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We investigated the temperature (T) dependence of the irreversibility field Hirr(T) in high-critical-temperature cuprate Bi2+xSr2-xCa1-yYyCu2O8+d (Bi-2212) single crystals over a wide range of hole doping level (p). Hirr(T) was evaluated by measuring the magnetization hysteresis loop. The value of Hirr(T) extrapolated to T = 0 K [Hirr(0)], is either equal to or sets the lower boundary for the upper critical field at T = 0 K [Hc2(0)]. Tc shows a parabolic p-dependence (peak at p = 0.16), whereas Hirr(0) increases monotonically with p by approximately one order of magnitude, from 19 T for the most underdoped sample (p = 0.065, Tc = 24 K) to 209 T for the most overdoped sample (p = 0.200, Tc = 75 K). The present results qualitatively agree with Hc2(0) values evaluated from the specific heat measurements. The observed p-dependence of Hirr(0) in Bi-2212 is distinct from those in YBa2Cu3O7-d and HgBa2CuO6+d, in which a pronounced dip structure appears in the underdoped region. Considering that the dip structures observed in these two systems are likely associated with the formation of competing orders (most likely field-induced charge orders), the present results indicate that the influence of the competing order in Bi-2212 is less prominent than that in the other two systems., Comment: 32 pages, 9 figures, 1 table

Lanthanides ($Ln$) are notoriously difficult to intercalate into graphite. We investigated the possibility of using Na to catalyze the formation of $Ln$-intercalated graphite and successfully synthesized $Ln$C$_6$ ($Ln$ = Sm, Eu, and Yb) significantly rapidly in high yields. The synthesis process involves the formation of the reaction intermediate NaC$_x$, through the mixing of Na and C, which subsequently reacts with $Ln$ upon heating to form $Ln$C$_6$. Well-sintered $Ln$C$_6$ pellets with low residual Na concentrations ($Ln$:Na = 98:2) were fabricated by the two-step method. The pellets enabled the evaluation of $Ln$C$_6$ by powder X-ray diffraction and electrical resistivity measurements. This study highlights the versatility of the Na-catalyzed method and lays the foundation for the rapid mass production of $Ln$C$_6$, with potential applications in superconducting and rechargeable battery materials., Comment: 16 pages, 7 figures

Non-zero spin orbit coupling has been reported in several unconventional superconductors due to the absence of inversion symmetry breaking. This contrasts with cuprate superconductors, where such interaction has been neglected for a long time. The recent report of a non-trivial spin orbit coupling in overdoped Bi2212 cuprate superconductor, has re-opened an old debate on both the source and role of such interaction and its evolution throughout the superconducting dome. Using high-resolution spin- and angle-resolved photoemission spectroscopy, we reveal a momentum-dependent spin texture throughout the hole-doped side of the superconducting phase diagram for single- and double-layer bismuth-based cuprates. The universality of the reported effect among different dopings and the disappearance of spin polarization upon lead substitution, suggest a common source. We argue that local structural fluctuations of the CuO planes and the resulting charge imbalance may cause local inversion symmetry breaking and spin polarization, which might be crucial for understanding cuprates physics., Comment: 6 figures

Recent developments in laser-excited photoemission electron microscopy (laser-PEEM) advance the visualization of electronic nematicity and nematic domain structures in iron-based superconductors. In FeSe and BaFe$_2$(As$_{0.87}$P$_{0.13}$)$_2$ superconductors, it has been reported that the thickness of the electronic nematic domain walls is unexpectedly long, leading to the formation of mesoscopic nematicity wave [T. Shimojima $\textit{et al.}$, Science $\textbf{373}$ (2021) 1122]. This finding demonstrates that the nematic coherence length $\xi_{\rm nem}$ can be decoupled from the lattice domain wall. Here, we report that the electronic domain wall thickness shows a distinct variation in related materials: it is similarly long in FeSe$_{0.9}$S$_{0.1}$ whereas it is much shorter in undoped BaFe$_2$As$_2$. We find a correlation between the thick domain walls and the non-Fermi liquid properties of normal-state resistivity above the nematic transition temperature. This suggests that the nematic coherence length can be enhanced by underlying spin-orbital fluctuations responsible for the anomalous transport properties., Comment: 5 pages, 3 figures

Grain alignment is a key factor that determines the performance of a superconducting bulk. In this study, the spark plasma texturing (SPT) technique was used to fabricate a CaKFe$_4$As$_4$ superconducting bulk. X-ray diffraction and electron backscatter diffraction revealed that the $c$-axes of the CaKFe$_4$As$_4$ grains in the SPT bulk are aligned, demonstrating that the SPT technique is effective in achieving $c$-axis texture. In addition, chemical composition analysis showed that oxide impurities, which affect the grain boundary characteristics that determine the inter-grain critical current density ($J_c$), are randomly distributed in the SPT bulk. Magnetization measurements showed high $J_c$ values of the SPT bulk, reaching 127 kA cm$^{-2}$ and 26 kA cm$^{-2}$ at 4.2 K under a self-field and magnetic field of 5 T, respectively. These results suggest that the SPT technique is a promising approach for obtaining a high-performance superconducting bulk material for high-field applications.

