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Energy Frontier Research Centers: Center for the Computational Design of Functional Layered Materials (CCDM) August 1, 2014 - July 31, 2018; Center for Complex Materials from First Principles (CCM) August 1, 2018 - July 31, 2021 (Final Report)

The mission of the DOE Energy Frontier Research Centers CCDM (2014-2018) and CCM (2018-2021) was to theoretically develop, computationally apply, and experimentally validate electronic structure methods for all materials, with a focus on the complex materials, especially layered and two-dimensional materials, strongly-correlated materials, and liquid water. This was achieved by over 200 published journal articles authored by about 17 senior investigators from physics and chemistry and from theory, computation, and experiment, plus their collaborators. In particular, the Centers confirmed the predictive power of the SCAN (strongly constrained and appropriately normed) density functional, which was constructed to satisfy 17 known exact constraints and several appropriate norms. Without being fitted to real bonded systems, and at a modest computational cost, SCAN correctly predicted covalent, ionic, metallic, hydrogen, and van der Waals bonds in many challenging materials. SCAN gave an improved description of defects in semiconductors, surface properties of metals, seven phases of ice, liquid water, liquid and supercooled silicon, subtle structural distortions in ferroelectrics, formation energies and structural predictions for solids, and critical pressures for structural phase transitions. Perhaps most remarkably, SCAN correctly described some strongly-correlated materials that were previously believed to be beyond the reach of density-functional approximations. SCAN is the only density functional that correctly predicts the band gap closing under chemical doping of the cuprate high-temperature superconducting materials. SCAN also predicts a landscape of competing stripe and magnetic phases in the cuprates. For some materials with some codes, SCAN has convergence problems that are greatly reduced by the CCM-developed r 2 SCAN, without loss of accuracy or rigor. SCAN and r 2 SCAN still make some self-interaction error, which is greatly reduced by the CCDM/ CCM-developed local orbital scaling correction (LOSC). These Centers further proved that the fundamental energy gaps of a solid from an orbital energy difference and from total energy differences are the same for a large class of generalized Kohn-Sham (GKS) functionals, including SCAN and standard hybrid functionals, and that symmetry breaking arises when a dynamic density fluctuation drops to zero frequency. The Centers identified new mechanisms for catalysis in layered materials with ions intercalated between the layers, investigated charge density waves both in model systems and in real layered materials, studied changes of band gap with the number of layers, and explored topological ultrathin films, bent nanoribbons, and defects.

08 HYDROGEN↗

Data Files for P. Mai et al., "Fluctuating charge-density-wave correlations in the three-band Hubbard model" (2024)

The high-temperature superconducting cuprates host unidirectional spin- and charge-density-wave orders that can intertwine with superconductivity in nontrivial ways. While the charge components of these stripes have now been observed in nearly all cuprate families, their detailed evolution with doping varies across different materials and at high and low temperatures. We address this problem using nonperturbative determinant quantum Monte Carlo calculations for the three-band Hubbard model. Using an efficient implementation, we can resolve the model’s fluctuating spin and charge modulations and map their evolution as a function of the charge transfer energy and doping. We find that the incommensurability of the charge modulations is decoupled from the spin modulations and decreases with hole doping, consistent with experimental measurements at high temperatures. These findings support the proposal that the high-temperature charge correlations are distinct from the intertwined stripe order observed at low-temperature and in the single-band Hubbard model.

cuprates↗

Optical non-reciprocity in magnetic structures related to high-T_c superconductors

Rotation of the plane of polarization of reflected light (Kerr effect) is a direct manifestation of broken time reversal symmetry and is generally associated with the appearance of a ferromagnetic moment. Here I identify magnetic structures that may arise within the unit cell of cuprate superconductors that generate polarization rotation despite the absence of a net moment. For these magnetic symmetries the Kerr effect is mediated by magnetoelectric coupling, which can arise when antiferromagnetic order breaks inversion symmetry. The structures identifed are candidates for a time-reversal breaking phase in the pseudogap regime of the cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Probing the Fine Symmetry Breaking in High-Temperature Superconductor Bi 2 Sr 2 CaCu 2 O 8+δ with Angle-Resolved Nonreciprocal Transport

