Session T16: Competing Orders in the Cuprate and Nickelate Superconductors

Model of the commensurate charge-density wave in bilayer cuprate superconductors

We propose a two-layer Ising model of the commensurate charge-density wave (CCDW) that can form in bilayer cuprate superconductors such as YBa₂Cu3O_7-δ (YBCO) and Bi₂Sr₂CaCu₂O_8+δ (Bi2212).  The excess oxygen concentrations on neighboring oxygen sites within the superconducting CuO₂ layers is opposite in sign, and is represented in this model by the repulsive interaction J.  There is also a repulsive interaction J' between excess oxygen concentrations on near-neighbor interlayer sites, where J' > J.  We calculated the partition function for continuous blocks of NM11 sites within the same layer and NM12 sites containing both layers.  We found that for all of the blocks studies, in the limit that J'→ ∞, the effective coupling between the intralayer oxygen sites becomes 2J.  This implies that the bilayer cuprates are likely to have a stronger CCDW that are single layer cuprates such as Bi₂Sr_2-xLa_xCuO_6+y (Bi2201).  This implies also that the enhanced emission power observed in underdoped Bi2212 may be stabilized by the CCDW.  In addition, the spatial form of the CCDW has d_x²-y² symmetry that is rotated by 45°from the Cu-Cu near-neighbor directions, suppressing the superconducting order parameter in those directions.  In addition, the symmetry of the CCDW is difficult to distinguish from the orbital symmetry of the superconducting order parameter, and has likely confused many workers.   

The fate of superconductivity and charge order in underdoped YBa2Cu3O6.7 under high magnetic fields

Due to the small coherence lengths, large anisotropies and high critical temperatures cuprate superconductors exhibit extremely strong superconducting fluctuations. High-resolution capacitance dilatometry on YBa₂Cu₃O_x has proven to be particularly useful in studying these fluctuation [1-3].   At optimal doping the sc transition is described well by a 3D-XY phase-ordering transition (analogous to the lambda transition in superfluid 4He) [1,2].  For underdoped crystals fluctuations increase and were attributed to anisotropic 3D-XY behavior [3].  Here, using magnetostriction measurements up to 30 T, we investigate how large a magnetic field is necessary to suppress the superconducting transition in an underdoped crystal with an oxygen content of 6.7.  We find that 30 T is far from sufficient to fully suppress the transition, in stark contrast to previous work claiming an H_c2 of roughly 20-25 T for this doping [4,5].  Further, we see little thermodynamic evidence in the magnetostriction data at 10 K for a field-induced charge-ordering transition [6].

[1] V. Pasler et al., Phys. Rev. Lett. 81, 1094 (1998).

[2] R. Lortz et al., Phys. Rev. Lett. 91, 207001 (2003).

[3] C. Meingast et al., Phys. Rev. Lett. 86, 1606 (2001).

[4] G. Grissonnanche et al., Nat. Comm. 5, 3280 (2014).

[5] C. Marcenat et al., Nature Comm. 6, 7927 (2015).

[6] J. Chang et al., Nat. Comm 7, 11494 (2016).   

A mechanism for Planckian metal phase in overdoped cuprate superconductors

The mysterious strange metallic state showing perfect T-linear resistivity and an associated universal scattering rate 1/τ = 2 π α k_b T/h with α ~1 a constant prefactor (h being Planck's constant) as well as logarithmic-in-temperature singular specific heat coefficient, so-called “Planckian metal state” was observed in various overdoped high-Tc cuprate superconductors [1]. The microscopic origin of these exotic behaviors remains elusive. Here, we offer a mechanism for this phenomenon based on quantum critical charge fluctuations within slave-boson approach to the two-dimensional t-J model. This model is further mapped onto an effective Kondo-Heisenberg-like model Hamiltonian. Via perturbative renormalization group analysis of the effective model, a quantum critical Planckian metal phase over a finite range in hole doping is realized near a localized-delocalized (Kondo breakdown) transition where bosonic charge (effective Kondo) fluctuations coupled to conduction band and gapless fermionic spinons [2]. The relevance of our results for overdoped high-Tc cuprate superconductors is discussed.     

Atomic fluctuations reveal phase transitions in underdoped YBCO

Glassy, fluctuating charge order is intertwined with superconductivity in underdoped YBa₂Cu₃O_6+y (YBCO). Here we report momentum-resolved measurements of slow atomic fluctuations using the x-ray photon correlation spectroscopy (XPCS) technique. We provide evidence of sensitivity to charge ordering, and surprisingly, to the onset of superconductivity. We discuss new insights into the complex phase competition in the cuprate superconductors.   