A high density CaKFe$_4$As$_4$ bulk sample was successfully synthesized using a spark plasma sintering (SPS) technique. The density of the synthesized sample was 5.02 g cm$^{-3}$, corresponding to 96.2% of the theoretical density of CaKFe$_4$As$_4$. Moreover, a reasonably high Vickers hardness of 1 GPa was measured. The electrical resistivity of the SPS bulk sample was as low as approximately 600 $\mu\Omega$ cm at 300 K, which is smaller than that of the ordinary sintered polycrystalline sample by nearly one order of magnitude, and exhibited a sharp superconducting transition, with the transition width $\Delta\textit{T}_c$ less than 2 K, indicating an improved grain connectivity. The critical current density of the SPS bulk sample, as calculated from the magnetization hysteresis loops (magnetic $\textit{J}_c$), reached 18 kA cm$^{-2}$ at 4.2 K under 5 T, which is the highest among the iron-based superconductor polycrystalline samples reported thus far., Comment: 13 pages, 6 figures, 1 table

We grew (Hg,Re)Ba$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ ((Hg,Re)1223) single crystals with good reproducibility via the single-step flux method using monoxides as raw materials. A double-sealing method using a thick-walled quartz tube and a stainless-steel container was adopted for explosion protection. The maximum crystal size was approximately 1 mm x 1 mm in the ab plane and 0.04 mm in thickness. The crystal was square-shaped, reflecting the tetragonal crystal structure of (Hg,Re)1223. Magnetic susceptibility measurements indicated a critical temperature of 130 K. The in-plane resistivity exhibited a linear temperature dependence, indicating that the sample was close to optimal doping level. The out-of-plane resistivity was also measured, and the anisotropy parameter was 250-650 at 300 K., Comment: 21 pages, 9 figures, 2 tables

Atomically thin cuprates exhibiting a superconducting phase transition temperature similar to bulk have recently been realized, although the device fabrication remains a challenge and limits the potential for many novel studies and applications. Here we use an optical pump-probe approach to noninvasively study the unconventional superconductivity in atomically thin Bi$_2$Sr$_2$Ca$_{0.92}$Y$_{0.08}$Cu$_2$O$_{8+{\delta}}$ (Y-Bi2212). Apart from finding an optical response due to the superconducting phase transition that is similar to bulk Y-Bi2212, we observe that the sign and amplitude of the pump-probe signal in the atomically thin flake vary significantly in different dielectric environments depending on the nature of the optical excitation. By exploiting the spatial resolution of the optical probe, we uncover the exceptional sensitivity of monolayer Y-Bi2212 to the environment. Our results provide the first optical evidence for the intralayer nature of the superconducting condensate in Bi2212, and highlight the role of double-sided encapsulation in preserving superconductivity in atomically thin cuprates., Comment: To be published in Nano Letters

In the cuprates, the opening of a d-wave superconducting (SC) gap is accompanied by a redistribution of spectral weight at energies two orders of magnitude larger than this gap. This indicates the importance to the pairing mechanism of on-site electronic excitations, such as orbital transitions or charge transfer excitations. Here, we resort to a three-pulse pump-probe scheme to study the broadband non-equilibrium dielectric function in optimally-doped $Bi_2Sr_2Ca_{0.92}Y_{0.08}Cu_2O_{8+{\delta}}$ and we identify two distinct dynamical responses: i) a blueshift of the central energy of an interband excitation peaked at 2 eV and ii) a change in spectral weight in the same energy range. Photoexcitation with near-IR and mid-IR pulses, with photon energies respectively above and below the SC gap, reveals that the transient changes in the central energy are not modified by the onset of superconductivity and do not depend on the pump photon energy. Conversely, the spectral weight dynamics strongly depends on the pump photon energy and has a discontinuity at the critical temperature. The picture that emerges is that, while high-energy pulses excite quasiparticles in both nodal and thermally inaccessible antinodal states, photoexcitation by low-energy pulses mostly accelerates the condensate and creates excitations predominantly at the nodes of the SC gap. These results, rationalized by kinetic equations for d-wave superconducting gaps, indicate that dynamical control of the momentum-dependent distribution of non-thermal quasiparticles may be achieved by the selective tuning of the photoexcitation.

Even before its role in electroweak symmetry breaking, the Anderson-Higgs mechanism was introduced to explain the Meissner effect in superconductors. Spontaneous symmetry-breaking yields massless phase modes representing the low-energy excitations of the Mexican-Hat potential. Only in superconductors does the gauge field move the phase mode towards higher energies, as a consequence of the charged condensate. This results in a low-energy excitation spectrum governed by the amplitude mode - the Higgs mode. Consequently, the Meissner effect signifies a macroscopic quantum condensate in which a photon acquires mass, representing a one-to-one analogy to high-energy physics. We report on the direct observation of the Higgs particle in the high-temperature superconductor Bi-2212 by developing an innovative technique to study its distinct symmetries and energies after a soft quench of the Mexican-Hat potential. By comparing transient Stokes and anti-Stokes data, we identify the Higgs particle as an additional anti-Stokes Raman cross section after quenching. With our technique we discriminate quasi-particle excitations from excitations in the Cooper channel and argue that alternatives to the Higgs excitation can be ruled out. This opens the avenue for Higgs Spectroscopy in quantum condensates and provides a unique pathway to control and explore Higgs physics., Comment: Revised version with rewritten text elements and added references, new section in SI, updated author list, results unchanged

In this study, we conducted experiments on CaC6 for elucidating the Na-catalyzed formation mechanism and achieving rapid mass synthesis of graphite intercalation compounds (GICs). Rapidly synthesized CaC6 was characterized by analysis of its crystal structure and physical properties. We found that the formation of the reaction intermediate Na-GIC (NaCx, x = 64) requires a larger amount of Na than is intercalated between the graphite interlayers. The requirement for excess Na may provide insights into the mechanism of Na-catalyzed GIC formation. A Na-to-C molar mixing ratio of 1.5-2.0:6 was suitable for the efficient formation of CaC6 under heat treatment at 250{\deg}C for 2 h, and the catalytic Na remaining in the sample was demonstrably reduced to a Na:Ca ratio of approximately 3:97. The upper critical field Hc2 was enhanced approximately three times compared to those of previous reports. Based on X-ray diffraction and experimental parameter analysis, we concluded that the enhancement of Hc2 was attributed to the disordered stacking sequence in CaC6, possibly because of the rapid and low-temperature formation. Physical properties derived from specific heat measurements were comparable to those of high-quality CaC6, which is slowly synthesized using the molten Li-Ca alloy method. This study provides new avenues for future research and exploration in the rapid mass synthesis of GICs as practical materials, for applications such as battery electrodes and superconducting wires., Comment: 17 pages, 6 figures, 1 table

