Session S48: Copper Oxides: Superconductivity and Charge Order

Phonon-Induced Emergent Charge Order in Cuprates

Charge-density modulations are inevitably accompanied by a distortion of the crystalline lattice. Electronic or phononic origins of charge order are therefore difficult to distinguish. Here we propose a mechanism which traces the charge-density wave formation in underdoped cuprates to the incipient softening of a bond-buckling phonon. The momentum dependence of its coupling to the electrons in the copper oxygen planes favourably selects the incommensurate and axial ordering wavevector. But, it requires strong electronic correlations via their cuprate specific renormalization of the weight and the dispersion of quasiparticles to enable a unique enhancement of the charge susceptibility near the B_1g -phonon selected wavevector. The frequency of the B_1g phonon softens by a few percent, and a lattice instability with concomitant finite range charge-density wave correlations will form locally, if nucleated by materials’ defects or dopant disorder.   

Superconducting order in the doped Holstein model

The Holstein model (HM) is a tight-binding Hamiltonian which describes the interaction between electrons and local phonon modes on a lattice. Although charge density wave (CDW) order dominates at half-filling, the electron-phonon interaction is known to give rise to superconducting (SC) order away from half-filling. We use Quantum Monte Carlo simulations to explore the onset of SC order in doped systems through measurements of the s-wave pair susceptibility. We provide estimates for the critical temperature of the SC transition, obtained through a scaling analysis, for various values of the electron-phonon coupling λ and phonon frequency ω. We complement our calculation of the pair susceptibility with measurements of the electron kinetic energy and nearest-neighbor charge correlator.   

Charge Density Wave and Superconductivity in the Disordered Holstein Model

The interplay between electron-electron correlations and disorder has
been a central theme of condensed matter physics over the last several
decades, with the possibility that interactions might cause
delocalization of an Anderson insulator into a metallic state, and the
disrupting effects of randomness on magnetic order and the Mott phase
both being central themes of investigation. Here we extend this
physics to explore electron-phonon interactions and
show, via exact quantum Monte Carlo simulations, that the suppression
of the charge density wave correlations in the half-filled Holstein
model by disorder can stabilize a superconducting phase.
We discuss the relationship of our work to studies of the
disorder quenching of the charge ordered phase in ZrTe₃ through Se doping, and the
interplay with the observed superconductivity in that material,
reproducing the qualitative features of the phase diagram in the
temperature-disorder strength plane.   

Charge ordering due to topological reconstruction of the Fermi surface

Numerous experiments in recent years indicate presence of charge ordering such as charge density wave (CDW) in layered 2D materials among which we single out HiTC cuprates in pseudogap regime and intercalated graphite. External magnetic field leads to the stabilization of long-ranged CDW. We show that topological reconstruction of the Fermi surface (FS), appearing as a consequence of spontaneously created CDW of such wave vector to bring closed electron pockets to touching, lowers the total energy of electron condensate. Opening the gap Δ at the touching points transforms the chain of closed electron pockets into a continuous open FS. Such CDW appears as rather peculiar quantum phase transition, with nonstandard dependence of condensate energy on Δ for coupling constant of responsible interaction exceeding the critical value [PRB 97 235439]. It appears in the regime opposite to the standard CDW mechanism related to the FS nesting. Introducing external magnetic field, and taking into account magnetic breakdown, even more strengthens the spontaneous FS reconstruction because open FS does not undergo the energy-increasing Landau quantization [PRB 100 115108]. Reconstruction in two directions changes sign of the Hall constant.   

Enhanced electron-phonon coupling for charge-density-wave formation in La1.8-xEu0.2SrxCuO4

Charge density waves (CDW) are prevalent in all copper-oxide superconductors and their connection to high-temperature superconductivity is hotly debated. A key issue is that, although widely studied, that the microscopic origin of CDW is still unclear. For conventional CDWs in metals, electron-phonon coupling (EPC) plays an important role for the CDW formation. Resonant inelastic X-ray scattering (RIXS) has recently become an effective tool to directly determine the momentum dependence of the electron-phonon coupling strength. Here we present the first RIXS study of the CDW and Cu-O bond-stretching phonons in La_1.8-xEu_0.2Sr_xCuO₄ compounds. By varying the sample doping and temperature, we show that the EPC is surprisingly enhanced around the CDW wave vector. Our results support a picture in which lattice excitations play a central role in the formation of the CDW, and furthermore exhibit a feedback effect in which the CDW enhances the EPC.
  