After decades of research, symmetry breaking in high-temperature cuprate superconductors remains a key issue to resolve and is relevant to understanding their exotic quantum phases. In the prototypical cuprate superconductor, Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212), the possible symmetry breaking has been mostly examined microscopically with scanning tunneling microscopy and photoemission spectroscopy. However, macroscopic evidence and the direct implications for electronic transport have remained elusive. Using superconductivity-enhanced nonreciprocal transport, we report macroscopic evidence of inversion symmetry breaking in Bi2212. While the inversion symmetry breaking is subtle, its effect on nonreciprocal transport is significantly enhanced by the vortex motion during the superconducting transition, leading to a robust manifestation of inversion symmetry breaking in macroscopic transport. Combining angle-resolved nonreciprocal transport and 3D tight-binding model calculations, we derive that the inversion symmetry breaking is due to subtle crystal distortions that give rise to both in-plane and out-of-plane polar axes. Our work not only establishes nonreciprocal transport as a sensitive macroscopic probe to provide electrical transport-based evidence of fine symmetry breaking in Bi2212, but also paves the way for novel device applications such as high-temperature superconducting diodes and superconducting spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Direct Visualization of Current-Stimulated Oxygen Migration in YBa 2 Cu 3 O 7–δ Thin Films

The past years have witnessed major advancements in all-electrical doping control on cuprates. In the vast majority of cases, the tuning of charge carrier density has been achieved via electric field effect by means of either a ferroelectric polarization or using a dielectric or electrolyte gating. Unfortunately, these approaches are constrained to rather thin superconducting layers and require large electric fields in order to ensure sizable carrier modulations. In this work, we focus on the investigation of oxygen doping in an extended region through current-stimulated oxygen migration in YBa 2 Cu 3 O 7–δ superconducting bridges. The underlying methodology is rather simple and avoids sophisticated nanofabrication process steps and complex electronics. Here, a patterned multiterminal transport bridge configuration allows us to electrically assess the directional counterflow of oxygen atoms and vacancies. Importantly, the emerging propagating front of current-dependent doping δ is probed in situ by optical microscopy and scanning electron microscopy. The resulting imaging techniques, together with photoinduced conductivity and Raman scattering investigations, reveal an inhomogeneous oxygen vacancy distribution with a controllable propagation speed permitting us to estimate the oxygen diffusivity. These findings provide direct evidence that the microscopic mechanism at play in electrical doping of cuprates involves diffusion of oxygen atoms with the applied current. The resulting fine control of the oxygen content would permit a systematic study of complex phase diagrams and the design of electrically addressable devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Observation of a three-dimensional quasi-long-range electronic supermodulation in YBa 2 Cu 3 O 7-x /La 0.7 Ca 0.3 MnO 3 heterostructures

Recent developments in high-temperature superconductivity highlight a generic tendency of the cuprates to develop competing electronic (charge) supermodulations. While coupled with the lattice and showing different characteristics in different materials, these supermodulations themselves are generally conceived to be quasi-two-dimensional, residing mainly in individual CuO 2 planes, and poorly correlated along the c axis. Here we observed with resonant elastic X-ray scattering a distinct type of electronic supermodulation in YBa 2 Cu 3 O 7–x (YBCO) thin films grown epitaxially on La 0.7 Ca 0.3 MnO 3 (LCMO). This supermodulation has a periodicity nearly commensurate with four lattice constants in-plane, eight out of plane, with long correlation lengths in three dimensions. It sets in far above the superconducting transition temperature and competes with superconductivity below this temperature for electronic states predominantly in the CuO 2 plane. Our finding sheds light on the nature of charge ordering in cuprates as well as a reported long-range proximity effect between superconductivity and ferromagnetism in YBCO/LCMO heterostructures.

36 MATERIALS SCIENCE↗

Pairing in a dry Fermi sea

In the traditional Bardeen–Cooper–Schrieffer theory of superconductivity, the amplitude for the propagation of a pair of electrons with momentum k and -k has a log singularity as the temperature decreases. This so-called Cooper instability arises from the presence of an electron Fermi sea. It means that an attractive interaction, no matter how weak, will eventually lead to a pairing instability. However, in the pseudogap regime of the cuprate superconductors, where parts of the Fermi surface are destroyed, this log singularity is suppressed, raising the question of how pairing occurs in the absence of a Fermi sea. In this paper, we report Hubbard model numerical results and the analysis of angular-resolved photoemission experiments on a cuprate superconductor. Finally, in contrast to the traditional theory, we find that in the pseudogap regime the pairing instability arises from an increase in the strength of the spin–fluctuation pairing interaction as the temperature decreases rather than the Cooper log instability.