Charge order in the highly overdoped region of the cuprate superconductor La2-xCaxCuO4

The interplay between charge density wave (CDW) order and superconductivity in cuprates has been a subject of wide debate. Most early studies observed the disappearance of CDW just above optimal doping and well below the doping at which superconductivity disappears [1]. This brought into question the role of CDW in shaping the superconducting dome of the cuprates. Intriguingly, several recent  studies in overdoped cuprates have found the existence of CDW in the overdoped regime [1-5], thus reviving the question of CDW as an order competing against superconductivity also on the overdoped side of the phase diagram. In this talk, I will report on our resonant x-ray scattering study of CDW in highly overdoped La_2-xCa_xCuO₄ thin films, in which superconductivity remarkably persists to a doping of at least x ~ 0.50 [6]. We find that CDW persists to a doping at least as high as x = 0.50, with a domain pattern that is distinct from that observed in bulk single crystals. Furthermore, the charge ordering wavevector is observed to lock into a commensurate q ~ 0.25 at high doping, and the onset temperature is observed to increase to above room temperature for x > 0.30. I will discuss the general implications of these findings.

[1] A. Frano et al., J. Phys. Cond. Matt. 32, 374005 (2020)

[2] Y. Y. Peng et al., Nat. Mater. 17, 697 (2018)

[3] H. Miao et al., npj Quantum Materials 6, 31 (2021)

[4] Q. Li et al., Phys. Rev. Lett. 131, 116002 (2023)

[5] C. C. Tam et al., Nat. Commun. 13, 570 (2022)

[6] G. Kim et al., Proc. Natl. Acad. Sci. 118, e2106170118 (2021)   

Anomalous lattice dynamics in superconducting La1.84Sr0.16CuO4

Although Lanthanum-based cuprates represent the first discovered high-T_c superconductors, they are still not fully understood, with even their microscopic lattice structures still under debate. There a variety of different orders coexist, favoring one structure over the other, partially even competing with superconductivity. Here, we present recent x-ray photon correlation spectroscopy measurements on optimally-doped La_1.84Sr_0.16CuO₄ which probes slow lattice dynamics. A rapid change in lattice dynamics and speckle contrast entering the superconducting state are shown, indicating a change from slower, cascade-like relaxation towards faster, more localized lattice relaxation with fluctuations driven by superconducting order. This underpins the influence of the superconductivity on the lattice stability and suggests an even higher importance of electron-lattice coupling than previously considered.   

Resolving the Pseudogap in theYxP r1-xBa2Cu3O7-δ system.

Synthesis of polycrystalline Y_xPr_1−xBa₂Cu₃O_7−δ(0 ≤ x ≤ 0.275, δ ≈ 0) samples has been achieved through solid state reaction. The samples are shown to be nearly single phase by XRD analysis. A recipe that had been used previously for making similar samples was found to yield large and inhomogeneous grain sizes. Improvements on the synthesis led to more homogeneous samples and smaller grain sizes. Samples prepared by both methods were subjected to resistance measurements within the temperature range of 20k and 300k. Samples where lead contacts showed signs of peeling off had relatively low signal to noise ratios with respect to samples for which the contacts were more robust. A linear fit method was used on the latter in order to detect deviations from linearity of resistance vs. temperature data in going from the normal to the superconducting state. Samples prepared using the old recipe did not yield detectable deviations. For the improved samples, the onset temperature of these deviations was marked as the Pseudogap Temperature (T*). The values of T* thus obtained are within the range that our collaborators have found in thin film samples with similar doping amounts. We present an updated phase diagram that includes our results.   

Evolution of nematic order through the pseudogap phase in stripe-ordered cuprate superconductors

Electronic nematic order – evidenced by the breaking of rotational symmetry of the electronic structure – has now been reported in several cuprate superconductors. Resonant x-ray scattering (RXS) measurements in the low temperature tetragonal (LTT) structural phase of Nd-doped (La, Sr)₂CuO₄ has established a correlation between the pseudogap phase of the cuprates and the observation of nematicity in overdoped samples, with nematicity vanishing above the pseudogap onset temperature T^∗ and doping p^∗. Here we employ RXS measurements over a wider range of Sr doping, covering more heavily underdoped samples in related materials, (La, Ba)₂CuO₄ and Eu-doped (La, Sr)₂CuO₄. Notably, Eu-doped (La, Sr)₂CuO₄ has a larger LTT transition temperature than Nd-LSCO, but otherwise similar structure and electronic structure. In overdoped samples, these measurements confirm the previous findings in Nd-LSCO, showing evidence for nematic order to vanish above T^∗ and p^∗, as well as a crossover in the structural phase transition from 1st order to 2nd order. We also confirm a cooperative coupling between the Q_x = Q_y = 0 electronic nematic order and CDW order, which breaks both rotational and translational symmetry. In contrast to overdoped samples, in heavily underdoped samples deep within the pseudogap phase, we observe a temperature-independent nematic susceptibility, which is interpreted as a regime of strong and saturated nematic order. These results are discussed in the context of Ginzburg-Landau theory to provide insights into the doping dependence of electronic and structural symmetry breaking. 