We investigated four single crystals of K-doped BaFe$_2$As$_2$ (Ba-122), Ba$_{1-x}$K$_x$Fe$_2$As$_2$ with $x$ = 0.29, 0.36, 0.40, and 0.51, using infrared spectroscopy. We explored a wide variety of doping levels, from under- to overdoped. We obtained the superfluid plasma frequencies ($\Omega_{\mathrm{sp}}$) and corresponding London penetration depths ($\lambda_{\mathrm{L}}$) from the measured optical conductivity spectra. We also extracted the electron-boson spectral density (EBSD) functions using a two-parallel charge transport channel approach in the superconducting (SC) state. From the extracted EBSD functions, the maximum SC transition temperatures ($T_c^{\mathrm{Max}}$) were determined using a generalized McMillan formula and the SC coherence lengths ($\xi_{\mathrm{SC}}$) were calculated using the timescales encoded in the EBSD functions and reported Fermi velocities. We identified some similarities and differences in the doping-dependent SC quantities between the K-doped Ba-122 and the hole-doped cuprates. We expect that the various SC quantities obtained across the wide doping range will provide helpful information for establishing the microscopic pairing mechanism in Fe-pnictide superconductors., Comment: 16 pages, 4 figures, 1 table

The pair density wave (PDW) is a novel superconducting state in which Cooper pairs carry center-of-mass momentum in equilibrium, leading to the breaking of translational symmetry. Experimental evidence for such a state exists in high magnetic field and in some materials that feature density wave orders that explicitly break translational symmetry. However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here, we show that such a state exists in the iron pnictide superconductor EuRbFe4As4 (Eu-1144), a material that features coexisting superconductivity (Tc ~ 37K) and magnetism (Tm ~ 15 K). We show from the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) measurements that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of ~8 unit cells. Upon raising the temperature above Tm, the modulated superconductor disappears, but a uniform superconducting gap survives to Tc. When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density wave orders, showing that the PDW state is a primary, zero-field superconducting state in this compound. Both four-fold rotational symmetry and translation symmetry are recovered above Tm, indicating that the PDW is a smectic order.

Identifying ordered phases and their underlying symmetries is the first and most important step toward understanding the mechanism of high-temperature superconductivity; critical behaviors of ordered phases are expected to be correlated with superconductivity. Efforts to find such ordered phases have been focused on symmetry breaking in the pseudogap region while the Fermi liquid-like metal region beyond the so-called critical doping $p_{c}$ has been regarded as a trivial disordered state. Here, we used rotational anisotropy second harmonic generation and uncovered a broken mirror symmetry in the Fermi liquid-like phase in (Bi,Pb)$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ with $p = 0.205 > p_{c}$. By tracking the temperature evolution of the symmetry-breaking response, we verify an order parameter-like behavior with the onset temperature $T_{up}$ at which the strange metal to Fermi liquid-like-metal crossover takes place. Complementary angle-resolved photoemission study showed that the quasiparticle coherence between $\mathrm{CuO_{2}}$ bilayers is enhanced in proportion to the symmetry-breaking response as a function of temperature, indicating that the change in metallicity and symmetry breaking are linked. These observations contradict the conventional quantum disordered scenario for over-critical-doped cuprates and provide new insight into the nature of the quantum critical point in cuprates., Comment: 8 pages, 4 figures

Graphite intercalation compounds (GICs) have a variety of functions due to their rich material variations, and thus,innovative methods for their synthesis are desired for practical applications. We have discovered that Na has a catalytic property that dramatically accelerates the formation of GICs. We demonstrate that LiC6n (n = 1, 2), KC8, KC12n (n = 2, 3, 4), and NaCx are synthesized simply by mixing alkali metals and graphite powder with Na at room temperature (~25 {\deg}C), and AEC6 (AE = Ca, Sr, Ba) are synthesized by heating Na-added reagents at 250 {\deg}C only for a few hours. The NaCx, formed by the mixing of C and Na, is understood to act as a reaction intermediate for a catalyst, thereby accelerating the formation of GICs by lowering the activation energy of intercalation. The Na-catalyzed method, which enables the rapid and mass synthesis of homogeneous GIC samples in a significantly simpler manner than conventional methods, is anticipated to stimulate research and development for GIC applications., Comment: 10 pages, 4 figures, 1 table

We have investigated the photoexcited transient responses of stripe-ordered phase in a cuprate superconductor, ${\rm La}_{1.6-x}{\rm Nd}_{0.4}{\rm Sr}_{x}{\rm CuO}_{4}~(x = 0.12)$ using optical-pump terahertz (THz)-probe spectroscopy. Upon the near-infrared photoexcitation with the electric field polarized along the $c$-axis, a clear plasma edge appears in the THz reflection spectrum along the $c$-axis with its position nearly coinciding with the Josephson plasma resonance of similarly doped ${\rm La}_{2-x}{\rm Sr}_{x}{\rm CuO}_{4}~(x = 0.125)$ in the low-temperature superconducting phase. The appearance of light-induced plasma edge sustains up to the onset temperature of the charge-stripe order, indicating the inherent interplay between the light-induced phase and the charge-stripe order. The optical conductivity spectrum of the light-induced state is mostly reproduced by the Drude model with a scattering rate as small as a few meV, and its imaginary part does not exhibit $1/{\omega}$-divergence behavior in any temporal region after the photoexcitation. We discuss the possible origin of the observed coherent interlayer transport behavior as manifested by the narrow Drude response in the THz reflectivity along the $c$-axis., Comment: 18 pages, 7 figures