Observation of two types of charge-density-wave orders in superconducting La2-xSrxCuO4

Density wave orders, including charge- and spin-density-wave (CDW/SDW), have been widely observed in cuprate superconductors. However, to fully elucidate the relationship between the density wave orders and high temperature superconductivity (SC) has been challenging. Here we use resonant soft X-ray scattering to study the CDW order in superconducting La_2-xSr_xCuO₄ (LSCO) over a broad doping range. We discover two types of CDW orders in LSCO, namely CDW stripe order and CDW short-range order (SRO). They exhibit distinct interactions with SC that are not simply competitive. While the CDW-SRO is suppressed by SC, it is partially transformed into the CDW stripe order which keeps growing with developing SDW stripe order below the superconducting T_c. Our findings suggest that the stripe orders and SC are inhomogeneously distributed in the superconducting CuO₂ planes, and point to the emergence of a heterogeneous low temperature state as a result of the intricate interplay between CDW, SDW, and SC in LSCO.   

Observation of an extended charge density wave boundary beyond the LTT phase in optimally doped LBCO

Charge density wave (CDW) correlation in cuprates has been deemed a key ingredient to understand high-Tc superconductivity (SC). Since CDW is intertwined with other phases in a complicated way, determining the phase diagram of CDW is of critical importance. Here we focus on an archetypal La-based cuprate La_2-xBa_xCuO₄ (LBCO) that has shown an interesting CDW behavior. The onset of CDW appears correlated with the low-temperature tetragonal (LTT) phase transition in the underdoped region whereas there is a big discrepancy above x=1/8. Particularly at the optimal doping of x=0.155, CDW was reported to occur at more than 20 K below the LTT transition. This contrasting behavior has not been well understood. Here, we present a resonant soft X-ray scattering (RSXS) study of CDW in optimally-doped LBCO, where we utilized a novel TES spectrometer with unprecedented sensitivity. Surprisingly, we detected short-ranged CDW up to T ~ 115 K, which is much higher than not just the previously reported CDW onset temperature but also the LTT transition temperature. We also observed behavior that suggests a positive correlation between CDW and SC, which are thought to be in general competing with each other. In this presentation, we will further discuss the implications of these new findings.   

Doping dependence study of CDW and its excitations via high resolution RIXS

Although it is now well established a charge order (CO) is ubiquitous high-temperature superconducting cuprates, its doping dependence, interplay with superconductivity, and more importantly, its relevance to the putative quantum critical fluctuation inside the superconducting dome remain an active area of research. To gain further insights, it is necessary to conduct a comprehensive doping and temperature dependence study. High energy resolution momentum-resolved resonant inelastic soft x-ray scattering (RIXS) experiments at the Cu L3-edge has been performed on the high-temperature superconductor Bi₂Sr₂CaCu₂O_8+x with 8 different doping concentration throughout the phase diagram, including antiferromagnetic, underdoped, optimally doped, and overdoped regime, at the superconducting critical temperature Tc and well below the Tc. Doping and temperature dependence of the CDW, the associated phonon softening, and excitations will be discussed.   

Resonant x-ray scattering studies of nematicity and charge order in the La-based superconducting cuprates

Charge-density waves (CDWs) are ubiquitous in the cuprates, however it is often difficult to distinguish between their different patterns and rotational symmetries. Additional phases, such as superconductivity and nematicity, further enrich the interplay between the low temperature phases in the cuprates and rotational symmetry. In particular, the La-based materials show an orthorhombic (LTO) to tetragonal (LTT) phase transition, with the LTT stabilizing stripes within the CuO₂ planes. Recent resonant inelastic x-ray scattering (RIXS) experiments also indicate the presence of high-temperature CDW correlations in these materials. In this study we use resonant x-ray scattering (RXS) to probe the energy and temperature dependent CDW correlations. We interpret our results in terms of the effects of uniaxial strain to the CDW correlations to uncover the nature of their interplay with nematic order.   

