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At least 577 records · Page 32

Grounding our Understanding of the Impacts of Boreal Forest Expansion on Shallow Cumulus Clouds with a Simple Modeling Framework

Abstract The expansion of the boreal forest poleward is a potentially important driver of feedbacks between the land surface and Arctic climate. A growing body of work has highlighted the importance of differences in evaporative resistance between different possible future Arctic land covers, which in turn alters humidity and cloudiness in the boundary layer, for these feedbacks. While thus far this problem has been studied primarily with complex Earth system models, we turn to a locally focused, idealized model capable of diagnosing and testing the sensitivity of first-order processes connecting vegetation, the atmospheric boundary layer, and low clouds in this critical region. This allows us to benchmark the mechanisms and results at the center of predictions from larger-scale simulations. A surface dominated by broadleaf trees, characterized by higher albedo and lower surface evaporative resistance, drives cooling and moistening of the boundary layer relative to a surface of needleleaf trees, characterized by lower albedo and higher surface evaporative resistance. Differences in evaporative resistance between these hypothetical Arctic vegetation covers are of equal importance to changes in albedo for the initial response of the boundary layer to boreal expansion, even with our idealized approach. However, compensation between the elevation of the lifting condensation level (LCL) and more rapid growth of the mixed layer over higher evaporative resistance surfaces can minimize changes in the favorability of shallow clouds over different land cover types under some conditions. We then perform two tests on the sensitivity of this compensating effect, to changes in water availability, represented first by a reduction in boundary layer humidity and then by both a reduction in humidity and soil moisture available to our vegetation surface. Finally, given the importance of this potential LCL–mixed-layer height compensation in our idealized modeling results, we look to determine its relevance in observational data from a field campaign in boreal Finland. These observations do confirm that such a coupling plays an important role in cumulus-topped boundary layers over a needleleaf forest surface. While our results confirm some underlying mechanisms at the center of prior work with Earth system models, they also provide motivation for future work to constrain the impact of boreal forest expansion. This will include both large eddy simulations to examine the impact of processes and feedbacks not resolved by a mixed-layer model, as well as a more systematic evaluation and comparison of relevant observations at the site in Finland and sites from prior boreal field campaigns. Significance Statement Clouds and vegetation are both important components of the climate system that interact across a range of scales. These interactions are central to understanding how changes at the land surface feedback on climate. For example, if a forest expands or recedes, diagnosing how that will impact clouds will determine whether you predict warming or cooling temperatures from that shift in the forest area. These predictions are often made with complex Earth system models, but we look to a more idealized representation of the land–atmosphere system to diagnose how shallow clouds should respond to changes in surface properties with different scenarios of boreal forest expansion at a more foundational level. This both grounds our understanding of previous analysis and provides helpful direction for future studies of this relevant and impactful land cover change.

Meteorology & Atmospheric Sciences↗

Low-energy parameters of neutron-neutron interaction in the effective-range approximation

The effect of the mass difference between the charged and neutral pions on the low-energy parameters of nucleon-nucleon interaction in the {sup 1}S{sub 0} state is studied in the effective-range approximation. On the basis of experimental values of the singlet parameters of neutron-proton scattering and the experimental value of the virtual-state energy for the neutron-neutron systemin the {sup 1}S{sub 0} state, the following values were obtained for the neutron-neutron scattering length and effective range: a{sub nn} = -16.59(117) fm and r{sub nn} = 2.83(11) fm. The calculated values agree well with present-day experimental results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Long-range quadrupole electron-phonon interaction from first principles