36 MATERIALS SCIENCE↗

Disorder-induced topological change of the superconducting gap structure in iron pnictides

In superconductors with unconventional pairing mechanisms, the energy gap in the excitation spectrum often has nodes, which allow quasiparticle excitations at low energies. In many cases, such as in d-wave cuprate superconductors, the position and topology of nodes are imposed by the symmetry, and thus the presence of gapless excitations is protected against disorder. Here we report on the observation of distinct changes in the gap structure of iron–pnictide superconductors with increasing impurity scattering. By the successive introduction of nonmagnetic point defects into BaFe 2 (As 1–x P x ) 2 crystals via electron irradiation, we find from the low-temperature penetration depth measurements that the nodal state changes to a nodeless state with fully gapped excitations. Moreover, under further irradiation the gapped state evolves into another gapless state, providing bulk evidence of unconventional sign-changing s-wave superconductivity. As a result, this demonstrates that the topology of the superconducting gap can be controlled by disorder, which is a strikingly unique feature of iron pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Direct Spectroscopic Evidence for Phase Competition between the Pseudogap and Superconductivity in Bi 2 Sr 2 CaCu 2 O 8+δ

In the high-temperature (T c ) cuprate superconductors, increasing evidence suggests that the pseudogap, existing below the pseudogap temperature T*, has a distinct broken electronic symmetry from that of superconductivity. Particularly, recent scattering experiments on the underdoped cuprates have suggested that a charge ordering competes with superconductivity. However, no direct link of this physics and the important low-energy excitations has been identified. We report an antagonistic singularity at Tc in the spectral weight of Bi 2 Sr 2 CaCu 2 O 8+δ as a compelling evidence for phase competition, which persists up to a high hole concentration p ~ 0.22. Comparison with a theoretical calculation confirms that the singularity is a signature of competition between the order parameters for the pseudogap and superconductivity. Our observation of the spectroscopic singularity at finite temperatures over a wide doping range provides new insights into the nature of the competitive interplay between the two intertwined phases and the complex phase diagram near the pseudogap critical point.

36 MATERIALS SCIENCE↗

Visualizing nodal heavy fermion superconductivity in CeCoIn 5

Understanding the origin of superconductivity in strongly correlated electron systems continues to be at the forefront of the unsolved problems of physics. Among the heavy f-electron systems, CeCoIn 5 is one of the most fascinating, as it shares many of the characteristics of correlated d-electron high-T c cuprate and pnictide superconductors, including competition between antiferromagnetism and superconductivity. Although there has been evidence for unconventional pairing in this compound, high-resolution spectroscopic measurements of the superconducting state have been lacking. Previously, we have used high-resolution scanning tunnelling microscopy (STM) techniques to visualize the emergence of heavy fermion excitations in CeCoIn 5 and demonstrate the composite nature of these excitations well above T c (ref. 12). Here we extend these techniques to much lower temperatures to investigate how superconductivity develops within a strongly correlated band of composite excitations. Furthermore, we find the spectrum of heavy excitations to be strongly modified just before the onset of superconductivity by a suppression of the spectral weight near the Fermi energy (E F ), reminiscent of the pseudogap state in the cuprates. By measuring the response of superconductivity to various perturbations, through both quasiparticle interference (QPI) and local pair-breaking experiments, we demonstrate the nodal d-wave character of superconducting pairing in CeCoIn 5 .

Superconducting properties and materials↗

Scaling between magnetic field and temperature in the high-temperature superconductor BaFe 2 (As 1- x P x ) 2

Many exotic metallic systems have a resistivity that varies linearly with temperature, and the physics behind this is thought to be connected to high-temperature superconductivity in the cuprates and iron pnictides. Although this phenomenon has attracted considerable attention, it is unclear how the relevant physics manifests in other transport properties, for example their response to an applied magnetic field. We report measurements of the high-field magnetoresistance of the iron pnictide superconductor BaFe 2 (As 1- x P x ) 2 and find that it obeys an unusual scaling relationship between applied magnetic field and temperature, with a conversion factor given simply by the ratio of the Bohr magneton and the Boltzmann constant. This suggests that magnetic fields probe the same physics that gives rise to the T -linear resistivity, providing a new experimental clue to this long-standing puzzle.

