specific heat measurements have revealed an abrupt transition at the pseudogap critical point, denoted p*, characterized by a drop in carrier density and a strong mass enhancement. In order to give more details about this transition at p*, we performed low-temperature infrared spectroscopy in the normal state of cuprate superconductors La2-xSrxCuO4 (LSCO) and La1.8-xEu0.2SrxCuO4 (Eu-LSCO) for doping contents across the pseudogap critical point p* (from p = 0.12 to 0.24). Through the complex optical conductivity we can extract the spectral weight, K*, of the narrow Drude peak due the coherent motion of the quasi-particles, and the spectral weight enclosed inside the mid-infrared (MIR) band, KMIR, caused by coupling of the quasi-particles to collective excitations of the many-body system. K* is smaller than a third of the value predicted by band calculations, and KMIR forms a dome as a function of doping. We observe a smooth doping dependence of K* through p*, and demonstrate that this is consistent with the observed doping dependence of the carrier density and the mass enhancement. We argue that the superconducting dome is the result of the confluence of two opposite trends, namely the increase of the density of the quasi-particles and the decrease of their coupling to the collective excitations as a function of doping., Comment: 8 pages, 4 figures

The elementary CuO2 plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO5 pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate $t/{\hbar}$ and across the charge-transfer energy gap E, generate 'superexchange' spin-spin interactions of energy $J\approx4t^4/E^3$ in an antiferromagnetic correlated-insulator state. However, Hole doping the CuO2 plane converts this into a very high temperature superconducting state whose electron-pairing is exceptional. A leading proposal for the mechanism of this intense electron-pairing is that, while hole doping destroys magnetic order it preserves pair-forming superexchange interactions governed by the charge-transfer energy scale E. To explore this hypothesis directly at atomic-scale, we combine single-electron and electron-pair (Josephson) scanning tunneling microscopy to visualize the interplay of E and the electron-pair density nP in ${Bi_2Sr_2CaCu_2O_{8+x}}$. The responses of both E and nP to alterations in the distance {\delta} between planar Cu and apical O atoms are then determined. These data reveal the empirical crux of strongly correlated superconductivity in CuO2, the response of the electron-pair condensate to varying the charge transfer energy. Concurrence of predictions from strong-correlation theory for hole-doped charge-transfer insulators with these observations, indicates that charge-transfer superexchange is the electron-pairing mechanism of superconductive ${Bi_2Sr_2CaCu_2O_{8+x}}$., Comment: 23 pages, 5 figures

Muon detectors and neutron monitors were recently installed at Syowa Station, in the Antarctic, to observe different types of secondary particles resulting from cosmic ray interactions simultaneously from the same location. Continuing observations will give new insight into the response of muon detectors to atmospheric and geomagnetic effects. Operation began in February, 2018 and the system has been stable with a duty-cycle exceeding 94%. Muon data shows a clear seasonal variation, which is expected from the atmospheric temperature effect. We verified successful operation by showing that the muon and neutron data are consistent with those from other locations by comparing intensity variations during a space weather event. We have established a web page to make real time data available with interactive graphics (http://polaris.nipr.ac.jp/~cosmicrays/)., Comment: Accepted for publication in the Journal of Space Weather and Space Climate

Hybridization of Bogoliubov quasiparticles (BQPs) between the CuO$_2$ layers in the triple-layer cuprate high-temperature superconductor Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ is studied by angle-resolved photoemission spectroscopy (ARPES). In the superconducting state, an anti-crossing gap opens between the outer- and inner-BQP bands, which we attribute primarily to interlayer single-particle hopping with possible contributions from interlayer Cooper pairing. We find that the $d$-wave superconducting gap of both BQP bands smoothly develops with momentum without abrupt jump in contrast to a previous ARPES study. Hybridization between the BQPs also gradually increases in going from the off-nodal to the anti-nodal region, which is explained by the momentum-dependence of the interlayer single-particle hopping. As possible mechanisms for the enhancement of the superconducting transition temperature, the hybridization between the BQPs, as well as the combination of phonon modes of the triple CuO$_2$ layers and spin fluctuations are discussed., Comment: 14 pages, 10 figures