Lattice vibrations in materials induce perturbations on the electron dynamics in the form of long-range (dipole and quadrupole) and short-range (octopole and higher) potentials. The dipole Fröhlich term can be included in current first-principles electron-phonon (e-ph) calculations and is present only in polar materials. The quadrupole e-ph interaction is present in both polar and nonpolar materials, but currently it cannot be computed from first principles. In this work, we show an approach to compute the quadrupole e-ph interaction and include it in ab initio calculations of e-ph matrix elements. The accuracy of the approach is demonstrated by comparing with direct density functional perturbation theory calculations. We apply our method to silicon as a case of a nonpolar semiconductor and tetragonal PbTiO 3 as a case of a polar piezoelectric material. In both materials we find that the quadrupole term strongly impacts the e-ph matrix elements. Analysis of e-ph interactions for different phonon modes reveals that the quadrupole term mainly affects optical modes in silicon and acoustic modes in PbTiO 3 , although the quadrupole term is needed for all modes to achieve quantitative accuracy. The effect of the quadrupole e-ph interaction on electron scattering processes and transport is shown to be important. Our approach enables accurate studies of e-ph interactions in broad classes of nonpolar, polar, and piezoelectric materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multicanonical sampling of the space of states of ℋ(2, n)-vector models

Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices with short-range (SR) dipole interaction, as well as with long-range (LR) dipole interaction and free boundary conditions, and models of spin quasilattices with finite interaction radius. It is established that systems of a finite number of Ising spins with LR dipole interaction can have unusual thermodynamic properties characterized by several specific-heat peaks in the absence of an external magnetic field. For a parallel multicanonical sampling method, optimal schemes are found empirically for partitioning the space of states into energy bands for Ising and SSI models, methods of concatenation and renormalization of histograms are discussed, and a flatness criterion of histograms is proposed. It is established that there is no phase transition in a model with nearest neighbor interaction on a hexagonal lattice, while the temperature behavior of specific heat exhibits singularity in the same model, in case of LR interaction. A spin quasilattice is found that exhibits a nonzero value of residual entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Neural network potentials with effective charge separation for non-equilibrium dynamics of ionic solids: a ZnO case study

Developing neural network potentials (NNPs) accurate under non-equilibrium dynamics is challenging, as such systems require extensive sampling beyond equilibrium phases. Here we construct high-fidelity NNPs for zinc oxide (ZnO), a polymorphic ionic solid, using density functional theory (DFT) reference data. To efficiently capture transitional configurations, we combine enhanced-sampling molecular dynamics with empirical potentials, data distillation, and pretraining on short-range atomic energies (A-Train), followed by transfer learning with DFT-relabeled datasets. This hierarchical approach improves transferability across polymorphs and stress states. We further introduce effective charge separation, treating long-range Coulombic terms analytically while short-range residual interactions are learned by the NNP. The optimal effective charges fall in the range 0.5–1.0 q e , consistent with dielectric-screened values derived from formal charges but distinct from Bader estimates. Motivated by this observation, we propose a simple data-driven protocol in which effective charges are optimized by comparing DFT reference energies with explicit Coulomb calculations, without additional NNP training. This strategy improves accuracy and transferability in DFT-level predictions of energies, forces, and stress. Together, these results provide a practical charge-selection framework for robust NNP development in ionic solids, enabling reliable simulation of polymorphic phase transformations and non-equilibrium dynamics.

Chemistry↗

Spontaneous Gap Opening and Potential Excitonic States in an Ideal Dirac Semimetal Ta 2 Pd 3 Te 5

The opening of an energy gap in the electronic structure generally indicates the presence of interactions. In materials with low carrier density and short screening length, long-range Coulomb interaction favors the spontaneous formation of electron-hole pairs, so called excitons, opening an excitonic gap at the Fermi level. Excitonic materials host unique phenomena associated with pair excitations. However, there is still no generally recognized single-crystal material with excitonic order, which is, therefore, awaited in condensed matter physics. Here, we show that excitonic states may exist in the quasi-one-dimensional material Ta 2 Pd 3 Te 5 , which has an almost ideal Dirac-like band structure, with the Dirac point located exactly at the Fermi level. We find that an energy gap appears at 350 K, and it grows with decreasing temperature. The spontaneous gap opening is absent in a similar material Ta 2 Ni 3 Te 5 . Intriguingly, the gap is destroyed by the potassium deposition on the crystal, likely due to extra-doped carriers. Furthermore, we observe a pair of in-gap flat bands, which is an analog of the impurity states in a superconducting gap. All these observations can be properly explained by an excitonic order, providing Ta 2 Pd 3 Te 5 as a new and promising candidate realizing excitonic states. Published by the American Physical Society 2024

