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Orbital polarization, charge transfer, and fluorescence in reduced-valence nickelates

Herein this paper presents a simple formalism for calculating X-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) that has as input orbital-resolved density of states from a single particle or many-body ab initio calculation and is designed to capture itinerant-like features. We use this formalism to calculate both the XAS and RIXS with input from DFT and DFT + DMFT for the recently studied reduced valence nickelates R 4 Ni 3 O 8 and RNiO 2 (R = rare earth), and these results are then contrasted with those for the cuprate CaCuO 2 and the unreduced nickelate R 4 Ni 3 O 10 . In contrast to the unreduced R 4 Ni 3 O 10 , the reduced valence nickelates as well as the cuprate show strong orbital polarization due to the dominance of x 2 – y 2 orbitals for the unoccupied 3d states. We also reproduce two key aspects of a recent RIXS experiment for R 4 Ni 3 O 8 : (i) a charge transfer feature between 3d and oxygen 2p states whose energy we find to decrease as one goes from RNiO 2 to R 4 Ni 3 O 8 to the cuprate, and (ii) an energy-dependent polarization reversal of the fluorescence line that arises from hybridization of the unoccupied 3z 2 –r 2 states with R 5d states. We end with some implications of our results for the nature of the 3d electrons in reduced valence nickelates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electronic structure, magnetic correlations, and superconducting pairing in the reduced Ruddlesden-Popper bilayer La 3 Ni 2 O 6 under pressure: Different role of d 3 z 2 - r 2 orbital compared with La 3 Ni 2 O 7

The recent discovery of superconductivity in bilayer La 3 Ni 2 O 7 (327-LNO) under pressure stimulated much interest in layered nickelates. However, superconductivity was not found in another bilayer nickelate system, La 3 Ni 2 O 6 (326-LNO), even under pressure. To understand the similarities and differences between 326-LNO and 327-LNO, using density functional theory and the random phase approximation (RPA), we systematically investigate 326-LNO under pressure. The large crystal-field splitting between the e g orbitals caused by the missing apical oxygen moves the d 3z 2 -r 2 orbital farther away from the Fermi level, implying that the d 3z 2 -r 2 orbital plays a less important role in 326-LNO than in 327-LNO. This also results in a smaller bandwidth for the d x 2 -y 2 orbital and a reduced energy gap for the bonding-antibonding splitting of the d 3z 2 -r 2 orbital in 326-LNO, as compared to 327-LNO. Moreover, the in-plane hybridization between the d x 2 -y 2 and d 3z 2 -r 2 orbitals is found to be small in 326-LNO, while it is much stronger in 327-LNO. Furthermore, the low-spin ferromagnetic state is found to be the likely ground state in 326-LNO under high pressure. The weak interlayer coupling suggests that s ± -wave pairing is unlikely in 326-LNO. The robust in-plane ferromagnetic coupling also suggests that d-wave superconductivity, which is usually caused by antiferromagnetic fluctuations of the d x 2 -y 2 orbital, is also unlikely in 326-LNO. These conclusions are supported by our many-body RPA calculations of the pairing behavior. Additionally, contrasting with the cuprates, for the bilayer cuprate HgBa 2 CaCu 2 O 6 , we find a strong self-doping effect of the d x 2 -y 2 orbital under pressure, with the charge of Cu being reduced by approximately 0.13 electrons from 0 GPa to 25 GPa. In contrast, we do not observe such a change in the electronic density in 326-LNO under pressure, establishing another important difference between the nickelates and the cuprates.