The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Here, theoretical attention usually concentrates on the intra-atom Coulombic interactions dominating the 3d^9 and 3d^10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p^6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long predicted intra-unit cell symmetry breaking should then generate an orbital ordered phase, for which the charge-transfer energy E separating the 2p^6 and 3d^10orbitals is distinct for the two oxygen atoms. Here we introduce sublattice resolved E(r) imaging techniques to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of E(r), with energy-level splitting between the two oxygen atoms on the 50 meV scale. Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order that appear bounded by dopant ions, and within whose domain walls low energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q=0 orbitally ordered state that splits the energy levels of the oxygen orbitals by ~50 meV, in underdoped CuO2., Comment: Manuscript: 21 pages, 4 figures. Methods: 40 pages, 23 figures

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios has been challenging for the short-range CDW in bismuth-based cuprates. Here, we employed high-resolution resonant inelastic x-ray scattering to uncover the spatial symmetry of the CDW in Bi$_2$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta}$. Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes were found in reciprocal space. Based on Fourier transform analysis of real-space models, we interpret the results as evidence of unidirectional charge stripes, hosted by mutually 90$^\circ$-rotated anisotropic domains. Our work paves the way for a unified symmetry and microscopic description of CDW order in cuprates., Comment: 9 pages, 3 figures and Supplementary Information; Under peer review

Identifying quantum critical points (QCPs) and their associated fluctuations may hold the key to unraveling the unusual electronic phenomena observed in cuprate superconductors. Recently, signatures of quantum fluctuations associated with charge order (CO) have been inferred from the anomalous enhancement of CO excitations that accompany the reduction of the CO order parameter in the superconducting state. To gain more insight about the interplay between CO and superconductivity, here we investigate the doping dependence of this phenomenon throughout the Bi-2212 cuprate phase diagram using resonant inelastic x-ray scattering (RIXS) at the Cu L3- edge. As doping increases, the CO wavevector decreases, saturating at a commensurate value of 0.25 r.l.u. beyond a characteristic doping pc, where the correlation length becomes shorter than the apparent periodicity (4a0). Such behavior is indicative of the fluctuating nature of the CO; and the proliferation of CO excitations in the superconducting state also appears strongest at pc, consistent with expected behavior at a CO QCP. Intriguingly, pc appears to be near optimal doping, where the superconducting transition temperature Tc is maximal., Comment: This is a submitted version of the manuscript. The revised manuscript is now published on Physical Review B

Recent studies in heavily hole-doped iron-based superconductor RbFe$_2$As$_2$ have suggested the emergence of novel electronic nematicity directed along the Fe-As direction, 45$^\circ$ rotated from the usual nematicity ubiquitously found in BaFe$_2$As$_2$ and related materials. This motivates us to study the physical properties of Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$, details of which remain largely unexplored. Here we report on the normal-state charge transport in Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ superconductors by using high-quality single crystals in the range of Rb concentration $0.14\le x \le 1.00$. From the systematic measurements of the temperature dependence of electrical resistivity $\rho(T)$, we find a signature of a deviation from the Fermi liquid behavior around the optimal composition, which does not seem related to the antiferromagnetic quantum criticality but has a potential link to hidden nematic quantum criticality. In addition, electron correlations derived from the coefficient of $T^2$ resistivity show a marked increase with Rb content near the heavily hole-doped end, consistent with the putative Mott physics near the $3d^5$ electron configuration in iron-based superconductors., Comment: 6 pages, 4 figures

Enriching the material variation often contributes to the progress of materials science. We have discovered for the first time antiperovskite arsenide SrPd$_{3}$As and revealed a hidden structural and superconducting phase in Sr(Pd$_{1-x}$Pt$_{x}$)$_{3}$As. The Pd-rich samples (0 $\leq$ x $\leq$ 0.2) had the same non-centrosymmetric (NCS) tetragonal structure (a space group of $I41md$) as SrPd$_{3}$P. For the samples with 0.3 $\leq$ x $\leq$ 0.7, a centrosymmetric (CS) tetragonal structure ($P4/nmm$) identical to that of SrPt$_{3}$P was found to appear, accompanied by superconductivity at a transition temperature ($T_\mathrm{c}$) up to 3.7 K. In the samples synthesized with Pt-rich nominal compositions (0.8 $\leq$ x $\leq$ 1.0), Sr$_{2}$(Pd,Pt)$_{8-y}$As$_{1+y}$ with an intergrowth structure (CS-orthorhombic with Cmcm) was crystallized. The phase diagram obtained for Sr(Pd,Pt)$_{3}$As was analogous to that of (Ca,Sr)Pd$_{3}$P in that superconductivity ($T_\mathrm{c}$ $\geq$ 2 K) occurred in the CS phases induced by substitutions to the NCS phases. This study indicates the potential for further material variation expansion and the importance of elemental substitutions to reveal hidden phases in related antiperovskites., Comment: 18 pages, 5 figures, 1 table

Superconductors comprising 5d transition metals of Ir and Pt have been widely explored because they have the potential of unique superconductivity caused by the strong spin-orbit interaction (SOI). We successfully synthesized BaIr2, the last Laves phase remaining unsynthesized in the MgCu2-type AM2 (A = Ca, Sr, Ba; M = Rh, Pd, Ir, Pt). BaIr2 was crystallized at 925 C under a pressure of 3.3 GPa via a solid-state reaction between Ba and Ir powders; it was found to have the longest a-lattice constant of 8.038(1) A among AM2. BaIr2 exhibited bulk superconductivity at a transition temperature (Tc) of 2.7 K. BaIr2 was found to have a type-II superconductor with an upper critical field of 67.7 kOe, which was above the Pauli paramagnetic limit (50 kOe). The electron-phonon coupling constant and normalized specific heat jump were measured to be 0.63 and 1.2, respectively, indicating that BaIr2 is a weak-coupling superconductor. The electronic-structure calculations for BaIr2 revealed that the Ir-5d states are dominant at the Fermi energy (EF) and the density of states at the EF is strongly affected by SOI as in the case of CaIr2 and SrIr2., Comment: 9 pages, 8 figures