Zhang, Peng (ORCID:0000000225634670)↗

Assessing Electronic Structure Methods for Long-Range Three-Body Dispersion Interactions: Analysis and Calculations on Well-Separated Metal Atom Trimers

Three-body dispersion interactions are much weaker than their two-body counterpart. However, their importance grows quickly as the number of interacting monomers rises. To explore the numerical performance of correlation methods for long-range three-body dispersion, we performed calculations on eight very simple dispersion-dominated model metal trimers: Na 3 , Mg 3 , Zn 3 , Cd 3 , Hg 3 , Cu 3 , Ag 3 , and Au 3 . One encouraging aspect is that relatively small basis sets of augmented triple-ζ size appear to be adequate for three-body dispersion in the long-range. Coupled cluster calculations were performed at high levels to assess MP3, CCSD, CCSD(T), empirical density functional theory dispersion (D3), and the many-body dispersion (MBD) approach. We found that the accuracy of CCSD(T) was generally significantly lower than for two-body interactions, with errors sometimes reaching 20% in the investigated systems, while CCSD and particularly MP3 were generally more erratic. MBD is found to perform better than D3 at large distances, whereas the opposite is true at shorter distances. When computing reference numbers for three-body dispersion, care should be taken to appropriately represent the effect of the connected triple excitations, which are significant in most cases and incompletely approximated by CCSD(T).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Communication: Polymer entanglement dynamics: Role of attractive interactions

The coupled dynamics of entangled polymers, which span broad time and length scales, govern their unique viscoelastic properties. To follow chain mobility by numerical simulations from the intermediate Rouse and reptation regimes to the late time diffusive regime, highly coarse grained models with purely repulsive interactions between monomers are widely used since they are computationally the most efficient. In this paper, using large scale molecular dynamics simulations, the effect of including the attractive interaction between monomers on the dynamics of entangled polymer melts is explored for the first time over a wide temperature range. Attractive interactions have little effect on the local packing for all temperatures T and on the chain mobility for T higher than about twice the glass transition T g . Finally, these results, across a broad range of molecular weight, show that to study the dynamics of entangled polymer melts, the interactions can be treated as pure repulsive, confirming a posteriori the validity of previous studies and opening the way to new large scale numerical simulations.

36 MATERIALS SCIENCE↗

Optomechanic interactions in phoxonic cavities

Phoxonic crystals are periodic structures exhibiting simultaneous phononic and photonic band gaps, thus allowing the confinement of both excitations in the same cavity. The phonon-photon interaction can be enhanced due to the overlap of both waves in the cavity. In this paper, we discuss some of our recent theoretical works on the strength of the optomechanic coupling, based on both photoelastic and moving interfaces mechanisms, in different (2D, slabs, strips) phoxonic crystals cavities. The cases of two-dimensional infinite and slab structures will enable us to mention the important role of the symmetry and degeneracy of the modes, as well as the role of the materials whose photoelastic constants can be wavelength dependent. Depending on the phonon-photon pair, the photoelastic and moving interface mechanisms can contribute in phase or out-of-phase. Then, the main part of the paper will be devoted to the optomechanic interaction in a corrugated nanobeam waveguide exhibiting dual phononic/photonic band gaps. Such structures can provide photonic modes with very high quality factor, high frequency phononic modes of a few GHz inside a gap and optomechanical coupling rate reaching a few MHz.

36 MATERIALS SCIENCE↗

Anisotropic quantum Hall states in the presence of interactions with fourfold rotational symmetry

We study the effects of anisotropic interactions in the quantum Hall effect in the presence of a fourfold discrete rotational (C 4 ) symmetry. Employing the density matrix renormalization group technique on an infinite cylinder geometry (iDMRG), we calculate the anisotropy response of the Laughlin state at ν = 1/3 and the composite-Fermi liquid (CFL) state at ν = 1/2. We find that the anisotropy transferred from the interaction potential to the ν = 1/3 state is stronger when compared with the complementary case of an anisotropic band. Further, the strength of anisotropy reduces as the interaction is made shorter ranged. Quite surprisingly, at ν = 1/2, the deformation in the CF Fermi surface changes sign as the interaction range is reduced. Our results imply that the short-distance and long-distance parts of the interaction potential have opposite effects on the CFL state in the presence of C 4 -symmetric anisotropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Active microrheology and dynamic phases for pattern-forming systems with competing interactions