Deep neural networks (DNNs) suffer from noisy-labeled data because of the risk of overfitting. To avoid the risk, in this paper, we propose a novel DNN training method with sample selection based on adaptive k-set selection, which selects k (< n) clean sample candidates from the whole n noisy training samples at each epoch. It has a strong advantage of guaranteeing the performance of the selection theoretically. Roughly speaking, a regret, which is defined by the difference between the actual selection and the best selection, of the proposed method is theoretically bounded, even though the best selection is unknown until the end of all epochs. The experimental results on multiple noisy-labeled datasets demonstrate that our sample selection strategy works effectively in the DNN training; in fact, the proposed method achieved the best or the second-best performance among state-of-the-art methods, while requiring a significantly lower computational cost. The code is available at https://github.com/songheony/TAkS.

The defining characteristic of hole-doped cuprates is $d$-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity (D. F. Agterberg et al., Annual Review of Condensed Matter Physics 11, 231 (2020)). Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, $d$-symmetry form factor, pair density wave (PDW) state coexisting with $d$-wave superconductivity (DSC). From this PDW+DSC model, the atomically-resolved density of Bogoliubov quasiparticle states N(r,E) is predicted at the terminal BiO surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ and compared with high-precision electronic visualization experiments using spectroscopic imaging STM. The PDW+DSC model predictions include the intra-unit-cell structure and periodic modulations of N(r,E), the modulations of the coherence peak energy $\Delta_p$ (r), and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space (q-space). Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi$_2$Sr$_2$CaCu$_2$O$_8$ does contain a PDW+DSC state. Moreover, in the model the PDW+DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ~ 19% occurs due to disappearance of this PDW.

Essentials of the scientific discovery process have remained largely unchanged for centuries: systematic human observation of natural phenomena is used to form hypotheses that, when validated through experimentation, are generalized into established scientific theory. Today, however, we face major challenges because automated instrumentation and large-scale data acquisition are generating data sets of such volume and complexity as to defy human analysis. Radically different scientific approaches are needed, with machine learning (ML) showing great promise, not least for materials science research. Hence, given recent advances in ML analysis of synthetic data representing electronic quantum matter (EQM), the next challenge is for ML to engage equivalently with experimental data. For example, atomic-scale visualization of EQM yields arrays of complex electronic structure images, that frequently elude effective analyses. Here we report development and training of an array of artificial neural networks (ANN) designed to recognize different types of hypothesized order hidden in EQM image-arrays. These ANNs are used to analyze an experimentally-derived EQM image archive from carrier-doped cuprate Mott insulators. Throughout these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs find these phenomena to be unidirectional, revealing a coincident nematic EQM state. Strong-coupling theories of electronic liquid crystals are congruent with all these observations., Comment: 44 pages, 15 figures

We have investigated the superconducting gap of optimally doped Ba(Fe$_{0.65}$Ru$_{0.35}$)$_2$As$_2$ by angle-resolved photoemission spectroscopy (APRES) using bulk-sensitive 7 eV laser and synchrotron radiation. It was found that the gap is isotropic in the $k_x$-$k_y$ plane both on the electron and hole Fermi surfaces (FSs). The gap magnitudes of two resolved hole FSs show similar $k_z$ dependences and decrease as $k_z$ approaches $\sim$ 2$\pi$/$c$ (i.e., around the Z point) unlike the other Fe-based superconductors reported so far, where the superconducting gap of only one hole FS shows a strong $k_z$ dependence. This unique gap structure can be understood in the scenario that the $d_{z^2}$ orbital character is mixed into both hole FSs due to the finite spin-orbit coupling between almost degenerate FSs and is reproduced by calculations within the random phase approximation including the spin-orbit coupling.

Theories based upon strong real space (r-space) electron electron interactions have long predicted that unidirectional charge density modulations (CDM) with four unit cell (4$a_0$) periodicity should occur in the hole doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector $Q_A$ of the CDM to evolve continuously as if driven primarily by momentum space (k-space) effects. Here we introduce phase resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this new technique reveals a virtually doping independent locking of the local CDM wavevector at $|Q_0|=2\pi/4a_0$ throughout the underdoped phase diagram of the canonical cuprate $Bi_2Sr_2CaCu_2O_8$. These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi surface) based picture of the cuprate CDM but are consistent with strong coupling r-space based theories. Our findings imply that it is the latter that provide the intrinsic organizational principle for the cuprate CDM state.