36 MATERIALS SCIENCE↗

Magnetic field dependence of high- T c interface superconductivity in L a 1.55 S r 0.45 Cu O 4 / L a 2 Cu O 4 heterostructures

Heterostructures made of a layer of a cuprate insulator La 2 CuO 4 on the top of a layer of a nonsuperconducting cuprate metal La 1.55 Sr 0.45 CuO 4 show high-T c interface superconductivity confined within a single CuO 2 plane. Given this extreme quasi-two-dimensional quantum confinement, it is of interest to find out how interface superconductivity behaves when exposed to an external magnetic field. With this motivation, we have performed contactless tunnel-diode-oscillator-based measurements in pulsed magnetic fields up to 56 T as well as measurements of the complex mutual inductance between a spiral coil and the film in static fields up to 3 T. Remarkably, we observe that interface superconductivity survives up to very high perpendicular fields, in excess of 40 T. Additionally, the critical magnetic field H m (T) reveals an upward divergence with decreasing temperature, in line with vortex melting as in bulk superconducting cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnon Splitting Induced by Charge Transfer in the Three-Orbital Hubbard Model

Understanding spin excitations and their connection to unconventional superconductivity have remained central issues since the discovery of cuprates. Direct measurement of the dynamical spin structure factor in the parent compounds can provide key information on important interactions relevant in the doped regime, and variations in the magnon dispersion have been linked closely to differences in crystal structure between families of cuprate compounds. In this paper, we elucidate the relationship between spin excitations and various controlling factors thought to be significant in high-T c materials by systematically evaluating the dynamical spin structure factor for the three-orbital Hubbard model, revealing differences in the spin dispersion along the Brillouin zone axis and the diagonal. Generally, we find that the absolute energy scale and momentum dependence of the excitations primarily are sensitive to the effective charge-transfer energy, while changes in the on-site Coulomb interactions have little effect on the details of the dispersion. In particular, our result highlights the splitting between spin excitations along the axial and diagonal directions in the Brillouin zone. Finally, this splitting decreases with increasing charge-transfer energy and correlates with changes in the apical oxygen position, and general structural variations, for different cuprate families.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Superconducting Dome in Nd 1-x Sr x NiO 2 Infinite Layer Films

We show the phase diagram of Nd 1-x Sr x NiO 2 infinite layer thin films grown on SrTiO 3 . A superconducting dome spanning 0.125 < x < 0.25 is found, remarkably similar to cuprates, albeit over a narrower doping window. However, while cuprate superconductivity is bounded by an insulator for underdoping and a metal for overdoping, here we observe weakly insulating behavior on either side of the dome. Furthermore, the normal state Hall coefficient is always small and proximate to a continuous zero crossing in doping and in temperature, in contrast to the ~ 1/x dependence observed for cuprates. This suggests the presence of both electronlike and holelike bands, consistent with band structure calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fermi arcs in a doped pseudospin-1/2 Heisenberg antiferromagnet

High temperature superconductivity arises from an electronic state that remains poorly understood and is unstable against forming various other competing orders such as spin/charge density waves and electronic liquid crystal. A signature of this anomalous electronic state is its ‘strange’ metal behaviors at high temperatures. We report the observation of a homologous electronic state in a non-cuprate material Sr2IrO4 as evidenced by the unique cuprate Fermiology reproduced in this material. Upon surface electron doping through in situ deposition of alkali-metal atoms, angle-resolved photoemission spectra of Sr2IrO4 display disconnected segments of zero-energy states, known as ‘Fermi arcs’, and a gap as large as 80 meV. Its evolution toward a normal metal phase with a closed Fermi surface as a function of doping and temperature parallels that in the cuprates. Our result suggests a novel route to high temperature superconductivity.

Kim, Y. K.↗

Theory of unconventional superconductivity in the 1/4-filled band correlated-electron super-conductors [and previous titles]. Final Report, DOE-BES grant DE-FG02-06ER46315

Determination of the mechanism of correlated-electron superconductivity (SC) has turned out to be the hardest problem in condensed matter physics. After nearly three decades of intense investigation of the high-T c cuprates it now appears that one key idea, viz., - weak doping of Mott-Hubbard semiconductors leads to SC -may not be correct, or is at least incomplete. This conclusion is arrived from recent experiments that have clearly indicated that the pseudogap state in the cuprates, separated by a thermodynamic phase transition from the undoped antiferromagnet, is significantly more complicated than thought before. Buried inside it there is a distinct charge-ordered (CO) state. Understanding the complete set of competing and coexisting phases in the pseudogap state is thus a formidable challenge. It follows that research on other correlated superconductors, which have also been known for a long time, may be able to give much needed fresh insight. It is with this motivation in this project we pursued theoretical research to understand the unconventional SC that is found in an apparently completely separate family of materials, the organic charge-transfer solids (CTS). A unique feature of the CTS is that SC there universally occurs at the carrier concentration $\rho$ of 0.5 per organic molecule, rather than under carrier doping as in the cuprates. Our work in this project focused on the correlated physics of the organic CTS as well as other inorganic materials with the same carrier density, $\rho$=0.5. This project resulted in several theoretical advances in understanding these materials.