Two contradictory phase diagrams have dominated the literature of high-$T_c$ cuprate superconductors. Does the pseudogap line cross the superconducting $T_c$-dome or not? To answer, we have revisited the experimental magnetic susceptibility and knight shift of four different compounds, La$_{1-x}$Sr$_x$CuO$_4$, Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_8$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$, and YBa$_2$Cu$_3$O$_{6+y}$, as a function of temperature and doping. The susceptibility can be described by the same function for all materials, having a magnetic and an electronic contributions. The former is the 2D antiferromagnetic (AF) square lattice response, with a characteristic temperature of magnetic correlations $T_{max}$. The latter is the `Pauli' term, revealing the gap opening in the electronic density of states at the pseudogap temperature $T^*$. From precise fits of the data, we find that $T_{max}(p)$ decreases linearly as a function of doping ($p$) over a wide range, but saturates abruptly in the overdoped regime. Concomitantly, $T^*(p)$ is {\it linear and tangent} to the dome, either crossing or approaching $T_{max}(p)$ at the top of the dome, indicating a qualitative change of behavior from underdoped to overdoped regimes. Contrary to the idea that the pseudogap terminates just above optimal doping, our analysis suggests that the gap exists throughout the phase diagram. It is consistent with a pseudogap due to hole pairs, or `pairons', above $T_c$. We conclude that $T_{max}$, reflecting the AF magnetic correlations, has often been misinterpreted as the pseudogap temperature $T^*$., Comment: Solid State Communications (in press, February 2022)

We report the effects of low-temperature postannealing on the structural and superconducting properties of the recently discovered Ca-free double-layered cuprate, Sr$_2$SrCu$_2$O$_{4+y}$F$_{2-y}$. Although the as-synthesized sample prepared under high pressure has a tetragonal structure with a rock-salt-type blocking layer (the so-called $T$-phase), we found that the symmetry of the structure lowered to that of an orthorhombic system when annealed with CuF$_2$. The structural refinements reveal that such a topochemical reaction leads not only to the removal of excess O$^{2-}$ from the apical site but also to the intercalation of extra F$^-$ into the interstitial site. The orthorhombic phase exhibits bulk superconductivity at a critical temperature of 107 K, which is significantly higher than that of the $T$-phase ($\sim$50 K). Meanwhile, the $T$-phase turns into another structure possessing a fluorite-type blocking layer without apical fluorine (known as the $T^\prime$-phase) by annealing without CuF$_2$. Density functional theory calculations show that the $T^\prime$-phase is more stable than the $T$-phase. This is the first report on the formation of a $T^\prime$-type double-layered cuprate. Furthermore, the structural stability of the three phases of Sr$_2$SrCu$_2$O$_{4+y}$F$_{2-y}$ is discussed in terms of lattice matching between the blocking and conducting layers., Comment: 18 pages, 9 figures, 3 tables (including 3 pages, 3 figures for the Supporting Information)

Antiperovskites are a promising candidate structure for the exploration of new materials. We discovered an antiperovskite phosphide, LaPd$_{3}$P, following our recent synthesis of $A$Pd$_{3}$P ($A$ = Ca, Sr, Ba). While $A$Pd$_{3}$P and (Ca,Sr)Pd$_{3}$P were found to be tetragonal or orthorhombic systems, LaPd$_{3}$P is a new prototype cubic system ($a$ = 9.0317(1) A) with a noncentrosymmetric space group ($I-43m$). LaPd$_{3}$P exhibited superconductivity with a transition temperature ($T_\mathrm{c}$) of 0.28 K. The upper critical field, Debye temperature, and Sommerfeld constant ($\gamma$) were determined as 0.305(8) kOe, 267(1) K, 6.06(4) mJ mol-1 K-2 f.u.-1, respectively. We performed first-principles electronic band structure calculations for LaPd$_{3}$P and compared the theoretical and experimental results. The calculated Sommerfeld constant (2.24 mJ mol-1 K-2 f.u.-1) was much smaller than the experimental value of $\gamma$ because the Fermi energy ($E_\mathrm{F}$) was located slightly below the density of states (DOS) pseudogap. This difference was explained by the increase in the DOS at $E_\mathrm{F}$ due to the approximately 5 at.% La deficiency (hole doping) in the sample. The observed Tc value was much lower than that estimated using the Bardeen-Cooper-Schrieffer equation. To explain the discrepancy, we examined the possibility of an unconventional superconductivity in LaPd$_{3}$P arising from the lack of space inversion symmetry., Comment: 13 pages, 5 figures, 4 tables

Magnetic superconductors are specific materials exhibiting two antagonistic phenomena, superconductivity and magnetism, whose mutual interaction induces various emergent phenomena, such as the reentrant superconducting transition associated with the suppression of superconductivity around the magnetic transition temperature (Tm), highlighting the impact of magnetism on superconductivity. In this study, we report the experimental observation of the ferromagnetic order induced by superconducting vortices in the high-critical-temperature (high-Tc) magnetic superconductor EuRbFe4As4. Although the ground state of the Eu2+ moments in EuRbFe4As4 is helimagnetism below Tm, neutron diffraction and magnetization experiments show a ferromagnetic hysteresis of the Eu2+ spin alignment. We demonstrate that the direction of the Eu2+ moments is dominated by the distribution of pinned vortices based on the critical state model. Moreover, we demonstrate the manipulation of spin texture by controlling the direction of superconducting vortices, which can help realize spin manipulation devices using magnetic superconductors., Comment: Main text: 16 pages, 6 figures, Supplementary Information: 9 pages, 5 figures, 1 table

