Smectic pair-density-wave order in EuRbFe4As4.

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry1-4. Experimental evidence for such a state exists in high magnetic field5-8 and in some materials that feature density-wave orders that explicitly break translational symmetry9-13. 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, a material that features co-existing superconductivity (superconducting transition temperature (Tc) ≈ 37 kelvin) and magnetism (magnetic transition temperature (Tm) ≈ 15 kelvin)14,15. Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing 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, indicating 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.

Unconventional spectral signature of Tc in a pure d-wave superconductor.

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap1. In the high-transition-temperature (high-Tc) cuprates, although the transport, magnetic and thermodynamic signatures of Tc have been known since the 1980s2, the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)2Sr2CaCu2O8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at Tc, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across Tc. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle-hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped cuprates.

Discovery of orbital ordering in Bi2Sr2CaCu2O8+x.

The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d9 and 3d10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p6 and 3d10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order 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 oxygen energy levels by ~50 meV, in underdoped CuO2.

Optically Probing Unconventional Superconductivity in Atomically Thin Bi2Sr2Ca0.92Y0.08Cu2O8+δ.

Atomically thin cuprates exhibiting a superconducting phase transition temperature similar to that of the 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 Bi2Sr2Ca0.92Y0.08Cu2O8+δ (Y-Bi2212). Apart from finding an optical response due to the superconducting phase transition that is similar to that of bulk Y-Bi2212, we observe that the sign and amplitude of the pump-probe signal in atomically thin flakes 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.

Superconductivity-driven ferromagnetism and spin manipulation using vortices in the magnetic superconductor EuRbFe4As4.

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 (T m), 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-T c) magnetic superconductor EuRbFe4As4 Although the ground state of the Eu2+ moments in EuRbFe4As4 is helimagnetism below T m, 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.

Novel electronic nematicity in heavily hole-doped iron pnictide superconductors.

Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics), resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba1-x Rb x Fe2As2 iron-based superconductors. While for [Formula: see text], the nematic director points along the in-plane diagonals of the tetragonal lattice, for [Formula: see text], it points along the horizontal and vertical axes. Remarkably, for intermediate doping, the susceptibilities of these two symmetry-irreducible nematic channels display comparable Curie-Weiss behavior, thus revealing a nearly XY-nematic state. This opens a route to assess this elusive electronic quantum liquid-crystalline state.

Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ.

Charge-density waves (CDWs) are ubiquitous in underdoped 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 underdoped Bi2Sr1.4La0.6CuO6+δ 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 overdoped Bi2Sr1.8La0.2CuO6+δ, 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 quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.

Hidden Structural and Superconducting Phase Induced in Antiperovskite Arsenide SrPd3As.

Enriching the material variation often contributes to the progress of materials science. We have discovered for the first time antiperovskite arsenide SrPd3As and revealed a hidden structural and superconducting phase in Sr(Pd1-xPtx)3As. The Pd-rich samples (0 ≤ x ≤ 0.2) had the same noncentrosymmetric (NCS) tetragonal structure (a space group of I41md) as SrPd3P. For the samples with 0.3 ≤ x ≤ 0.7, a centrosymmetric (CS) tetragonal structure (P4/nmm) identical to that of SrPt3P was found to appear, accompanied by superconductivity at a transition temperature (Tc) up to 3.7 K. In the samples synthesized with Pt-rich nominal compositions (0.8 ≤ x ≤ 1.0), Sr2(Pd,Pt)8-yAs1+y with an intergrowth structure (CS-orthorhombic with Cmcm) was crystallized. The phase diagram obtained for Sr(Pd,Pt)3As was analogous to that of (Ca,Sr)Pd3P in which superconductivity (Tc ≥ 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.

Evidence for a vestigial nematic state in the cuprate pseudogap phase.

The CuO2 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| < [Formula: see text], where [Formula: see text] is the PG 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 PG energy [Formula: see text] 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 PG 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 may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi2Sr2CaCu2O8.

Antiperovskite Superconductor LaPd3P with Noncentrosymmetric Cubic Structure.

Antiperovskites are a promising candidate structure for the exploration of new materials. We discovered an antiperovskite phosphide, LaPd3P, following our recent synthesis of APd3P (A = Ca, Sr, Ba). While APd3P and (Ca,Sr)Pd3P were found to be tetragonal or orthorhombic systems, LaPd3P is a new prototype cubic system (a = 9.0317(1) Å) with a noncentrosymmetric space group (I4̅3m). LaPd3P exhibited superconductivity with a transition temperature (Tc) of 0.28 K. The upper critical field, Debye temperature, and Sommerfeld constant (γ) were determined to be 0.305(8) kOe, 267(1) K, and 6.06(4) mJ mol-1 K-2 f.u.-1, respectively. We performed first-principles electronic band structure calculations for LaPd3P 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 γ because the Fermi energy (EF) was located slightly below the density of states (DOS) pseudogap. This difference was explained by the increase in the DOS at EF due to the approximately 5 atom % 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 LaPd3P arising from the lack of space inversion symmetry.