 

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada First Research Excellence Fund, the Canada Foundation for Innovation, the National Research Council Canada, the Canadian Institutes of Health Research, the Government of Saskatchewan, the University of Saskatchewan and CIFAR.   

Oxygen ordered phases and resonant scattering measurements of the infinite-layer nickelates

Materials hosting unconventional and high T_c superconductivity demonstrate complex phase diagrams where superconductivity cooperates and competes with other ground states involving entangled charge, lattice, and spin degrees of freedom. The infinite-layer nickelates, RENiO₂, RE=La, Nd, Pr, offer a novel platform to study the nature of high T_c superconductivity and the normal state from which it emerges – possibly allowing discernment of the universal elements of the high T_c phase diagram. While the normal state of the infinite-layer nickelates shows noticeable differences from that of the cuprates (lacking a long-range ordered AFM insulating phase), recent work has shed light on some of the similarities, including the presence of magnetic fluctuations and a purported charge ordered phase in the undoped material.  However, this class of materials poses significant synthesis challenges which must be overcome to reveal their intrinsic ground state properties. Here, we discuss the synthesis of perovskite and infinite-layer nickelates by reactive oxide molecular beam epitaxy and activated hydrogen reduction. We then reexamine the presence of charge density wave order in NdNiO₂ and, using a multimodal approach, show that the previously reported 3a₀ ordering can be attributed to interstitial oxygen ordering rather than a correlation driven density wave.   

Electronic Structure of Topological Defects in the Pair-Density-Wave (PDW) Superconductor

The cuprates display a rich phase diagram supporting many kinds of orders, some of which co-exist. Generically, certain regions of the cuprates phase diagrams support both charge-density-wave (CDW) and superconducting (SC) orders, which are typically thought of as competing with one another. It has been proposed that certain CDWs are composite order parameters secondary to an elusive phase of matter: the pair-density-wave (PDW) state. The PDW is an exotic superconducting order where the Cooper pairs have a finite COM momentum, resulting in a gap function which oscillates in space. Studying the quasi-particle structure of the topological defects of the PDW phase we discuss smoking gun signatures associated with this state of matter and their relevance to experiment. In this talk we will discuss the experimental signatures in the tunneling density of states and in the electron spectral functions as experimental tools to detect the signatures of the PDW state in its topological defects.   

Mean-field study of pair density wave order in multiband models

One of the indispensable ingredients for pair density wave (PDW) superconductivity is the presence of an attractive pairing interaction, i.e. attraction in the BCS channel, at finite momentum. Here we show that in multiband systems, this condition can be met with straightforward electron-density interactions. The electron-density interaction, when projected to the band basis, acquires form factors with nontrivial momentum dependence and thereby exhibits a potential tendency to a finite-momentum pairing instability. By applying a mean-field analysis to two simple multiband models, we find that PDW order can indeed become the leading instability over a wide range of interaction parameters. Moreover, the condition for the transition from a uniform superconductor to a PDW superconductor is shown via a simple quantum geometric argument.   

Pair density wave, FFLO, and re-entrance in multi-orbital superconductors

In a spin-singlet superconductor, finite-momentum superconductivity, known as the FFLO phase, arises as a field-driven instability of the uniform state. In contrast, finite-momentum spin-triplet pairing can not be stabilized in the same way due to the different pair-breaking effects of the field on a triplet state. However, finite-momentum pairing in zero field, a pair-density wave, has been conjectured to be present in a variety of correlated materials of interest. Nonetheless, this phenomenon remains relatively less explored. Here we study how such a state can arise in a correlated multi-orbital system in the presence of the magnetic field and spin-orbit coupling. We show how the pair density wave and FFLO phases, as well as field-induced and re-entrant phases for large fields arise in correlated metals. The application to several correlated materials of interest is briefly discussed.