In the recently discovered antiperovskite phosphide (Ca,Sr)Pd$_3$P, centrosymmetric (CS) and non-centrosymmetric (NCS) superconducting phases appear depending on the Sr concentration, and their transition temperatures ($T_\mathrm{c}$) differ by as much as one order of magnitude. In this study, we investigated the superconducting properties and electronic band structures of CS orthorhombic (CSo) (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P ($T_\mathrm{c}$ = 3.5 K) and NCS tetragonal (NCSt) (Ca$_{0.25}$Sr$_{0.75}$)Pd$_3$P ($T_\mathrm{c}$ = 0.32 K) samples with a focus on explaining their large $T_\mathrm{c}$ difference. Specific heat measurements indicated that CSo (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P was an s-wave superconductor in a moderate-coupling regime with a 2$\Delta$$_0$/k$_B$$T_\mathrm{c}$ value of 4.0. Low-lying phonons leading to the strong coupling in the structurally analogous SrPt$_3$P were unlikely to be present in CSo (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P. Given that CSo (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P and NCSt (Ca$_{0.25}$Sr$_{0.75}$)Pd$_3$P exhibited similar Debye temperatures ($\Theta$$_D$) of approximately 200 K, the large $T_\mathrm{c}$ difference could not be attributed to $\Theta$$_D$.$T_\mathrm{c}$ of each phase was accurately reproduced based on the Bardeen-Cooper-Schrieffer (BCS) theory using experimental data and the density of states of the Fermi level $N$(0) calculated from their band structures. We concluded that the considerable suppression of $T_\mathrm{c}$ in NCSt (Ca$_{0.25}$Sr$_{0.75}$)Pd$_3$P can be primarily attributed to the decrease in $N$(0) associated with the structural phase transition without considering the lack of inversion symmetry., Comment: 14 pages, 8 figures

Alkali metal dosing (AMD) has been widely used as a way to control doping without chemical substitution. This technique, in combination with angle resolved photoemission spectroscopy (ARPES), often provides an opportunity to observe unexpected phenomena. However, the amount of transferred charge and the corresponding change in the electronic structure vary significantly depending on the material. Here, we report study on the correlation between the sample work function and alkali metal induced electronic structure change for three iron-based superconductors: FeSe, Ba(Fe$_{0.94}$Co$_{0.06}$)$_{2}$As$_{2}$ and NaFeAs which share a similar Fermi surface topology. Electronic structure change upon monolayer of alkali metal dosing and the sample work function were measured by ARPES. Our results show that the degree of electronic structure change is proportional to the difference between the work function of the sample and Mulliken's absolute electronegativity of the dosed alkali metal. This finding provides a possible way to estimate the AMD induced electronic structure change., Comment: 4 pages

Superconductivity in the cuprates is characterized by spatial inhomogeneity and an anisotropic electronic gap of d-wave symmetry. The aim of this work is to understand how this anisotropy affects the non-equilibrium electronic response of high-Tc superconductors. We compare the nodal and antinodal non-equilibrium response to photo-excitations with photon energy comparable to the superconducting gap and polarization along the Cu-Cu axis of the sample. The data are supported by an effective d-wave BCS model indicating that the observed enhancement of the superconducting transient signal mostly involves an increase of pair coherence in the antinodal region, which is not induced at the node., Comment: 14 pages, 8 figures

We deduce the symmetry of the pseudogap state in the single and double layer bismuth-based cuprate superconductors by measuring and analyzing their circular and linear photogalvanic responses, which are related linearly to the chirality and inversion breaking respectively of the order parameter. After separating out the trivial contribution arising from the surface where inversion symmetry is already broken, we show that both responses start below the pseudogap temperature $T^*$ and grow below it to a sizable magnitude, revealing the broken symmetries in the bulk of the crystal. Through a detailed analysis of the dependence of the signals on the angle of incidence, the polarization of the light, and the orientation of the crystal, we are able to discover that the point group symmetry below $T^*$ is limited to $mm2$ or $mm2\underline{1}$ groups. Taking into account formation of domains and previous measurements, our results narrow down the possible symmetries of the microscopic origin of the phase transition(s) at $T^*$., Comment: 19 pages, 9 figures

Understanding the thermodynamic properties of high-$T_c$ cuprate superconductors is a key step to establish a satisfactory theory of these materials. The electronic specific heat is highly unconventional, distinctly non-BCS, with remarkable doping-dependent features extending well beyond $T_c$. The pairon concept, bound holes in their local antiferromagnetic environment, has successfully described the tunneling and photoemission spectra. In this article, we show that the model explains the distinctive features of the entropy and specific heat throughout the temperature-doping phase diagram. Their interpretation connects unambiguously the pseudogap, existing up to $T^*$, to the superconducting state below $T_c$. In the underdoped case, the specific heat is dominated by pairon excitations, following Bose statistics, while with increasing doping, both bosonic excitations and fermionic quasiparticles coexist.

