Session K61: Superconductivity: Copper Oxide and Related Systems-I

Quantum Oscillations for a Pair Density Wave State

Pair density waves lead to a reconstruction of the Fermi surface because of the non-zero momentum of the pairs.  But it has been controversial whether such a reconstruction shows up in quantum oscillation measurements because of particle-hole mixing.  In this work, we study this problem by solving the Bogoliubov-deGennes equation for a vortex lattice pair density wave state using a Landau level basis and calculating how the density of states varies as a function of magnetic field.  We then use this to address the relation of the quantum oscillation period to the reconstructed and unreconstructed Fermi surfaces.   

Atomic-Scale Visualization of the Cuprate Pair Density Wave State

A Pair Density Wave (PDW) state brings up an attention to uncover the mysterious pesudogap states of the cuprate. Recently, we have observed a modulating gap in Bi₂Sr₂CaCu₂O_8+δ by the Spectroscopic Imaging-Scanning Tunneling Microscopy (SI-STM) technique, indicating a presence of the PDW order in this system¹. The gap modulation shows 8-unit-cell spatial periodicity along the Cu-O-Cu bond directions at the pesudogap energy. We also observed local density of states modulations at 4-unit-cell and 8-unit-cell periodicities along the Cu-O-Cu bond directions in the electronic structures. These results can be understood as a coupling of the PDW order itself inducing a CDW with 4-unit-cell periodicity, and a coupling between d-wave superconductivity and PDW order inducing a CDW with 8-unit-cell periodicity, respectively. In addition, we have identified edge dislocations (2p phase winding) in the CDW with 4-unit-cell periodicity, implying that there would be a p phase winding in the PDW order if they are coupled. Indeed, we observed the  p phase winding (a half-vortex) in the PDW order. Overall, we have observed canonical signatures of the PDW that is intertwined with the d-wave superconducting order. In this talk, we will discuss how they are related to each other in detail².

1, Zengyi Du, Hui Li, Sanghyun Joo, Elizabeth P. Donoway, Jinho Lee, J. C. Séamus Davis, Genda Gu, Peter D. Johnson & Kazuhiro Fujita, Nature 580 6570 (2020);

2, Zengyi Du, Hui Li, Kazuhiro Fujita, Journal of the Physical Society of Japan 90, 11103 (2021)   

Design of an array of stand-alone Bi2Sr2CaCu2O8+δ intrinsic Josephson junction terahertz emitters suitable for applications.

We modelled the output from an array of two shapes of Bi₂Sr₂CaCu₂O_8+δ (Bi2212) stand-alone mesas.  The two shapes are constructed from a  disk that is first cut into a smaller disk surrounded by an annulus, and then with six straight line cuts through the centroid equally dividing the orginal disk into six congruent pie-shaped wedges and six congruent hexaslitted annuli.  The lowest cavity mode frequencies for both types of  mesas are calculated for various ratios of the inner  ρ_i to outer ρ_o radii  of the annulus.  When the resonant cavity mode frequencies of the two mesa shapes are within 1% of each other, they are considered to be matching.  Then, the uniform and cavity mode output power distributions are calculated, and the shapes of the cavity mode output power distributions at thoses matching frequencies are sufficiently similar, they are considered to be  good candidates for the construction of the desired array.  Such an array of 12 closely positioned stand-alone mesas could have an output power well in excess of 1 mW.   

THz emission with low DC power dissipation from stacked intrinsic Josephson junction Bi2Sr2CaCu2O8 terahertz sources

The extremely anisotropic high-temperature superconductor Bi₂Sr₂CaCu₂O₈ contains stacked 'intrinsic' Josephson junctions with a large superconducting gap energy. Mesa-shaped devices constructed from this material therefore show promise as a source of coherent, continuous-wave radiation in the 'terahertz gap' range.

THz emission from these devices has previously been typically observed at frequencies between around 0.4 THz – 2 THz, corresponding to Josephson voltages of between 0.8 mV and 4 mV per intrinsic junction. However, we have recently observed a new mode of emission which occurs at bias currents below the retrapping current of the stacked Josephson junctions. The maximum emitted THz power that can be generated from this mode is comparable to that generated by the more well-established and better-understood THz emission modes in Bi₂Sr₂CaCu₂O₈ mesa sources. We will discuss the most likely mechanism for this emission mode, which can most probably be ascribed to the stacked intrinsic Josephson junctions acting as an antenna for other current-biased junctions located in the Bi₂Sr₂CaCu₂O₈ base crystal of the device. We will also discuss possible future directions of related research.   