Intrinsic defect structures of polycrystalline CaKFe4As4 superconductors.

We investigated the defect structures of polycrystalline CaKFe4As4 (CaK1144) superconductors by scanning transmission electron microscopy (STEM). The STEM studies revealed the presence of a one-layer CaFe2As2 (∼1 nm size) defect along the ab-plane, as observed in single crystalline CaK1144. Step-like CaFe2As2 defects are also observed. These nanoscale defects generate fine-sized stacking faults, a lattice mismatch, and stress field defects in the matrix of CaK1144 owing to the different sizes. Correlation of the defects in polycrystalline and single crystalline samples suggests that the defects type and their density depend on the synthesis conditions. A self-field critical current density (Jc) of 15.2 kA cm-2 was obtained at 5 K, and the curves were sustained above 30 K with a considerable Jc value of 1.4 kA cm-2. We investigated the relationship between the observed intrinsic defects and the behavior of the field dependence of Jc. The intrinsically intergrown planar defects, even in polycrystalline samples, are expected to be advantageous for various high-field applications of bulk CaK1144 superconductors.

Structural Phase Transitions and Superconductivity Induced in Antiperovskite Phosphide CaPd3P.

In this study, we succeeded in synthesizing new antiperovskite phosphides MPd3P (M = Ca, Sr, Ba) and discovered the appearance of a superconducting phase (0.17 ≤ x ≤ 0.55) in a solid solution (Ca1-xSrx)Pd3P. Three perovskite-related crystal structures were identified in (Ca1-xSrx)Pd3P, and a phase diagram was built on the basis of experimental results. The first phase transition from centrosymmetric (Pnma) to noncentrosymmetric orthorhombic (Aba2) occurred in CaPd3P near room temperature. The phase transition temperature decreased as Ca2+ was replaced with a larger-sized isovalent Sr2+. Bulk superconductivity at a critical temperature (Tc) 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 noncentrosymmetric tetragonal phase (I41md) remained stable for 0.6 ≤ x ≤ 1.0, and superconductivity was significantly suppressed as samples with x = 0.75 and 1.0 showed Tc values as low as 0.32 K and 57 mK, respectively. For further substitution with a larger-sized isovalent Ba2+, namely, (Sr1-yBay)Pd3P, the tetragonal phase continued throughout the composition range. BaPd3P no longer showed superconductivity down to 20 mK. Since the inversion symmetry of structure and superconductivity can be precisely controlled in (Ca1-xSrx)Pd3P, this material may offer a unique opportunity to study the relationship between inversion symmetry and superconductivity.

Experimental and Computational Determination of Optimal Boron Content in Layered Superconductor Sc20C8-xBxC20.

It is generally difficult to quantify the amount 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, Sc20C8-xBxC20, 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 experimental and computational approaches. Using the high-pressure synthesis approach, which can maintain the starting composition even after sintering, we obtain the Sc20(C,B)8C20 phase by the reaction of the previously reported Sc15C19 and B (Sc15ByC19). Our experiments demonstrate that an increase in y values promotes the phase formation of the Sc20(C,B)8C20 structure; however, there appears to be an upper limit to the nominal y value to form this phase. The maximum critical temperature (Tc = 7.6 K) is found to correspond with the actual x value of x ≈ 5 under the assumption that the sample with the same Tc as the reported value (7.7 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 Sc20C4B4C20 (x = 4) is the most thermodynamically stable, which is reasonably consistent with the experimentally obtained value.

Superconductivity in a Scandium Borocarbide with a Layered Crystal Structure.

The discovery of nearly room-temperature superconductivity in superhydrides has motivated further materials research for conventional superconductors. To realize the moderately high critical temperature (Tc) 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 Sc20C8-xBxC20 (x = 1 or 2). Interestingly, a small amount of B is essential to stabilize the present structure. Our experiments revealed the typical type-II superconductivity at Tc = 7.7 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.

Commensurate 4a0-period charge density modulations throughout the Bi2Sr2CaCu2O8+x pseudogap regime.

Theories based upon strong real space (r-space) electron-electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4a0) 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 QA 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 technique reveals a virtually doping-independent locking of the local CDM wavevector at [Formula: see text] throughout the underdoped phase diagram of the canonical cuprate Bi2Sr2CaCu2O8 These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi-surface)-based picture of the cuprate CDMs but are consistent with strong-coupling r-space-based theories. Our findings imply that it is the latter that provides the intrinsic organizational principle for the cuprate CDM state.

Superconductivity on Hole-Doping Side of (La0.5-xNa0.5+x)Fe2As2.