We consider the driven dynamics of a probe particle moving through an assembly of particles with competing long-range repulsive and short-range attractive interactions, which form crystal, stripe, labyrinth, and bubble states as the ratio of attraction to repulsion is varied. We show that the probe particle exhibits a depinning-like threshold from an elastic regime, where the probe particle is trapped by interactions with the other particles, to a plastic flow regime, where the probe particle can break bonds in the surrounding medium. For a fixed particle density, the depinning threshold and sliding velocity of the probe particle vary nonmonotonically as the attraction term is increased. A velocity minimum appears near the crystal to stripe crossover, and there is a significant increase in the depinning threshold in the bubble regime when the probe particle is strongly confined inside the bubbles. For fixed attractive interaction but increasing particle density, the behavior is also nonmonotonic, and there are jumps and drops in the velocity and depinning threshold corresponding to points at which the system transitions between different structures. There are also several distinct flow states that can be characterized by the amount of plastic deformation induced by the probe particle in the surrounding medium. Each flow state generates a different amount of effective drag on the probe particle, and there can be jumps in the velocity-force curve at transitions between the states. In conclusion, we also find that when oriented stripes are present, the probe particle can move along the stripe in an edge transport state that has a finite Hall angle.

36 MATERIALS SCIENCE↗

A recipe for free-energy functionals of polarizable molecular fluids

Classical density-functional theory is the most direct approach to equilibrium structures and free energies of inhomogeneous liquids, but requires the construction of an approximate free-energy functional for each liquid of interest. We present a general recipe for constructing functionals for small-molecular liquids based only on bulk experimental properties and ab initio calculations of a single solvent molecule. This recipe combines the exact free energy of the non-interacting system with fundamental measure theory for the repulsive contribution and a weighted density functional for the short-ranged attractive interactions. We add to these ingredients a weighted polarization functional for the long-range correlations in both the rotational and molecular-polarizability contributions to the dielectric response. We also perform molecular dynamics calculations for the free energy of cavity formation and the high-field dielectric response, and show that our free-energy functional adequately describes these properties (which are key for accurate solvation calculations) for all three solvents in our study: water, chloroform, and carbon tetrachloride.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The effect of metal-contacts on carbon nanotube for high frequency interconnects and devices

High frequency characterisation of platinum and tungsten contacts on individual multi-walled carbon nanotubes (MWNT) is performed from 10 MHz to 50 GHz. By measuring the scattering parameters of aligned individual MWNTs, we show that metal contacts enhance an inductive response due to the improved MWNT-electrode coupling reducing the capacitive effect. This behaviour is pronounced in the frequency below 10 GHz and strong for tungsten contacts. We explain the inductive response as a result of the interaction of stimulus current with the localized (or defects) states present at the contact region resulting in the current lagging behind the voltage. The results are further supported by direct current measurements that show tungsten to significantly increase carbon nanotube-electrode coupling. The immediate consequence is the reduction of the contact resistance, implying a reduction of electron tunnelling barrier from the electrode to the carbon nanotube.

36 MATERIALS SCIENCE↗

'Self-absorbed' GeV light curves of gamma-ray burst afterglows

We investigate the effect that the absorption of high-energy (above 100 MeV) photons produced in gamma-ray burst afterglow shocks has on the light curves and spectra of Fermi Large Area Telescope (LAT) afterglows. Afterglows produced by the interaction of a relativistic outflow with a wind-like medium peak when the blast wave deceleration sets in, and the afterglow spectrum could be hardening before that peak, as the optical thickness to pair formation is decreasing. In contrast, in afterglows produced in the interaction with a homogeneous medium, the optical thickness to pair formation should increase and yield a light curve peak when it reaches unity, followed by a fast light curve decay, accompanied by spectral softening. If energy is injected in the blast wave, then the accelerated increase of the optical thickness yields a convex afterglow light curve. Other features, such as a double-peak light curve or a broad hump, can arise from the evolution of the optical thickness to photon-photon absorption. Fast decays and convex light curves are seen in a few LAT afterglows, but the expected spectral softening is rarely seen in (and difficult to measure with) LAT observations. Furthermore, for the effects of photon-photon attenuation to shape the high-energy afterglow light curve without attenuating it too much, the ejecta initial Lorentz factor must be in a relatively narrow range (50-200), which reduces the chance of observing those effects.