We investigate the in-plane anisotropy of Fe 3d orbitals occurring in a wide temperature and composition range of BaFe2(As1-xPx)2 system. By employing the angle-resolved photoemission spectroscopy, the lifting of degeneracy in dxz and dyz orbitals at the Brillouin zone corners can be obtained as a measure of the orbital anisotropy. In the underdoped regime, it starts to evolve on cooling from high temperatures above both antiferromagnetic and orthorhombic transitions. With increasing x, it well survives into the superconducting regime, but gradually gets suppressed and finally disappears around the non-superconducting transition (x = 0.7). The observed spontaneous in-plane orbital anisotropy, possibly coupled with anisotropic lattice and magnetic fluctuations, implies the rotational-symmetry broken electronic state working as the stage for the superconductivity in BaFe2(As1-xPx)2.

The quantum condensate of Cooper-pairs forming a superconductor was originally conceived to be translationally invariant. In theory, however, pairs can exist with finite momentum $Q$ and thereby generate states with spatially modulating Cooper-pair density. While never observed directly in any superconductor, such a state has been created in ultra-cold $^{6}$Li gas. It is now widely hypothesized that the cuprate pseudogap phase contains such a 'pair density wave' (PDW) state. Here we use nanometer resolution scanned Josephson tunneling microscopy (SJTM) to image Cooper-pair tunneling from a $d$-wave superconducting STM tip to the condensate of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. Condensate visualization capabilities are demonstrated directly using the Cooper-pair density variations surrounding Zn impurity atoms and at the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ crystal-supermodulation. Then, by using Fourier analysis of SJTM images, we discover the direct signature of a Cooper-pair density modulation at wavevectors $Q_{p} \approx (0.25,0)2\pi / a_{0}$;$(0,0.25)2\pi / a_{0}$ in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. The amplitude of these modulations is ~5% of the homogenous condensate density and their form factor exhibits primarily $s$/$s'$-symmetry. This phenomenology is expected within Ginzburg-Landau theory when a charge density wave with $d$-symmetry form factor and wave vector $Q_{c}=Q_{p}$ coexists with a homogeneous $d$-symmetry superconductor ; it is also encompassed by several contemporary microscopic theories for the pseudogap phase.

We have performed an angle-resolved photoemission study of the nodal quasi-particle spectra of the high-Tc cuprate tri-layer Bi2Sr2Ca2Cu3O10+d (Tc~ 110 K). The spectral weight Z of the nodal quasi-particle increases with decreasing temperature across the Tc. Such a temperature dependence is qualitatively similar to that of the coherence peak intensity in the anti nodal region of various high-Tc cuprates although the nodal spectral weight remains finite and large above Tc. We attribute this observation to the reduction of electron correlation strength in going from the normal metallic state to the superconducting state, a characteristic behavior of a superconductor with strong electron correlation., Comment: 13 pages, 5 figures

Recent studies establish that the cuprate pseudogap phase is susceptible at low temperatures to forming not only a $d$-symmetry superconducting (SC) state, but also a $d$-symmetry form factor (dFF) density wave (DW) state. The concurrent emergence of such distinct and unusual states from the pseudogap motivates theories that they are "intertwined" i.e derived from a quantum composite of dissimilar broken-symmetry orders. Some composite order theories predict that the balance between the different components can be altered, for example at superconducting vortex cores. Here, we introduce sublattice phase-resolved electronic structure imaging as a function of magnetic field and find robust dFF DW states induced at each vortex. They are predominantly unidirectional and co-oriented (nematic), exhibiting strong spatial-phase coherence. At each vortex we also detect the field-induced conversion of the SC to DW components and demonstrate that this occurs at precisely the eight momentum-space locations predicted in many composite order theories. These data provided direct microscopic evidence for the existence of composite order in the cuprates, and new indications of how the DW state becomes long-range ordered in high magnetic fields., Comment: Content, analysis and conclusions have been superseded by new and improved experimental data and analysis techniques. New results are reported in arXiv:1802.04673

