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Motivated by the recently discovered high- T c superconductor La 3 Ni 2 O 7 , we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y 2− mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y 2− mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector ( π , 0) was stable at the intermediate region. Pairing is induced in the s ± -wave channel due to partial nesting between the M  = ( π ,  π ) centered pockets and portions of the Fermi surface centered at the X  = ( π , 0) and Y  = (0,  π ) points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest La 3 Ni 2 O 7 is qualitatively different from infinite-layer nickelates and cuprate superconductors. Recently superconductivity with T c of about 80 K was discovered in a bilayer nickelate La 3 Ni 2 O 7 under high pressure. Here the authors report a density functional theory and random phase approximation study of structural and electronic properties as a function of pressure and discuss the pairing mechanism.

The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite-cluster methods typically indicate that stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides an opportunity to study the influence of fluctuating stripe correlations on the model’s pairing correlations within a unified numerical framework. Using this approach, we also find evidence for pair-density-wave correlations whose strength is correlated with that of the stripes.

There is growing evidence that the hole-doped single-band Hubbard and t  −  J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates. It has been debated whether the single-band Hubbard model describes the physics of the cuprates. Mai et al. numerically study the spin and charge correlations in the electron-doped model and conclude that, in contrast to the hole-doped one, it captures the corresponding side of the cuprate phase diagram.

In ultrathin films of FeSe grown on SrTiO 3 (FeSe/STO), the superconducting transition temperature T c is increased by almost an order of magnitude, raising questions on the pairing mechanism. As in other superconductors, antiferromagnetic spin fluctuations have been proposed to mediate SC making it essential to study the evolution of the spin dynamics of FeSe from the bulk to the ultrathin limit. Here, we investigate the spin excitations in bulk and monolayer FeSe/STO using resonant inelastic x-ray scattering (RIXS) and quantum Monte Carlo (QMC) calculations. Despite the absence of long-range magnetic order, bulk FeSe displays dispersive magnetic excitations reminiscent of other Fe-pnictides. Conversely, the spin excitations in FeSe/STO are gapped, dispersionless, and significantly hardened relative to its bulk counterpart. By comparing our RIXS results with simulations of a bilayer Hubbard model, we connect the evolution of the spin excitations to the Fermiology of the two systems revealing a remarkable reconfiguration of spin excitations in FeSe/STO, essential to understand the role of spin fluctuations in the pairing mechanism. Here, Pelliciari et al. present resonant inelastic X-ray scattering on monolayer samples of unconventional superconductor FeSe, finding evidence for gapped and dispersionless spin excitations. These experiments are very difficult due to the extremely small scattering volume of the FeSe monolayer.

The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO2 planes. Here, we use a dynamical cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.

At temperatures above the superconducting transition temperature, the pairfield susceptibility provides information on the nature of the pairfield fluctuations. Here, we study the d-wave pairfield susceptibility of a 2D Hubbard model for a doping which has a pseudogap (PG) and for a doping which does not. In both cases, there will be a region of Kosterlitz–Thouless fluctuations as the transition at TKT is approached. Above this region, we find evidence for pairfield-order parameter-phase fluctuations for dopings with a PG and BCS Cooper pair fluctuations for dopings without a PG.

Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon ( e -ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping t ′ or phonon energy Ω. Our results help elucidate how the e -ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high- T c cuprates. Experiments indicate that the cuprates exhibit intertwined spin- and charge-stripe orders and have sizable electron-phonon interactions. Here, the authors use quantum Monte Carlo methods to investigate stripe orders in the Hubbard-Holstein model to shed light on the influence of electron-phonon coupling on static and fluctuating stripe order.

The discovery of T c ~ 80 K superconductivity in pressurized La 3 Ni 2 O 7 has launched a new platform to study high-temperature superconductivity. Using non-perturbative dynamic cluster approximation quantum Monte Carlo calculations, we characterize the magnetic and superconducting pairing behavior of a realistic bilayer two-orbital Hubbard-Hund model of this system that describes the relevant Ni e g states with physically relevant interaction strengths. We find a leading s ± superconducting instability in this model at a temperature T ~ 100 K close to the experimentally observed T c . Analyzing the orbital and spatial structure of the effective pairing interaction giving rise to this state reveals that the interaction predominantly acts between local interlayer pairs of the d 3 z 2 - r 2 orbital. By correlating the strength of the interaction with that of the magnetic spin fluctuations we show that it is driven by strong interlayer spin-fluctuations arising from the d 3 z 2 - r 2 orbital. These results provide first-time non-perturbative evidence supporting the picture that a simple single-orbital bilayer Hubbard model for the Ni d 3 z 2 - r 2 orbital provides an excellent low-energy effective description of the superconducting behavior of La 3 Ni 2 O 7 .

Resolving the microscopic pairing mechanism and its experimental identification in unconventional superconductors is among the most vexing problems of contemporary condensed matter physics. We show that Raman spectroscopy provides an avenue towards this aim by probing the structure of the pairing interaction at play in an unconventional superconductor. As we study the spectra of the prototypical Fe-based superconductor Ba 1−x K x Fe 2 As 2 for 0.22 ≤  x  ≤ 0.70 in all symmetry channels, Raman spectroscopy allows us to distill the leading s -wave state. In addition, the spectra collected in the B 1 g symmetry channel reveal the existence of two collective modes which are indicative of the presence of two competing, yet sub-dominant, pairing tendencies of d x 2 - y 2 symmetry type. A comprehensive functional Renormalization Group and random-phase approximation study on this compound confirms the presence of the two sub-leading channels, and consistently matches the experimental doping dependence of the related modes. The consistency between the experimental observations and the theoretical modeling suggests that spin fluctuations play a significant role in superconducting pairing. Iron-based superconductors: competing pairing interactions Two collective Raman modes are observed in an iron-based superconductor, indicative of the presence of two competing pairing tendencies alongside the dominant s-wave state. An international team led by R. Hackl from the Walther Meissner Institut perform Raman spectroscopy measurements to probe the structure of pairing interactions in Ba 1− x K x Fe 2 As 2 for 0.22 ≤  x  ≤ 0.70 for all symmetry channels. The Raman spectra not only shows the dominant peak marking the dominant s-wave superconducting pairing state, but also reveals the existence of two collective modes in the B 1 g symmetry channel, indicative of two competing, sub-dominant, paring tendencies of d x 2 - y 2 symmetry type. Numerical calculations confirm the finding and consistently match the doping dependencies of the related modes. The results suggest a significant role of spin-fluctuations in superconducting pairing.

Observations of robust superconductivity in some of the iron based superconductors in the vicinity of a Lifshitz point where a spin density wave instability is suppressed as the hole band drops below the Fermi energy raise questions for spin-fluctuation theories. Here we discuss spin-fluctuation pairing for a bilayer Hubbard model, which goes through such a Lifshitz transition. We find s ± pairing with a transition temperature that peaks beyond the Lifshitz point and a gap function that has essentially the same magnitude but opposite sign on the incipient hole band as it does on the electron band that has a Fermi surface.