(La0.5-xNa0.5+x)Fe2As2 ((La,Na)122) is an interesting system in the sense that either electrons (x < 0) or holes (x > 0) can be doped into the Fe2As2 layers, simply by changing the composition value x. However, only nonbulk superconducting samples (single crystals) with x = 0.1 have been synthesized to date. Here, we successfully synthesize polycrystalline samples with a wide hole-doping composition range of 0 ≤ x ≤ 0.35 via a conventional solid-state reaction, by tuning the reaction temperature according to x. The parent compound, (La0.5Na0.5)Fe2As2 (x = 0), is a nonsuperconductor with a resistivity anomaly at 130 K due to structural and antiferromagnetic transitions. We find that the temperature of the resistivity anomaly decreases with increasing x and that bulk superconductivity emerges for 0.15 ≤ x ≤ 0.35. The maximum transition temperature is 27.0 K, for x = 0.3. An electronic phase diagram for the hole-doping side is constructed. However, electron-doped samples (x < 0) cannot be synthesized; thus, the other half of the electronic phase diagram of (La,Na)122 requires resolution to study the electron-hole symmetry in Fe-based superconductors.

Fe-Based Superconductors of ( Ln0.5- xNa0.5+ x)Fe2As2 ( Ln = Ce, Pr).

Recently, we succeeded in synthesizing (La0.5- xNa0.5+ x)Fe2As2 ((La,Na)122) with a solid solution range of 0 ≤ x ≤ 0.35. Superconductivity was induced for 0.15 ≤ x ≤ 0.35, with the highest transition temperature Tc = 27.0 K for x = 0.3. Here, we report the synthesis and physical properties of analogous compounds ( Ln0.5- xNa0.5+ x)Fe2As2 (( Ln,Na)122) ( Ln = Ce, Pr). Samples were synthesized by precisely tuning the reaction temperature according to Ln and x. The solid solution ranges, 0.1 ≤ x ≤ 0.3 ( Ln = Ce) and 0.15 ≤ x ≤ 0.25 ( Ln = Pr), become narrower with increasing atomic number of Ln (which decreases the ionic radius of Ln3+). Bulk superconductivity emerged for 0.2 ≤ x ≤ 0.3 and 0.15 ≤ x ≤ 0.25 with the highest Tc of 25.6 K ( x = 0.3) and 24.7 K ( x = 0.25) for Ln = Ce and Pr, respectively. Crystal structures refined via the Rietveld analysis method showed that the ( Ln,Na)122 compounds ( Ln = La, Ce, Pr) with the highest Tc have almost the same As-Fe-As bond angles (∼107°) and As heights from Fe planes (∼1.43 Å). In addition to the solid solution ranges, the phases in the samples changed depending on the ionic radius of Ln3+. The ( Ln,Na)122 phase competes with the non-superconducting CaFe4As3(143)-type phase of ( Ln,Na)Fe4As3 for Ln = Ce and Pr, whereas only the ( Ln,Na)122 phase was stable for Ln = La. The 143-type phase alone was observed for Ln = Nd, and neither 122- nor 143-type phases were observed for Ln = Sm and Gd.

Particle-Hole Asymmetry in the Cuprate Pseudogap Measured with Time-Resolved Spectroscopy.

One of the most puzzling features of high-temperature cuprate superconductors is the pseudogap state, which appears above the temperature at which superconductivity is destroyed. There remain fundamental questions regarding its nature and its relation to superconductivity. But to address these questions, we must first determine whether the pseudogap and superconducting states share a common property: particle-hole symmetry. We introduce a new technique to test particle-hole symmetry by using laser pulses to manipulate and measure the chemical potential on picosecond time scales. The results strongly suggest that the asymmetry in the density of states is inverted in the pseudogap state, implying a particle-hole asymmetric gap. Independent of interpretation, these results can test theoretical predictions of the density of states in cuprates.

Synthesis and Superconductivity of a Strontium Digermanide SrGe2-δ with ThSi2 Structure.

We have succeeded in crystallizing a new strontium digermanide (SrGe2-δ) with the ThSi2-type structure (tetragonal SrGe2), which is theoretically predicted to compete with the EuGe2-type one (trigonal SrGe2) under pressure. The tetragonal SrGe2 appeared as a metastable phase in samples at approximately 900 °C under a pressure of 2 GPa. X-ray diffraction studies show that the tetragonal SrGe2 is formed by the reaction between trigonal SrGe2 and excess Sr. The composition of the tetragonal SrGe2 was analyzed to be SrGe1.66(4). Lattice parameters for the tetragonal SrGe2 are determined to be a = 4.559(4) Å and c = 14.42(1) Å. The tetragonal SrGe2 shows metallic resistivity behavior and exhibits superconductivity with a critical temperature (Tc) of 7.3 K, which is the highest among compounds with the ThSi2-type structure. Superconducting properties of the tetragonal SrGe2, such as the upper critical field, and the effect of pressure on Tc, are presented and superconductivity is discussed on the basis of electronic band structure calculations.

Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates.

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 CuO2 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 [Ox(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 π. 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 intraunit-cell states that exhibit a predominantly d-symmetry form factor.