Extensive research into high temperature superconducting cuprates is now focused upon identifying the relationship between the classic 'pseudogap' phenomenon$^{1,2}$ and the more recently investigated density wave state$^{3-13}$. This state always exhibits wave vector $Q$ parallel to the planar Cu-O-Cu bonds$^{4-13}$ along with a predominantly $d$-symmetry form factor$^{14-17}$ (dFF-DW). Finding its microscopic mechanism has now become a key objective$^{18-30}$ of this field. To accomplish this, one must identify the momentum-space ($k$-space) states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization$^{14}$ of electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy $\Delta_{1}$. Moreover, we demonstrate that the dFF-DW modulations at $E=-\Delta_{1}$ (filled states) occur with relative phase $\pi$ compared to those at $E=\Delta_{1}$ (empty states). Finally, we show that the dFF-DW $Q$ corresponds directly to scattering between the 'hot frontier' regions of $k$-space beyond which Bogoliubov quasiparticles cease to exist$^{31,32,33}$. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in $k$-space where the pseudogap opens.

The iron chalcogenide Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ on the Te-rich side is known to exhibit the strongest electron correlations among the Fe-based superconductors, and is non-superconducting for $x$ < 0.1. In order to understand the origin of such behaviors, we have performed ARPES studies of Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ ($x$ = 0, 0.1, 0.2, and 0.4). The obtained mass renormalization factors for different energy bands are qualitatively consistent with DFT + DMFT calculations. Our results provide evidence for strong orbital dependence of mass renormalization, and systematic data which help us to resolve inconsistencies with other experimental data. The unusually strong orbital dependence of mass renormalization in Te-rich Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ arises from the dominant contribution to the Fermi surface of the $d_{xy}$ band, which is the most strongly correlated and may contribute to the suppression of superconductivity.

We have studied the anisotropy in the in-plane resistivity and the electronic structure of isovalent Ru-substituted BaFe$_2$As$_2$ in the antiferromagnetic-orthorhombic phase using well-annealed crystals. The anisotropy in the residual resistivity component increases in proportional to the Ru dopant concentration, as in the case of Co-doped compounds. On the other hand, both the residual resistivity and the resistivity anisotropy induced by isovalent Ru substitution is found to be one order of magnitude smaller than those induced by heterovalent Co substitution. Combined with angle-resolved photoemission spectroscopy results, which show almost the same anisotropic band structure both for the parent and Ru-substituted compounds, we confirm the scenario that the anisotropy in the residual resistivity arises from anisotropic impurity scattering in the magneto-structurally ordered phase rather than directly from the anisotropic band structure of that phase., Comment: 13 pages, 4 figures

We systematically investigated the anisotropic in-plane resistivity of the iron telluride including three kinds of impurity atoms: excess Fe, Se substituted for Te, and Cu substituted for Fe. Sizable resistivity anisotropy was found in the magneto-structurally ordered phase whereas the sign is opposite ($\rho_a$ $>$ $\rho_b$, where the $b$-axis parameter is shorter than the $a$-axis one) to that observed in the transition-metal doped iron arsenides ($\rho_a$ $<$ $\rho_b$). On the other hand, our results demonstrate that the magnitude of the resistivity anisotropy in the iron tellurides is correlated with the amount of impurities, implying that the resistivity anisotropy originates from an exotic impurity effect like that in the iron arsenides. This suggests that the anisotropic carrier scattering by impurities is a universal phenomenon in the magneto-structurally ordered phase of the iron-based materials., Comment: 18 pages, 8 figures

The discovery of high temperature superconductivity in the cuprates in 1986 triggered a spectacular outpouring of creative and innovative scientific inquiry. Much has been learned over the ensuing 28 years about the novel forms of quantum matter that are exhibited in this strongly correlated electron system. This progress has been made possible by improvements in sample quality, coupled with the development and refinement of advanced experimental techniques. In part, avenues of inquiry have been motivated by theoretical developments, and in part new theoretical frameworks have been conceived to account for unanticipated experimental observations. An overall qualitative understanding of the nature of the superconducting state itself has been achieved, while profound unresolved issues have come into increasingly sharp focus concerning the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the "normal" state at elevated temperatures. New conceptual approaches, drawing from string theory, quantum information theory, and various numerically implemented approximate approaches to problems of strong correlations are being explored as ways to come to grips with this rich tableaux of interrelated phenomena.