X-ray scattering study of the role of charge-order in enhancing the superconducting transition

We combined proton irradiation (PI) and x-ray scattering to controllably tune and probe the competition between superconductivity (SC) and spatially modulated orders (e.g. charge order, CO). In particular, in La_2-xBa_xCuO₄ (LBCO) complementary magnetization, tunnel diode oscillator, and resistivity measurements discovered that, despite being a d-wave superconductor, disorder induced by PI increases the superconducting critical temperature (T_c) by up to 50 % (4 K to 6 K) near x = 1/8 doping. X-ray scattering revealed that this T_c increase coincides with a substantial suppression in CO strength and correlation length, providing clear evidence of strong competition between CO and bulk SC in LBCO. Insight from scattering and TDO suggest this competition originates from the cancellation of the interlayer Josephson coupling between CuO₂ planes.   

Time-resolved resonant soft x-ray scattering study on charge density wave in YBCO

Charge order / charge density wave (CO/CDW) have been observed in the most of cuprate superconductor families by x-ray scattering and they are considered as ubiquitous features in cuprate superconductors. To understand their properties and relation to superconductivity, the CDW have been investigated as a function of temperature, external magnetic field, doping, and other conditions.
In this study, we have investigated the temporal dynamics of the CDW in YBa₂Cu₃O_6+x single crystal using time-resolved resonant soft x-ray scattering (tr-RSXS) at the newly developed RSXS endstation of the PAL-XFEL. Using infrared optical pump, CDW correlation changes within a few picosecond time window. Detailed results, i.e. temperature and fluence dependence, will be discussed in the presentation.   

Search for charge density wave order in (Y1-xPrx) Ba2Cu307

High-T_c superconductivity in cuprates occurs in proximity to competing low-temperature density-wave-order states. Superconductivity appears when spin order of the parent compound is destroyed and for underdoped compounds it competes with charge density wave (CDW) order. Resonant elastic soft x-ray scattering (RSXS) combines x-ray scattering with x-ray spectroscopy, making it possible to probe a variety of exotic spin, charge, orbital and structural ordering phenomena. We report on the growth and characterization of single crystals of Y_1-xPr_xBa₂Cu₃0₇ cuprate superconductors with 0 < x < 1.0 by means of XRD, magnetic susceptibility, and electrical resistivity measurements, as well as RSXS measurements performed to probe the relationship between CDW order, the pseudogap, and high T_c superconductivity in this unexplored system.   

Visualizing charge ordering in a charge-transfer insulating cuprate

Although numerous symmetry-broken electronic states have been detected in metallic and superconducting cuprates at relative high carrier doping, there still exists little information about the “parent” state of cuprates after the first few charge carriers are introduced. The bottleneck in large part lies in the difficulty of synthesizing and characterizing bulk cuprates in the very lightly doped insulating regime at low temperatures. We demonstrate that by annealing the surface of optimally-doped superconducting Bi₂Sr₂CaCu₂O_8+x (T_c ~ 91 K) in ultra-high vacuum, we can reduce the oxygen dopant density near the surface and extend the hole doping range to achieve the previously inaccessible charge-transfer insulating state at low temperature (Zhao et al., Nat. Mater. 18, 103 (2019)). At this low doping, we discover a unidirectional charge-stripe order with a commensurate 4a₀ period, the same as the charge ordering wave vector previously seen across the pseudogap phase and the superconducting dome. Our work provides strong evidence that charge ordering in cuprates is unlikely to be related to the pseudogap phase.   

The effect of magnetic field on the charge density wave in La2−xSrxCuO4 near the critical end point

The interplay between superconductivity and other competing tendencies has been intensely investigated in high temperature cuprate superconductors. In underdoped La- based cuprates, the charge and spin orders appear to be intertwined to form stripes with the incommensurability δ_charge = 2δ_spin [1]. In contrast, in YBa₂Cu₃O_6+x (YBCO), charge density waves (CDW) and spin density waves (SDW) emerge at different doping indicating that they might compete with each other. These competing tendencies can be tuned by a magnetic field. In YBCO, a magnetic field can give rise to a ferro-type long-range CDW in-phase along the c direction, distinct from the short-range anti-phase CDW at zero field [2,3]. Here, we study the effects of a magnetic field on the CDW of La_2−xSr_xCuO₄ (x = 0.132), a composition close to the end point of the SDW where no SDW is observed at zero field. We find that the magnetic field induces a CDW such that its intensity grows linearly with field. A similar increase in the SDW intensity is observed for the SDW suggesting that the SDW and CDW modulations are strongly coupled as required for example in stripe theories.
[1] J. M. Tranquada et al, Nature 375, 561 (1995).
[2] J. Chang et al, Nat. Comm. 7, 11494 (2016).
[3] J. Choi et al, arXiv 1909.09359 (2019).