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Soft X-Ray Spectroscopy of Low-Valence Nickelates

Low-valence nickelates—including infinite-layer (IL) and trilayer (TL) compounds—are longstanding candidates for mimicking the high-temperature superconductivity of cuprates. A recent breakthrough in the field came with the discovery of superconductivity in hole-doped IL nickelates. Yet, the degree of similarity between low-valence nickelates and cuprates is the subject of a profound debate for which soft x-ray spectroscopy experiments at the Ni L - and O K -edge provided critical input. In this review, we will discuss the essential elements of the electronic structure of low-valance nickelates revealed by x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS). Furthermore, we will review magnetic excitations observed in the RIXS spectra of IL and TL nickelates, which exhibit characteristics that are partly reminiscent of those of cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

SISGR: Atom chip microscopy: A novel probe for strongly correlated materials

Microscopy techniques co-opted from nonlinear optics and high energy physics have complemented solid-state probes in elucidating the order manifest in condensed matter materials. Up until now, however, no attempts have been made to use modern techniques of ultracold atomic physics to directly explore properties of strongly correlated or topologically protected materials. Our current program is focused on introducing a novel magnetic field microscopy technique into the toolbox of imaging probes. Our prior DOE ESPM program funded the development of a novel instrument using a dilute gas Bose-Einstein condensate (BEC) as a scanning probe capable of measuring tiny magnetic (and electric) DC and AC fields above materials. We successfully built the world's first “scanning cryogenic atom chip microscope”, and we now are in the process of characterizing its performance before using the instrument to take the first wide-area images of transport flow within unconventional superconductors, pnictides and oxide interfaces (LAO/STO), topological insulators, and colossal magnetoresistive manganites. We will do so at temperatures outside the capability of scanning SQUIDs, with ~10x better resolution and without 1/f-noise. A notable goal will be to measure the surface-to-bulk conductivity ratio in topological insulators in a relatively model-independent fashion. We have completed the construction of this magnetic microscope. The instrument uses atom chips—substrates supporting micron-sized current-carrying wires that create magnetic microtraps near surfaces for ultracold thermal gases and BECs—to enable single-shot and raster-scanned large-field-of-view detection of magnetic fields. The fields emanating from electronic transport may be detected at the 10 -7 flux quantum (Φ0) level and below; that is, few to sub-micron resolution of sub-nanotesla fields over single-shot, millimeter-long detection lengths. By harnessing the extreme sensitivity of atomic clocks and BECs to external perturbations, we are now in a position to use atom chips for imaging transport in new regimes. Scanning quantum gas atom chip microscopy introduces three very important features to the toolbox of high-resolution scanning microscopy of strongly correlated or topological materials: simultaneous detection of magnetic and electric fields (down to the sub-single electron charge level; no invasive large magnetic fields or gradients; simultaneous micro- and macroscopic spatial resolution; DC to MHz detection bandwidth; freedom from 1/ƒ flicker noise at low frequencies; and, perhaps most importantly, the complete decoupling of probe and sample temperatures. The atom chip microscope can operate at maximum sensitivity and resolution without regard to the substrate temperature. While the BEC is among the coldest objects realizable (100 nK temperatures are typical), the atom chip substrate can be positioned 1 μm away from the BEC and be as hot as 400 K or as cold as the cryostat can cool. This is because unlike superconducting probes, whose temperature is closely coupled to nearby materials, quantum gases are immune to radiative heating. The energy gap between a Rb atom’s ground state and first excited state far exceeds the typical energy of room-temperature blackbody radiation; such atoms are therefore transparent to radiation heating by materials at room temperature or below. We experimentally demonstrated a new atom chip trapping system that allows the placement and high-resolution imaging of ultracold atoms within microns from any ≤100 μm-thin, UHV-compatible material, while also allowing sample exchange with minimal experimental downtime. The sample is not connected to the atom chip, allowing rapid exchange without perturbing the atom chip or laser cooling apparatus. Exchange of the sample and retrapping of atoms has been performed within a week turnaround, limited only by chamber baking. Moreover, the decoupling of sample and atom chip provides the ability to independently tune the sample temperature and its position with respect to the trapped ultracold gas, which itself may remain in the focus of a high-resolution imaging system. We confine 100-nK BECs of 104 87Rb atoms near a gold-mirrored 100-μm-thick silicon substrate. The substrate can be cooled to 35 K without use of a heat shield, while the atom chip, 120-μm away, remains at room temperature. Atoms may be imaged with 1-μm resolution and retrapped every 16 s, allowing rapid data collection. Straightforward improvements will allow us to push sample temperatures close to 4 K, and improve imaging resolution from 1 μm down to a few-100 nm, thereby providing 10 -9 Φ0 detection sensitivity. We will test the utility of this technique by imaging the magnetic fields emanating from electronic transport and domain percolation in several interesting examples of strongly correlated or topologically protected materials. STM, transport, and x-ray scattering experiments have, among others, revealed the existence of a quantum liquid crystal state in iron (pnictide) and cuprate superconductors. This strongly correlated state of matter could also be detected by imaging the fluctuating transport (spatially and in time) of electrons as the phase/regime boundary is crossed between the pnictide non-Fermi liquid (cuprate strange metal) and the pnictide magnetic phase (cuprate pseudogap regime). Our ability to image wide-area inhomogeneous current flow from room-temperature to <10 K will allow us to study the developing domain structure and transport near twin boundary interfaces through the T N ≈50–150 K nematic transition recently identified in bulk transport experiments by Ian Fisher's group in underdoped Fe-arsinide superconductors. Again, this highlights a main feature of our cryogenic atom chip microscope: the ability to image transport regardless of the sample temperature since the BEC, at nK temperatures, is transparent to blackbody radiation, even when held a microns from the surface.