We have observed a magnetic vortex lattice (VL) in BaFe2(As_{0.67}P_{0.33})2 (BFAP) single crystals by small-angle neutron scattering (SANS). With the field along the c-axis, a nearly isotropic hexagonal VL was formed in the field range from 1 to 16 T, which is a record for this technique in the pnictides, and no symmetry changes in the VL were observed. The temperature-dependence of the VL signal was measured and confirms the presence of (non d-wave) nodes in the superconducting gap structure for measurements at 5 T and below. The nodal effects were suppressed at high fields. At low fields, a VL reorientation transition was observed between 1 T and 3 T, with the VL orientation changing by 45{\deg}. Below 1 T, the VL structure was strongly affected by pinning and the diffraction pattern had a fourfold symmetry. We suggest that this (and possibly also the VL reorientation) is due to pinning to defects aligned with the crystal structure, rather than being intrinsic., Comment: 9 pages, 9 figures

The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO$_2$ unit-cell, segregating the results into three separate electronic structure images containing only the Cu sites (Cu(r)) and only the x/y-axis O sites (O$_x$(r) and O$_y$(r)). Phase resolved Fourier analysis reveals directly that the modulations in the O$_x$(r) and O$_y$(r) sublattice images consistently exhibit a relative phase of ${\pi}$. We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intra-unit-cell states that exhibit a predominantly d-symmetry form factor.

The existence of electronic symmetry breaking in the underdoped cuprates, and its disappearance with increased hole-density $p$, are now widely reported. However, the relationship between this transition and the momentum space ($\vec{k}$-space) electronic structure underpinning the superconductivity has not been established. Here we visualize the $\vec{Q}$=0 (intra-unit-cell) and $\vec{Q}\neq$0 (density wave) broken-symmetry states simultaneously with the coherent $\vec{k}$-space topology, for Bi$_2$Sr$_2$CaCu$_2$O$_{8+d}$ samples spanning the phase diagram 0.06$\leq p \leq$0.23. We show that the electronic symmetry breaking tendencies weaken with increasing $p$ and disappear close to $p_c$=0.19. Concomitantly, the coherent $\vec{k}$-space topology undergoes an abrupt transition, from arcs to closed contours, at the same $p_c$. These data reveal that the $\vec{k}$-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point., Comment: Journal reference added. Main materials: 13 pages, 4 figures. Supplementary materials: 18 pages, 9 figures

We performed a Laser angle-resolved photoemission spectroscopy (ARPES) study on a wide doping range of Ba1-xKxFe2As2 (BaK) iron-based superconductor. We observed a robust low-binding energy (BE) kink structure in the dispersion which is doping dependent where its energy peaks at the optimally-doped (OP) level (x~0.4) and decreases towards the underdoped (UD) and overdoped (OD) sides. It is also temperature-dependent and survives up to ~90K. We attribute this kink to electron-mode coupling in good agreement with the inelastic neutron scattering (INS) and scanning tunneling microscopy (STM) results on the same compound which observed a similar bosonic mode associated with spin excitations. The relation between the mode energy ({\Omega}) and the SC transition temperature (Tc) deduced from our Laser ARPES data follow the universal relation deduced from INS and STM. In addition, we could resolve another kink at higher BE showing less doping and temperature dependence and may thus be of different origin., Comment: 5 pages, 3 figures

We have performed an angle-resolved photoemission spectroscopy (ARPES) study of BaNi$_2$P$_2$ which shows a superconducting transition at $T_c$ $\sim$ 2.5 K. We observed hole and electron Fermi surfaces (FSs) around the Brillouin zone center and corner, respectively, and the shapes of the hole FSs dramatically changed with photon energy, indicating strong three-dimensionality. The observed FSs are consistent with band-structure calculation and de Haas-van Alphen measurements. The mass enhancement factors estimated in the normal state were $m^*$/$m_b$ $\leq$ 2, indicating weak electron correlation compared to typical iron-pnictide superconductors. An electron-like Fermi surface around the Z point was observed in contrast with BaNi$_2$As$_2$ and may be related to the higher $T_c$ of BaNi$_2$P$_2$., Comment: 6 figures