Generic character of charge and spin density waves in superconducting cuprates

Understanding the nature of charge density waves (CDW) in cuprate superconductors has been complicated by material specific differences. A striking example is the opposite doping dependence of the CDW ordering wavevector in La-based and Y-based compounds, the two families where charge ordering is strongest and best characterized. Here we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched

La_1.8-xEu_0.2Sr_xCuO₄ over a range of doping 0.07 ≤ x ≤ 0.20. For all dopings studied by RSXS,   the CDW amplitude is approximately temperature-independent and develops well above experimentally accessible temperatures. Surprisingly, the CDW ordering wavevector shows a non-monotonic temperature dependence, with a sudden change occurring at temperatures near the SDW onset temperature. We describe this behavior with a Landau-Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and CDW-SDW coupling. Our Laudau-Ginzburg analysis suggests that the ordering wavevector at high temperatures decreases with increased doping. This behavior is opposite to the trend at low temperatures and highly reminiscent of the doping dependence seen in YBa₂Cu₃O_6+δ, suggesting a common origin of the CDW in hole-doped cuprate superconductors.   

Doping a Moire Mott insulator: t-J model study of twisted cuprates

We theoretically investigate twisted structures where each layer is composed of a strongly correlated material. In particular, we study a twisted t-J model of cuprate multilayers  within the slave-boson mean field theory. This treatment encompasses the Mott physics at small doping and self consistently generates d-wave pairing. Furthermore, including the  correct inter-layer tunneling form factor consistent with the symmetry of the Cu d_{x^2-y^2} orbital proves to be crucial for the phase diagram. We find spontaneous time reversal (T) breaking around twist angle of 45 deg, although only in a narrow window of twist angles. Moreover, the gap obtained is small and the Chern number vanishes, implying a non-topological superconductor. 

At smaller twist angles, driving an interlayer current however can lead to a gapped topological phase. The energy-phase relation of the  interlayer Josephson junction displays notable double-Cooper-pair tunneling which dominates around 45 deg. The twist angle dependence of the Josephson critical current and the Shapiro steps are consistent with  recent experiments. Utilizing the moire structure as a  probe of correlation physics, in particular of the pair density wave state, is discussed.   

Unconventional short-range structural fluctuations in the cuprate high-Tc superconductors

An overarching question in the study of quantum materials is the nature of the relation between structural and electronic properties. A prime example is the cuprate superconductors, for which the role of structural inhomogeneity has remained unclear. We have carried out diffuse X-ray and neutron scattering experiments on La_2-xSr_xCuO₄ and Tl₂Ba₂CuO_6+δ and observed prominent short-range orthorhombic fluctuations across the temperature-doping phase diagram, including for nominally tetragonal compositions [1]. The measured intensity exhibits exponential scaling in temperature, analogous to recent findings for the superconducting precursor of cuprates [2,3] and other oxides [4]. More recent X-ray scattering experiments extend these findings to additional temperatures and doping levels. Our results point to the relevance of structural inhomogeneity for the emergence of superconductivity in the cuprates.

[1] D. Pelc et al., arXiv:2103.05482 (2021)

[2] D. Pelc et al., Nat. Commun. 9, 4327 (2018)

[3] G. Yu et al., Phys. Rev. B. 99, 214502 (2019)

[4] D. Pelc et al., Nat. Commun. 10, 2729 (2019)

Work supported by the U.S. Department of Energy through the University of Minnesota Center for Quantum Materials under Grant No. DE-SC0016371.   

Enhanced charge density wave with mobile superconducting vortices in La1.885Sr0.115CuO4

High-T_c cuprates exhibit a rich phase diagram featuring intertwined density wave orders and superconductivity. It is crucial to unravel the interactions between different orders to understand these important materials. Combining x-ray free electron laser with a pulsed magnet, we elucidate these interactions in a prototypical cuprate La_1.885Sr_0.115CuO₄, by studying the charge density wave (CDW) and effects of large magnetic fields (H) up to 24 Tesla. We show the CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). At low magnetic fields, the CDW intensity grows smoothly in a manner like the SDW. However, at high fields upon entering the vortex-liquid state, we discover a sudden increase in the CDW amplitude. Our result signifies a strong response of the CDW to mobile superconducting vortices, and further suggests an intimate connection between enhanced CDW amplitude and local superconducting pairing across the H-T phase diagram.   