36 MATERIALS SCIENCE↗

A Model of Competing Orders and Its Application to a Novel Junction

We introduce a simple Ginzburg-Landau model to describe coupled orders, such as antiferromagnetism and superconductivity in high-T{sub c} cuprate superconductors, using which we can study the spatial modulation of the doping rate. We study junctions between non-doped and highly doped materials of cuprates. Possibility of a novel superconducting boundary state is suggested, which appears at temperatures higher than the maximum transition temperature of the bulk material at optimal doping. Experimental possibilities to realize this state is also discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pseudogap formation and quantum phase transition in strongly-correlated electron systems

Pseudogap formation is a ubiquitous phenomenon in strongly-correlated superconductors, for example cuprates, heavy-fermion superconductors, and iron pnictides. As the system is cooled, an energy gap opens in the excitation spectrum before entering the superconducting phase. The origin of formation and the relevancy to the superconductivity remain unclear, which is the most challenging problem in condensed matter physics. Here, using the cuprate as a model, we demonstrate that the formation of pseudogap is due to a massive gauge interaction between electrons, where the mass of the gauge boson, determining the interaction length scale, is the consequence of the remnant antiferromagnetic fluctuation inherited from the parent compounds. Extracting from experimental data, we predict that there is a quantum phase transition belonging to the 2D XY universality class at the critical doping where pseudogap transition vanishes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hyperbolic Cooper-Pair Polaritons in Planar Graphene/Cuprate Plasmonic Cavities