Fluctuating superconductivity - vestigial Cooper pairing in the resistive state of a material - is usually associated with low dimensionality, strong disorder or low carrier density. Here, we report single particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in heavily hole-doped cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ ($T_c$ = 66~K) despite the high carrier density. With a sign-problem free quantum Monte Carlo calculation, we show how a partially flat band at ($\pi$,0) can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors., Comment: main: 8 pages, 6 figures + supplement: 10 pages, 15 figures

It is generally difficult to quantify the amounts of light elements in materials because of their low X-ray-scattering power, as this means that they cannot be easily estimated via X-ray analyses. Meanwhile, the recently reported layered superconductor, Sc$_{20}$C$_{8-x}$B$_x$C$_{20}$, requires a small amount of boron, which is a light element, for its structural stability. In this context, here, we quantitatively evaluate the optimal $x$ value using both the experimental and computational approaches. Using the high-pressure synthesis approach that can maintain the starting composition even after sintering, we obtain the Sc$_{20}$(C,B)$_{8}$C$_{20}$ phase by the reaction of the previously reported Sc$_{15}$C$_{19}$ and B (Sc$_{15}$B$_y$C$_{19}$). Our experiments demonstrate that an increase in $y$ values promotes the phase formation of the Sc$_{20}$(C,B)$_{8}$C$_{20}$ structure; however, there appears to be an upper limit to the nominal $y$ value to form this phase. The maximum $T_\mathrm{c}$ $(=7.6\text{ K})$ is found to correspond with the actual $x$ value of $x \sim 5$ under the assumption that the sample with the same $T_\mathrm{c}$ as the reported value $(=7.7\text{ K})$ possesses the optimal $x$ amount. Moreover, we construct the energy convex hull diagram by calculating the formation enthalpy based on first principles. Our computational results indicate that the composition of Sc$_{20}$C$_4$B$_4$C$_{20}$ $(x=4)$ is the most thermodynamically stable, which is reasonably consistent with the experimentally obtained value., Comment: 10 pages, 1 table, 7 figures

In this study, we succeeded in synthesizing new antiperovskite phosphides $M$Pd$_3$P ($M$ = Ca, Sr, Ba) and discovered the appearance of a superconducting phase (0.17 $\leq$ $x$ $\leq$ 0.55) in a solid solution (Ca$_{1-x}$Sr$_x$)Pd$_3$P. Three perovskite-related crystal structures were identified in (Ca$_{1-x}$Sr$_x$)Pd$_3$P and a phase diagram was built on the basis of experimental results. The first phase transition from centrosymmetric ($Pnma$) to non-centrosymmetric orthorhombic ($Aba$2) occurred in CaPd$_3$P near room temperature. The phase transition temperature decreased as Ca$^{2+}$ was replaced with a larger-sized isovalent Sr$^{2+}$. Bulk superconductivity at a critical temperature ($T$$_c$) of approximately 3.5 K was observed in a range of $x$ = 0.17 - 0.55; this was associated with the centrosymmetric orthorhombic phase. Thereafter, a non-centrosymmetric tetragonal phase ($I$41$md$) remained stable for 0.6 $\leq$ $x$ $\leq$ 1.0, and superconductivity was significantly suppressed as samples with $x$ = 0.75 and 1.0 showed ($T$$_c$) values as low as 0.32 K and 57 mK, respectively. For further substitution with a larger-sized isovalent Ba$^{2+}$, namely (Sr$_{1-y}$Ba$_y$)Pd$_3$P, the tetragonal phase continued throughout the composition range. BaPd$_3$P no longer showed superconductivity down to 20 mK. Since the inversion symmetry of structure and superconductivity can be precisely controlled in (Ca$_{1-x}$Sr$_x$)Pd$_3$P, this material may offer a unique opportunity to study the relationship between inversion symmetry and superconductivity., Comment: 7 pages, 8 figures, 3 tables

Charge density waves (CDWs) are ubiquitous in under-doped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate under-doped Bi$_2$Sr$_{1.4}$La$_{0.6}$CuO$_{6+\delta}$ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly over-doped Bi$_2$Sr$_{1.8}$La$_{0.2}$CuO$_{6+\delta}$, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW. Our results provide a comprehensive picture of the quasi-static CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates., Comment: 25 pages + Supplementary Information. Proc. Natl Acad. Sci. USA, (2020)

We report resistance and elastoresistance measurements on (Ba$_{0.5}$K$_{0.5}$)Fe$_2$As$_2$, CaKFe$_4$As$_4$, and KCa$_2$Fe$_4$As$_4$F$_2$. The Fe-site symmetry is $D_{2d}$ in the first compound but $C_{2v}$ in the latter two, which lifts the degeneracy of the Fe $d_{xz}$ and $d_{yz}$ orbitals. The temperature dependence of the resistance and elastoresistance is similar between the three compounds. Especially, the [110] elastoresistance is enhanced with decreasing temperature irrespective of the Fe-site symmetry. This appears to be in conflict with recent Raman scattering studies on CaKFe$_4$As$_4$, which suggest the absence of nematic fluctuations. We consider possible ways of reconciliation and suggest that the present result is important in elucidating the origin of in-plane resistivity anisotropy in iron-based superconductors., Comment: 8 pages, 5 figures, 1 table

For the recently discovered cuprate superconductor $\mathrm{Ba_{2}CuO_{3+\delta}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that $s$-wave and $d$-wave pairings closely compete with each other, and, more interestingly, that the intra-orbital and inter-orbital pairings coexist. We further show that, if the energy of the $d_{3z^2-r^2}$ band is raised to make it "incipient" with the lower edge of the band close to the Fermi level within a realistic band filling regime, $s\pm$-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K$_2$NiF$_4$ structure where a close competition between $s-$ and $d-$wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band., Comment: 19 pages, 20 figures; references and figures updated

The discovery of nearly room-temperature superconductivity in superhydrides has motivated further materials research for conventional superconductors. To realize the moderately high critical temperature $(T_\mathrm{c})$ in materials containing light elements, we explored new superconducting phases in a scandium borocarbide system. Here, we report the observation of superconductivity in a new ternary Sc-B-C compound. The crystal structure, which was determined through a Rietveld analysis, belongs to tetragonal space group $P4/ncc$. By complementarily using the density functional theory calculations, a chemical formula of the compound was found to be expressed as Sc$_{20}$C$_{8-x}$B$_x$C$_{20}$($x=1\:\mathrm{or}\:2$). Interestingly, a small amount of B is essential to stabilize the present structure. Our experiments revealed the typical type-II superconductivity at $T_\mathrm{c}=7.7\:\mathrm{K}$. Additionally, we calculated the density of states within a first-principles approach and found that the contribution of the Sc-3d orbital was mainly responsible for the superconductivity., Comment: 13 pages, 3 tables, 8 figures