79 ASTRONOMY AND ASTROPHYSICS↗

From direct detection to relic abundance: the case of proton-philic spin-dependent inelastic Dark Matter

We discuss strategies to make inferences on the thermal relic abundance of a Weakly Interacting Massive Particle (WIMP) when the same effective dimension-six operator that explains an experimental excess in direct detection is assumed to drive decoupling at freeze-out, and apply them to the explicit scenario of WIMP inelastic up-scattering with spin-dependent couplings to protons (proton-philic Spin-dependent Inelastic Dark Matter, pSIDM), a phenomenological set-up containing two Dark Matter (DM) particles χ{sub 1} and χ{sub 2} with masses m {sub χ}= m {sub χ{sub 1}} and m {sub χ{sub 2}}= m {sub χ}+δ that we have shown in a previous paper to explain the DAMA effect in compliance with the constraints from other detectors. We also update experimental constraints on pSIDM, extend the analysis to the most general spin-dependent momentum-dependent interactions allowed by non-relativistic Effective Field Theory (EFT), and consider for the WIMP velocity distribution in our Galaxy f ( v ) both a halo-independent approach and a standard Maxwellian. Under these conditions we find that the DAMA effect can be explained in terms of the particle χ{sub 1} in compliance with all the other constraints for all the analyzed EFT couplings and also for a Maxwellian f ( v ). As far as the relic abundance is concerned, we show that the problem of calculating it by using direct detection data to fix the model parameters is affected by a strong sensitivity on f ( v ) and by the degeneracy between the WIMP local density ρ{sub χ} and the WIMP-nucleon scattering cross section, since ρ{sub χ} must be rescaled with respect to the observed DM density in the neighborhood of the Sun when the calculated relic density Ω is smaller than the observed one Ω{sub 0}. As a consequence, a DM direct detection experiment is not directly sensitive to the physical cut-off scale of the EFT, but on some dimensional combination that does not depend on the actual value of Ω. However, such degeneracy can be used to develop a consistency test on the possibility that the WIMP is a thermal relic in the first place. When we apply it to the pSIDM scenario we find that only a WIMP with the standard spin-dependent interaction O=χ-bar {sub 1γ}{sup μ}γ{sup 5χ{sub 2}} q-bar γ{sub μ}γ{sup 5} q + h.c. with quarks can be a thermal relic for, approximately, 10 GeV\;≲ m {sub χ}≲ 16 GeV, 17 keV\;≲ δ≲ 28 keV, and a large uncertainty on Ω, 6× 10{sup −7}Ω{sub 0≲} Ω ≲ Ω{sub 0}. In order for the scenario to work the WIMP galactic velocity distribution must depart from a Maxwellian. Moreover, all the χ{sub 2} states must have already decayed today, and this requires some additional mechanism besides that provided by the O operator.