Hyperbolic Cooper-pair polaritons (HCP) in cuprate superconductors are of fundamental interest due to their potential for providing insights into the nature of unconventional superconductivity. In this study, we critically assess an experimental approach using near-field imaging to probe HCP in Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) in the presence of graphene surface plasmon polaritons (SPP). Our simulations show that inherently weak HCP features in the near-field can be strongly enhanced when coupled to graphene SPP in layered graphene/hexagonal boron nitride (hBN)/Bi-2212 heterostructures. This enhancement arises from our multilayered structures effectively acting as plasmonic cavities capable of altering collective modes of a layered superconductor by modifying its electromagnetic environment. The degree of enhancement can be selectively controlled by tuning the insulating spacer thickness with atomic precision. Finally, we verify the expected renormalization of room-temperature graphene SPP using near-field infrared imaging. Our modeling, augmented with data, attests to the validity of our approach for probing HCP modes in cuprate superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Applying Configurational Complexity to the 2D Ruddlesden–Popper Crystal Structure

The layered Ruddlesden–Popper crystal structure can host a broad range of functionally important behaviors. In this work, we establish extraordinary configurational disorder in a layered Ruddlesden–Popper (RP) structure using entropy stabilization assisted synthesis. A protype A 2 CuO 4 RP cuprate oxide with five cations on the A-site sublattice is designed and fabricated into epitaxial single crystal films using pulsed laser deposition. When grown on a near lattice matched substrate, the (La 0.2 Pr 0.2 Nd 0.2 Sm 0.2 Eu 0.2 ) 2 CuO 4 film features a T'-type RP structure with uniform A-site cation mixing and square-planar CuO4 units. These observations are made with a range of combined characterizations using X-ray diffraction, atomic-resolution scanning transmission electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray absorption spectroscopy measurements. It is further found that heteroepitaxial strain plays an important role in crystal phase formation during synthesis. Compressive strain over ~1.5% results in the formation of a non-RP cubic phase consistent with a Cu X 2O 4 spinel structure. The ability to manipulate configurational complexity and move between 2D layered RP and 3D cubic crystal structures in cuprate and related materials promises to enable flexible design strategies for a range of functionalities, such as magnetoresistance, unconventional superconductivity, ferroelectricity, catalysis, and ion transport.

36 MATERIALS SCIENCE↗

Tri-axial magnetic anisotropies in RE{sub 2}Ba{sub 4}Cu{sub 7}O{sub 15−y} superconductors

We report a novel quantification method of tri-axial magnetic anisotropy in orthorhombic substances containing rare earth (RE) ions using tri-axial magnetic alignment and tri-axial magnetic anisotropies depending on the type of RE in RE-based cuprate superconductors. From the changes in the axes for magnetization in magnetically aligned powders of (RE′{sub 1−x}RE″{sub x}){sub 2}Ba{sub 4}Cu{sub 7}O{sub y} [(RE′,RE″)247] containing RE ions with different single-ion magnetic anisotropies, the ratios of three-dimensional magnetic anisotropies between RE′247 and RE″247 could be determined. The results in (Y,Er)247, (Dy,Er)247, (Ho,Er)247, and (Y,Eu)247 systems suggest that magnetic anisotropies largely depended on the type of RE′ (or RE″), even in the heavy RE ions with higher magnetic anisotropies. An appropriate choice of RE ions in RE-based cuprate superconductors enables the reduction of the required magnetic field for the production of their bulks and thick films based on the tri-axial magnetic alignment technique using modulated rotation magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Higher superconducting transition temperature by breaking the universal pressure relation

By investigating the bulk superconducting state via dc magnetization measurements, we have discovered a common resurgence of the superconducting transition temperatures (T c s) of the monolayer Bi 2 Sr 2 CuO 6+δ (Bi2201) and bilayer Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) to beyond the maximum T c s (T c-max s) predicted by the universal relation between T c and doping ( p ) or pressure (P) at higher pressures. The T c of underdoped Bi2201 initially increases from 9.6 K at ambient to a peak at 23 K at 26 GPa and then drops as expected from the universal T c -P relation. However, at pressures above 40 GPa, T c rises rapidly without any sign of saturation up to 30 K at 51 GPa. Similarly, the T c for the slightly overdoped Bi2212 increases after passing a broad valley between 20 and 36 GPa and reaches 90 K without any sign of saturation at 56 GPa. We have, therefore, attributed this T c resurgence to a possible pressure-induced electronic transition in the cuprate compounds due to a charge transfer between the Cu 3 d x 2 - y 2 and the O 2 p bands projected from a hybrid bonding state, leading to an increase of the density of states at the Fermi level, in agreement with our density functional theory calculations. Similar T c -P behavior has also been reported in the trilayer Br 2 Sr 2 Ca 2 Cu 3 O 10+δ (Bi2223). These observations suggest that higher T c s than those previously reported for the layered cuprate high-temperature superconductors can be achieved by breaking away from the universal T c -P relation through the application of higher pressures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Local lattice distortions and dynamics in extremely overdoped superconducting YSr 2 Cu 2.75 Mo 0.25 O 7.54