Hayes, Ian M↗

Dispersive charge density wave excitations in Bi 2 Sr 2 CaCu 2 O 8+δ [Dispersive charge density wave excitations and temperature dependent commensuration in Bi 2 Sr 2 CaCu 2 O 8+δ ]

Experimental evidence on high-T c cuprates reveals ubiquitous charge density wave (CDW) modulations, which coexist with superconductivity. Although the CDW had been predicted by theory, important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap. We use ultrahigh-resolution resonant inelastic X-ray scattering to reveal new CDW character in underdoped Bi 2.2 Sr 1.8 Ca 0.8 Dy 0.2 Cu 2 O 8+δ . At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Furthermore, near the pseudogap temperature T*, the CDW persists, but the associated excitations significantly weaken with an indication of CDW wavevector shift. The dispersive CDW excitations, phonon anomaly, and analysis of the CDW wavevector provide a comprehensive momentum-space picture of complex CDW behaviour and point to a closer relationship with the pseudogap state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Unidirectional spin density wave state in metallic (Sr 1-x Lax) 2 IrO 4

Materials that exhibit both strong spin–orbit coupling and electron correlation effects are predicted to host numerous new electronic states. One prominent example is the J eff = 1/2 Mott state in Sr 2 IrO 4 , where introducing carriers is predicted to manifest high temperature superconductivity analogous to the S=1/2 Mott state of La 2 CuO 4 . While bulk super- conductivity currently remains elusive, anomalous quasiparticle behaviors paralleling those in the cuprates such as pseudogap formation and the formation of a d-wave gap are observed upon electron-doping Sr 2 IrO 4 . Here we establish a magnetic parallel between electron-doped Sr 2 IrO 4 and hole-doped La 2 CuO 4 by unveiling a spin density wave state in electron-doped Sr 2 IrO 4 . Our magnetic resonant X-ray scattering data reveal the presence of an incom- mensurate magnetic state reminiscent of the diagonal spin density wave state observed in the monolayer cuprate (La 1-x Sr x ) 2 CuO 4 . Furthermore, this link supports the conjecture that the quenched Mott phases in electron-doped Sr 2 IrO 4 and hole-doped La 2 CuO 4 support common competing electronic phases.

74 ATOMIC AND MOLECULAR PHYSICS↗

Stabilization of three-dimensional charge order in YBa 2 Cu 3 O 6+x via epitaxial growth

Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has confounded investigations of its impact on the transport and thermodynamic properties. The three-dimensional (3D) CO observed in YBa 2 Cu 3 O 6+x in high magnetic fields is of particular interest, because quantum transport measurements have revealed detailed information about the corresponding Fermi surface. Here we use resonant X-ray scattering to demonstrate 3D-CO in underdoped YBa 2 Cu 3 O 6+x films grown epitaxially on SrTiO 3 in the absence of magnetic fields. The resonance profiles indicate that Cu sites in the charge-reservoir layers participate in the CO state, and thus efficiently transmit CO correlations between adjacent CuO 2 bilayer units. The results offer fresh perspectives for experiments elucidating the influence of 3D-CO on the electronic properties of cuprates without the need to apply high magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observation of two types of charge-density-wave orders in superconducting La 2-x Sr x CuO 4

The discovery of charge- and spin-density-wave (CDW/SDW) orders in superconducting cuprates has altered our perspective on the nature of high-temperature superconductivity (SC). However, it has proven difficult to fully elucidate the relationship between the density wave orders and SC. Here, using resonant soft X-ray scattering, we study the archetypal cuprate La 2-x Sr x CuO 4 (LSCO) over a broad doping range. We reveal the existence of two types of CDW orders in LSCO, namely CDW stripe order and CDW short-range order (SRO). While the CDW-SRO is suppressed by SC, it is partially transformed into the CDW stripe order with developing SDW stripe order near the superconducting T c. These findings indicate that the stripe orders and SC are inhomogeneously distributed in the superconducting CuO 2 planes of LSCO. This further suggests a new perspective on the putative pair-density-wave order that coexists with SC, SDW, and CDW orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane

In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi 2 Sr 2 CaCu 2 O 8+δ , a prototypical cuprate superconductor, to probe electronic correlations within the CuO 2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Locally commensurate charge-density wave with three-unit-cell periodicity in YBa 2 Cu 3 O y

In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW’s microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa 2 Cu 3 O y is unidirectional with a commensurate period of three unit cells ( λ = 3 b ), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6 b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