We have investigated the elastic constant C33 of Ba(Fe1-xCox)2As2 with eight different Co concentrations by ultrasonic measurement. We found remarkable elastic anomalies near the quantum critical point. We have studied them by measuring the electrical resistivity, heat capacity, and ultrasonic attenuation in addition to the elastic constant. These results have revealed that the inter-layer three-dimensional properties appearing in C33 to be possibly originated from the magnetic character of these materials. Our data about the elastic constant C33 highlight the importance of controlling the c-axis length in the emergence of superconductivity in iron-based superconductors.

We carried out a comparative study of the in-plane resistivity and optical spectrum of doped BaFe2As2 and investigated the doping evolution of the charge dynamics. For BaFe2As2, charge dynamics is incoherent at high temperatures. Electron (Co) and isovalent (P) doping into BaFe2As2 increase coherence of the system and transform the incoherent charge dynamics into highly coherent one. On the other hand, charge dynamics remains incoherent for hole (K) doping. It is found in common with any type of doping that superconductivity with high transition temperature emerges when the normal-state charge dynamics maintains incoherence and when the resistivity associated with the coherent channel exhibits dominant temperature-linear dependence., Comment: 8 pages, 5 figures

We carried out combined transport and optical measurements for BaFe2As2 and five isostructural transition-metal (TM) pnictides. The low-energy optical conductivity spectra of these compounds are, to a good approximation, decomposed into a narrow Drude (coherent) component and an incoherent component. The iron arsenides, BaFe2As2 and KFe2As2, are distinct from other pnictides in their highly incoherent charge dynamics or bad metallic behavior with the coherent Drude component occupying a tiny fraction of the low-energy spectral weight. The fraction of the coherent spectral weight or the degree of coherence is shown to be well correlated with the TM-pnictogen bond angle and the electron filling of TM 3d orbitals, which are measures of the strength of electronic correlations. The iron arsenides are thus strongly correlated systems, and the doping into BaFe2As2 controls the strength of electronic correlations. This naturally explains a remarkable asymmetry in the charge dynamics of electron- and hole-doped systems, and the unconventional superconductivity appears to emerge when the correlations are fairly strong., Comment: 6 pages, 4 figures

The nature of the pseudogap in high transition temperature (high-Tc) superconducting cuprates has been a major issue in condensed matter physics. It is still unclear whether the high-Tc superconductivity can be universally associated with the pseudogap formation. Here we provide direct evidence of the existence of the pseudogap phase via angle-resolved photoemission spectroscopy in another family of high-Tc superconductor, iron-pnictides. Our results reveal a composition dependent pseudogap formation in the multi-band electronic structure of BaFe2(As1-xPx)2. The pseudogap develops well above the magnetostructural transition for low x, persists above the nonmagnetic superconducting dome for optimal x and is destroyed for x ~ 0.6, thus showing a notable similarity with cuprates. In addition, the pseudogap formation is accompanied by inequivalent energy shifts in xz/yz orbitals of iron atoms, indicative of a peculiar iron orbital ordering which breaks the four-fold rotational symmetry., Comment: 14 pages, 10 figures

In Fe-based superconductors, electron doping is often realized by the substitution of transition-metal atoms for Fe. In order to investigate how the electronic structure of the parent compound is influenced by Zn substitution, which supplies nominally four extra electrons per substituted atom but is expected to induce the strongest impurity potential among the transition-metal atoms, we have performed an angle-resolved photoemission spectroscopy measurements on Ba(Fe_{1-x}Zn_x)_2As_2 (Zn-122). In Zn-122, the temperature dependence of the resistivity shows a kink around T~135 K, indicating antiferromagnetic order below the Neel temperature of T_N ~ 135 K. In fact, folded Fermi surfaces (FSs) similar to those of the parent compound have been observed below T_N. The hole and electron FS volumes are, therefore, different from those expected from the rigid-band model. The results can be understood if all the extra electrons occupy the Zn 3d state ~10 eV below the Fermi level and do not participate in the formation of the FSs., Comment: 6 pages, 8 figures