The search for non-centrosymmetric superconductors that may exhibit unusual physical properties and unconventional superconductivity has yielded the synthesis of a non-centrosymmetric phosphide Mg$_2$Rh$_3$P with an Al$_2$Mo$_3$C-type structure. Although stoichiometric Mg$_2$Rh$_3$P does not exhibit superconductivity at temperatures above 2 K, we found that an Mg deficiency of approximately 5 at.% in the Mg$_2$Rh$_3$P induced superconductivity at 3.9 K. Physical properties such as the lattice parameter a = 0.70881 nm, Sommerfeld constant $\gamma_n$ = 5.36 mJ mol$^{-1}$ K$^{-2}$, specific heat jump $\Delta$C$_{el}$/$\gamma_n$Tc = 0.72, electron-phonon coupling constant $\lambda$$_{e-p}$ = 0.58, upper critical field H$_{c2}$(0) = 24.3 kOe, and pressure effect dTc/dP = -0.34 K/GPa were measured for the superconducting Mg$_{2-\delta}$Rh$_3$P ($\delta$ $\sim$ 0.1). Band-structure calculations indicate that exotic fermions, which are not present in high-energy physics, exist in Mg$_2$Rh$_3$P. Since Mg, Rh, and P are the first elements used at each crystal site of Al$_2$Mo$_3$C-type compounds, the discovery of Mg$_2$Rh$_3$P may guide the search for new related materials., Comment: 12 pages, 9 figures. arXiv admin note: text overlap with arXiv:1603.03093 by other authors

The lossless current-carrying capacity of a superconductor is limited by its critical current density (Jc). A key to enhance Jc towards real-life applications is engineering defect structures to optimize the pinning landscape. For iron-based superconductors (IBSs) considered as candidate materials for high-field applications, high Jc values have been achieved by various techniques to introduce artificial pinning centres. Here we report extraordinary vortex pinning properties in CaKFe4As4 (CaK1144) arising from the inherent defect structure. Scanning transmission electron microscopy revealed the existence of nanoscale intergrowths of the CaFe2As2 phase, which is unique to CaK1144 formed as a line compound. The Jc properties in CaK1144 are found to be distinct from other IBSs characterized by a significant anisotropy with respect to the magnetic field orientation as well as a remarkable pinning mechanism significantly enhanced with increasing temperature. We propose a comprehensive explanation of the Jc properties based on the unique intergrowths acting as pinning centres., Comment: 15 pages, 5 figures, and Supplementary Information. One literature on the calculation of anisotropic Jc [S. Pyon, et al. Phys. Rev. B 99, 104506 (2019)] was added to the reference list

We report synthesis, crystal structure and superconductivity in ThCr2Si2-type LaFe2As2 (La122). La122 was synthesized at 960{\deg}C for 1.5 h under a pressure of 3.4 GPa. An as-synthesized La122 (non-superconductor) had a collapsed tetragonal structure with a short c-axis length of 11.0144(4) {\AA} as observed in CaFe2As2 under pressure. The collapsed tetragonal transformed into an uncollapsed tetragonal by annealing the as-synthesized La122 at 500{\deg}C. The c-axis length remarkably extended to 11.7317(4) {\AA} and superconductivity emerged at 12.1 K in the uncollapsed tetragonal La122. A cylindrical hole-like Fermi-surface around the {\Gamma} point that plays an important role for an s+-wave paring in iron-based superconductors was missing in the uncollapsed tetragonal La122 due to heavily electron-doping. Superconductivity in La122 may be closely related to that induced in CaFe2As2 under pressure., Comment: 8 pages, 7 figures, 1 table

We report the dynamics of the cuprate superconductor La$_{2-x}$Sr$_{x}$CuO$_4$ ($x = 0.14$) after intense photoexcitation utilizing near-infrared (800 nm) optical pump-terahertz probe spectroscopy. In the superconducting state at 5 K, we observed a redshift of the Josephson plasma resonance that sustains for hundreds of picoseconds after the photoexcitation, indicating the destruction of the $c$-axis superconducting coherence. We show that the metastable spectral features can be described by the photoinduced surface heating of the sample. We also demonstrate that the conventional analysis used to extract the spectra of the photoexcited surface region can give rise to artifacts in the nonequilibrium response.

The CuO$_2$ antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E|<$\Delta^*$, where $\Delta^*$ is the pseudogap energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite Q density-wave (DW) state and a Q=0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken symmetry states to be visualized simultaneously. Using this approach, we show that, even though their reported ordering temperatures T$_{DW}$ and T$_{NE}$ are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the pseudogap energy $\Delta^*$. Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi-surface), while the observed pseudogap opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries can be understood as the natural consequence of a vestigial nematic state , within the pseudogap phase of Bi$_2$Sr$_2$CaCu$_2$O$_8$.

Three independent components of critical current density, one for the H//c axis and the other two for the H//ab plane, have been studied in CaKFe4As4 single crystals. When the magnetic field is applied along the c axis, we observed fish-tail-like peaks in the M-H hysteresis loop, and the magnetization at higher temperatures exceeds that at lower temperatures at high fields. When the field is applied parallel to the ab plane, a dip structure is observed in the M-H hysteresis loop near the self-field. In addition, for the H//ab plane, we succeeded in separately evaluating the large and significantly anisotropic in-plane and out-of-plane Jc. Transmission electron microscopy revealed the presence of planar defects parallel to the ab plane in CaKFe4As4, which have not been observed in any other iron-based superconductors. We discuss the possible relationship between the anomalous Jc behavior and the planar defects., Comment: 19 pages, 8 figures + supplemental material 6 pages, 4 figures To be published in Phys. Rev. B