79 ASTRONOMY AND ASTROPHYSICS↗

Phenomenological Model of Hydrophobic and Hydrophilic Interactions

Hydration forces acting between macroscopic bodies at distances L ≤ 3 nm in pure water are calculated based on the phenomenological model of polar liquids. It is shown that depending on the properties of the bodies, the interacting surfaces polarize the liquid differently, and wetting properties of the surfaces are completely characterized by two parameters. If the surfaces are hydrophilic, liquid molecules are polarized at right angles to the surfaces, and the interaction is the short-range repulsion (the forces of interaction decrease exponentially over the characteristic length λ ≈ 0.2 nm). The interaction between the hydrophobic surfaces is more diversified and has been studied less. For L ≤ 3 nm, the interaction exhibits universal properties, while for L ≤ 3 nm, it considerably depends on the properties of the surfaces and on the distances between them, as well as on the composition of the polar liquid. In full agreement with the available experimental results we find that if the interfaces are mostly hydrophobic, then the interaction is attractive and long-range (the interaction forces diminish exponentially with decay length 1.2 nm). In this case, the resultant polarization of water molecules is parallel to the surface. It is shown that hydration forces are determined by nonlinear effects of polarization of the liquid in the bulk or by analogous nonlinearity of the interaction of water with a submerged body. This means that the forces of interaction cannot be calculated correctly in the linear response approximation. The forces acting between hydrophobic or hydrophilic surfaces are of the entropy type or electrostatic, respectively. It is shown that hydrophobic and hydrophilic surfaces for L ≤ 3 nm repel each other. The calculated intensity of their interaction is in agreement with experimental data. We predict the existence of an intermediate regime in which a body cannot order liquid molecules, which results in a much weaker attraction that decreases in inverse proportion to the squared distance between the surfaces of bodies. The difference between the microscopic structures of liquids confined in nanovolumes from liquids in large volumes is considered. The proposed model is applicable for a quantitative description of the properties of water at temperatures T satisfying the condition 0 < (T–T{sub c})/T{sub c} ≪ 1, where T{sub c} ≈ 230 K is the temperature of the ferroelectric phase transition observed in supercooled water. Under standard conditions, the model can be used for obtaining qualitative estimates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NuSTAR discovery of a luminosity dependent cyclotron line energy in Vela X-1

We present NuSTAR observations of Vela X-1, a persistent, yet highly variable, neutron star high-mass X-ray binary (HMXB). Two observations were taken at similar orbital phases but separated by nearly a year. They show very different 3-79 keV flux levels as well as strong variability during each observation, covering almost one order of magnitude in flux. These observations allow, for the first time ever, investigations on kilo-second time-scales of how the centroid energies of cyclotron resonant scattering features (CRSFs) depend on flux for a persistent HMXB. We find that the line energy of the harmonic CRSF is correlated with flux, as expected in the sub-critical accretion regime. We argue that Vela X-1 has a very narrow accretion column with a radius of around 0.4 km that sustains a Coulomb interaction dominated shock at the observed luminosities of L {sub x} ∼ 3 × 10{sup 36} erg s{sup –1}. Besides the prominent harmonic line at 55 keV the fundamental line around 25 keV is clearly detected. We find that the strengths of the two CRSFs are anti-correlated, which we explain by photon spawning. This anti-correlation is a possible explanation for the debate about the existence of the fundamental line. The ratio of the line energies is variable with time and deviates significantly from 2.0, also a possible consequence of photon spawning, which changes the shape of the line. During the second observation, Vela X-1 showed a short off-state in which the power-law softened and a cut-off was no longer measurable. It is likely that the source switched to a different accretion regime at these low mass accretion rates, explaining the drastic change in spectral shape.

79 ASTRONOMY AND ASTROPHYSICS↗

Influence of extended interactions on spin dynamics in one-dimensional cuprates

Quasi-one-dimensional (1D) materials provide a unique platform for understanding the importance and influence of extended interactions on the physics of strongly correlated systems due to their relative structural simplicity and the existence of powerful theoretical tools well-adapted to one spatial dimension. Recently, this was highlighted by anomalous observations in the single-particle spectral function A(q, ω) of 1D cuprate chain compounds, measured by angle-resolved photoemission spectroscopy (ARPES), which were explained by the presence of a long-range attractive interaction. Such an extended interaction should leave its fingerprints on other observables, notably the dynamical spin structure factor S(q, ω), measured by neutron scattering or resonant inelastic x-ray scattering (RIXS). Starting from a simple Hubbard Hamiltonian in 1D and using time-dependent density matrix renormalization group (tDMRG) methods, we show that the presence of long-range attractive coupling, directly through an instantaneous Coulomb interaction V or retarded electron phonon (el-ph) coupling, can introduce significant spectral weight redistribution in S(q, ω) across a wide range of doping. Here, this underscores the significant impact that extended interactions can have on dynamical correlations among particles, and the importance of properly incorporating this influence in modeling. Our results demonstrate that S(q, ω) can provide a sensitive experimental constraint, which complements ARPES measurements, in identifying key interactions in 1D cuprates, beyond the standard Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