We demonstrate a general, computer automated procedure that inverts the q-space scattering data measured by spectroscopic imaging scanning tunneling microscopy (SI-STM) to determine the k-space scattering structure. This allows a detailed examination of the k-space origins of the quasiparticle interference (QPI) pattern in Bi2Sr2CaCu2O8+x. This new method allows the measurements of the differences between the positive and negative energy dispersions, the gap structure and it also measures energy dependent scattering length scale. Furthermore, the transitions between the dispersive QPI, the checkerboard and the pseudogap are mapped in detail allowing the exact nature of these transitions to be determined for both positive and negative energies. We are also able to measure the k-space scattering structure over a wide range of doping (p ~ 0.22 to 0.08), including regions where the octet model is not applicable. Our technique allows a complete picture of the k-space origins of the spatial excitations in Bi2Sr2CaCu2O8+x to be mapped out, providing for better comparisons between SI-STM and other experimental probes of the band structure and validating our new general approach for determining the k-space scattering origins from SI-STM data.

In the iron pnictide superconductors, two distinct unconventional mechanisms of superconductivity have been put forth: One is mediated by spin fluctuations leading to the s+- state with sign change of superconducting gap between the hole and electron bands, and the other is orbital fluctuations which favor the s++ state without sign reversal. Here we report direct observation of peculiar momentum-dependent anisotropy in the superconducting gap from angle-resolved photoemission spectroscopy (ARPES) in BaFe2(As1-xPx)2 (Tc=30 K). The large anisotropy found only in the electron Fermi surface (FS) and the nearly isotropic gap on the entire hole FSs are together consistent with modified s+- gap with nodal loops, which can be theoretically reproduced by considering both spin and orbital fluctuations whose competition generates the gap modulation. This indicates that these two fluctuations are nearly equally important to the high-Tc superconductivity in this system.

The cuprates contain a range of nanoscale phenomena that consist of both LDOS(E) features and spatial excitations. Many of these phenomena can only be observed through the use of a SI-STM and their disorder can be mapped out through the fitting of a phenomenological model to the LDOS(E). We present a study of the nanometer scale disorder of single crystal cryogenically cleaved samples of Bi2Sr2CaCu2O8+x whose dopings range from p = 0.19 to 0.06. The phenomenological model used is the Tripartite model that has been successfully applied to the average LDOS(E) previously. The resulting energy scale maps show a structured patchwork disorder of three energy scales, which can be described by a single underlying disordered parameter. This spatial disorder structure is universal for all dopings and energy scales. It is independent of the oxygen dopant negative energy resonances and the interface between the different patches takes the form of a shortened lifetime pseudogap/superconducting gap state. The relationship between the energy scales and the spatial modulations of the dispersive QPI, static q1* modulation and the pseudogap shows that the energy scales signatures in the LDOS(E) are tied to the onset and termination of the spatial excitations. The static q1* modulations local energy range is measured and its signature in the LDOS(E) is the kink, whose number of states are modulated with a wave vector of q1*. This analysis of both the LDOS(r,E) and the spatial modulations in q-space show a picture of a single underlying disordered parameter that determines both the LDOS(E) structure as well as the energy ranges of the QPI, q1* modulation and the pseudogap states. This parameter for a single patch can be defined by the Fermi surface crossing of the parent compound anti-ferromagnetic zone boundary for a model homogeneous superconductor with the same electronic properties as the patch.

A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials such as the cuprate high temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping-and-temperature dependence ARPES study of spectral gaps in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212), covering much of the superconducting portion of the phase diagram. In the ground state, abrupt changes in near-nodal gap phenomenology give spectroscopic evidence for two potential quantum critical points, p$=$0.19 for the pseudogap phase and p$=$0.076 for another competing phase. Temperature dependence reveals that the pseudogap is not static below T$_c$ and exists p$>$0.19 at higher temperatures. Our data imply a revised phase diagram which reconciles conflicting reports about the endpoint of the pseudogap in the literature, incorporates phase competition between the superconducting gap and pseudogap, and highlights distinct physics at the edge of the superconducting dome., Comment: to appear in PNAS