Roles of Lifshitz transition on thermodynamics and superconductivity in La2-xSrxCuO4

The effect of Lifshitz transition on thermodynamics and superconductivity in hole-doped cuprates has been heavily debated but remains an unanswered question. In particular, an observed maximum of electronic specific heat is proposed to originate from a quantum critical point associated with the Lifshitz transition. Here, we report an in situ angle-resolved photoemission spectroscopy study of three-dimensional Fermi surfaces in La_2-xSr_xCuO₄ thin films (x = 0.06 – 0.35). With accurate k_z dispersion quantification, the Lifshitz transition is determined to happen across a finite range x = 0.20 – 0.21. Normal state electronic specific heat, calculated from spectroscopy-derived band parameters, agrees with previous thermodynamic microcalorimetry measurements within experimental error. A d-wave superconducting gap smoothly across the Lifshitz transition demonstrates the insensitivity of superconductivity to the dramatic density of states enhancement.

    

Dynamic Parallel Spin Stripes from the 1/8 anomaly to the End of Superconductivity in La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$

Incommensurate magnetic structures based on spin stripes are known to be present across the phase diagram for hole-doped cuprates. These have been extensively studied in the 214 family of cuprates at low hole doping. The dynamic spectral weight associated with spin stripes has also been studied using inelastic neutron scattering and RIXS, with somewhat conflicting conclusions including a dimunition of spectral weight near (pi,pi) wavevectors and persistant paramagnon scattering at smaller wavevctors..  We have recently carried out inelastic neutron scattering experiments on four single crystals of Nd-LSCO with relatively high hole doping between x = 0.12 to 0.26 using time-of-flight techniques. Samples at these hole-doping levels are known to display static parallel spin stripes at low temperature, with onset temperatures and intensities which decrease rapidly with increasing x [1]. We report remarkably similar dynamic spectral weight for the corresponding dynamic parallel spin stripes, from the 1/8 anomaly near x=0.12,  to near x=0.26. Our new results are therefore consistent with persistent parallel spin stripe fluctuations around (pi, pi) across a wide range of Sr doping. These neutron scattering results, both the persistent  parallel spin stripe fluctuations and the rapid fall off with doping of the signal from the static parallel spin stripes show a remarkable similarity to the results of recent calculations for a quantum spin glass, based on a random t-J model [2].   

Coulomb blockade in strongly underdoped, strained LaSrCuO films

Many recent studies reveal the development of electronic granularity on the approach to superconductor-insulator transition in two dimensional superconductors. The role of inhomogeneity is particularly important for the understanding of the emergence of superconductivity in underdoped cuprates, which appear to be inherently inhomogeneous systems, possibly as a result of local character of pairing.

In this work we study the temperature dependence of resistance and of current-voltage characteristics for underdoped La_1.952Sr_0.048CuO₄ films with different thickness and different degree of built-in compressive strain, induced by the lattice mismatch between the film and the substrate. Strain produces inhomogeneous superconducting (SC) state in the films, evidenced by two-step SC transition, and lack of  the global phase coherence on cooling towards T=0. Instead, a reentrant increase of resistance appears, reaching several orders of magnitude in the thinner, more strongly strained film, and saturating at lowest temperatures. The saturation is accompanied by Coulomb blockade, which resembles blockade reported for Josephson junction arrays. The observation of Coulomb blockade indicates that Cooper pairs survive in the insulating state, suggesting the local character of pairing.   

Evidence of a Pair Density Wave Statein the Cuprate Pseudogap Phase

In cuprate superconductors a mysterious quantum fluid designated as the pseudogap is produced by electron-density depletion in the CuO₂ antiferromagnetic insulator. This phase appears to be the parent state to the highest temperature ambient superconductors but its nature remains unidentified. The possibility that the pseudogap of cuprates is a pair density wave (PDW) state, in which the density of electron pairs modulates spatially, has come into sharp and intense research focus. By studying strongly underdoped Bi₂Sr₂CaDyCu₂O₈ in the superconductive phase, we detect the 8a₀-periodic  modulations in real-space signifying a PDW coexisting with superconductivity. We develop a new theory for the quasiparticle interference signature (QPI) that provides a 'fingerprint' Λ(q) specifically for an 8a₀-periodic PDW. By visualizing the evolution with temperature of the electronic structure from the superconducting into the pseudogap phase, we find the temperature dependence of the QPI signature Λ(q) that is predicted for the PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi₂Sr₂CaDyCu₂O₈ pseudogap phase.