A common characteristic of many “overdoped” cuprates prepared with high-pressure oxygen is T c values ≥ 50 K that often exceed that of optimally doped parent compounds, despite O stoichiometries that place the materials at the edge or outside of the conventional boundary between superconducting and normal Fermi liquid states. X-ray absorption fine-structure (XAFS) measurements at 52 K on samples of high-pressure oxygen (HPO) YSr 2 Cu 2.75 Mo 0.25 O 7.54 , T c = 84 K show that the Mo is in the (VI) valence in an unusually undistorted octahedral geometry with predominantly Mo neighbors that is consistent with its assigned substitution for Cu in the chain sites of the structure. Perturbations of the Cu environments are minimal, although the Cu X-ray absorption near-edge structure (XANES) differs from that in other cuprates. The primary deviation from the crystal structure is therefore nanophase separation into Mo- and Cu-enriched domains. There are, however, indications that the dynamical attributes of the structure are altered relative to YBa 2 Cu 3 O 7 , including a shift of the Cu-apical O two-site distribution from the chain to the plane Cu sites. Another effect that would influence T c is the possibility of multiple bands at the Fermi surface caused by the presence of the second phase and the lowering of the Fermi level.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonadiabatic coupling of the dynamical structure to the superconductivity in YSr 2 Cu 2.75 Mo 0.25 O 7.54 and Sr 2 CuO 3.3

A crucial issue in cuprates is the extent and mechanism of the coupling of the lattice to the electrons and the superconductivity. Here we report Cu K edge extended X-ray absorption fine structure measurements elucidating the internal quantum tunneling polaron (iqtp) component of the dynamical structure in two heavily overdoped superconducting cuprate compounds, tetragonal YSr 2 Cu 2.75 Mo 0.25 O 7.54 with superconducting critical temperature, T c = 84 K and hole density p = 0.3 to 0.5 per planar Cu, and the tetragonal phase of Sr 2 CuO 3.3 with T c = 95 K and p = 0.6. In YSr 2 Cu 2.75 Mo 0.25 O 7.54 changes in the Cu-apical O two-site distribution reflect a sequential renormalization of the double-well potential of this site beginning at T c , with the energy difference between the two minima increasing by ~6 meV between T c and 52 K. Sr 2 CuO 3.3 undergoes a radically larger transformation at T c , >1-Å displacements of the apical O atoms. The principal feature of the dynamical structure underlying these transformations is the strongly anharmonic oscillation of the apical O atoms in a double-well potential that results in the observation of two distinct O sites whose Cu–O distances indicate different bonding modes and valence-charge distributions. The coupling of the superconductivity to the iqtp that originates in this nonadiabatic coupling between the electrons and lattice demonstrates an important role for the dynamical structure whereby pairing occurs even in a system where displacements of the atoms that are part of the transition are sufficiently large to alter the Fermi surface. The synchronization and dynamic coherence of the iqtps resulting from the strong interactions within a crystal would be expected to influence this process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Identification of a nematic pair density wave state in Bi 2 Sr 2 CaCu 2 O 8+x

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 that 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. In this work, we use SJTM to visualize the interplay of PDW and DSC states in Bi 2 Sr 2 CaCu 2 O 8+x at a carrier density where the charge density wave 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., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi 2 Sr 2 CaCu 2 O 8+x is a vestigial nematic pair density wave state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