Angle-resolved photoemission spectroscopy using tunable low energy photons allows us to study the quasi-particle (QP) dispersions of the inner and outer CuO2 planes (IP and OP) separately in the tri-layer cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ (Bi2223). The kink energy of the OP band is $\sim$ 70 meV, as observed in various high-$T_c$ cuprates, while that of the IP band is as large as 100 meV in the superconducting (SC) state. This large kink energy is attributed to the $\sim$ 35 meV buckling mode plus the large ($\sim$ 60 meV) SC gap of IP. The IP band also shows a weak kink feature at 70 meV in the SC state. The latter feature can be explained either by the 70 meV half-breathing mode or by the $\sim$ 35 meV buckling-phonon mode plus the $\sim$ 40 meV SC gap of OP if interlayer scattering of QP is involved., Comment: 5 pages, 2 figures

Relationship between the superconducting gap and the pseudogap has been the subject of controversies. In order to clarify this issue, we have studied the superconducting gap and pseudogap of the high-Tc superconductor La2-xSrxCuO4 (x=0.10, 0.14) by angle-resolved photoemission spectroscopy (ARPES). Through the analysis of the ARPES spectra above and below Tc, we have identified a superconducting coherence peak even in the anti-nodal region on top of the pseudogap of a larger energy scale. The superconducting peak energy nearly follows the pure d-wave form. The d-wave order parameter \Delta_0 [defined by \Delta(k)=\Delta_0(cos(kxa)-cos(kya)) ] for x=0.10 and 0.14 are nearly the same, \Delta_0 ~ 12-14 meV, leading to strong coupling 2\Delta_0/kB Tc ~ 10. The present result indicates that the pseudogap and the superconducting gap are distinct phenomena and can be described by the "two-gap" scenario., Comment: 5 pages, 4 figures

We investigated the anisotropy in the in-plane optical spectra of detwinned Ba(Fe1-xCox)2As2. The optical conductivity spectrum of BaFe2As2 shows appreciable anisotropy in the magnetostructural ordered phase, whereas the dc resistivity is almost isotropic at low temperatures. Upon Co doping, the resistivity becomes highly anisotropic, while the finite-energy intrinsic anisotropy is suppressed. It is found that anisotropy in resistivity arises from anisotropic impurity scattering from doped Co atoms, extrinsic in origin. Intensity of a specific optical phonon mode is also found to show striking anisotropy in the ordered phase. The anisotropy induced by Co impurity and that observed in the optical phonon mode are hallmarks of the highly polarizable electronic state in the ordered phase., Comment: 5 pages, 4 figures

We investigated the in-plane resistivity anisotropy for underdoped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals with improved quality. We demonstrate that the anisotropy in resistivity in the magnetostructural ordered phase arises from the anisotropy in the residual component which increases in proportion to the Co concentration $x$. This gives evidence that the anisotropy originates from the impurity scattering by Co atoms substituted for the Fe sites, rather than so far proposed mechanism such as the anisotropy of Fermi velocities of reconstructed Fermi surface pockets. As doping proceeds to the paramagnetic-tetragonal phase, a Co impurity transforms to a weak and isotropic scattering center., Comment: 12 pages, 3figures, published in PRL 110, 207001 (2013)

The electronic structure near the Fermi level (EF) of Ba1-xKxFe2As2 (BaK122 ; x = 0.2 - 0.7) is studied using laser ultrahigh-resolution angle-resolved photoemission spectroscopy(ARPES). For the optimally doped case of x = 0.4, we clearly observe two peaks below Tc in the ARPES spectra at a binding energies (BE) of 5 meV and 13meV. The former is assigned to a superconducting (SC) coherence peak since it appears and evolves below the bulk SC transition at Tc (= 36 K), accompanying a gap opening centered at EF. In contrast, the latter peak, which appears below ~ 90 K without any gap formation, is interpreted to be not directly related to a SC coherence peak. This high-BE peak is observed from x = 0.2 to 0.6, reduces in energy with overdoping (x > 0.4) and is absent for x = 0.7. The temperature(T)- and doping-dependent ARPES results suggest that the high-BE peak originates from coupling to a bosonic mode of energy ~ 8 meV., Comment: 8 pages, 5 figures