Despite extensive investigations, many aspects of charge-density waves (CDWs) remain elusive, especially the relative roles of electron-phonon coupling and Fermi surface nesting as the underlying driving mechanisms responsible for the emergence of CDW vector QCDW. It is puzzling that even though electrons interact strongly with optical phonons in many correlated systems, the actual mode softening is of an acoustic mode. Here, we consider monolayer 1H-NbSe2 as an exemplar system, and through an accurate computation of the phonon self-energy, including its off-diagonal components, we provide compelling evidence that the relevant mode is a longitudinal optical phonon that softens by anticrossing several intervening phonon bands, i.e., a Kohn ladder that has been only observed previously in high-temperature superconductors. We also show that QCDW is fixed by the convolution of the susceptibility and electron-phonon coupling and that the softened phonons are circularly polarized.

Electron-phonon coupling (EPC) is key for understanding many properties of materials such as superconductivity and electric resistivity. Although first principles density-functional-theory (DFT) based EPC calculations are used widely, their efficacy is limited by the accuracy and efficiency of the underlying exchange-correlation functionals. These limitations become exacerbated in complex d- and f-electron materials, where beyond-DFT approaches and empirical corrections, such as the Hubbard U, are commonly invoked. Here, using the examples of CoO and NiO, we show how the efficient r2scan density functional correctly captures strong EPC effects in transition-metal oxides without requiring the introduction of empirical parameters. We also demonstrate the ability of r2scan to accurately model phonon-mediated superconducting properties of the main group compounds (e.g., MgB_2), with improved electronic bands and phonon dispersions over those of traditional density functionals. Our study provides a pathway for extending the scope of accurate first principles modeling of electron-phonon interactions to encompass complex d-electron materials.

Intriguing analogies between the nickelates and the cuprates provide a promising avenue for unraveling the microscopic mechanisms underlying high-Tc superconductivity. While electron correlation effects in the nickelates have been extensively studied, the role of electron-phonon coupling (EPC) remains highly controversial. Here, by taking pristine LaNiO2 as an exemplar nickelate, we present an in-depth study of EPC for both the nonmagnetic (NM) and the C-type antiferromagnetic (C-AFM) phases using advanced density functional theory methods without invoking U or other free parameters. The weak EPC strength lambda in the NM phase is found to be greatly enhanced ('4x) due to the presence of magnetism in the C-AFM phase. This enhancement arises from strong interactions between the flat Ni-3dz2 bands and the low-frequency phonon modes associated with Ni and La vibrations, rather than solely from the high-frequency oxygen breathing modes. The resulting phonon softening is shown to yield a distinctive kink in the electronic structure around 15 meV, which would provide an experimentally testable signature of our predictions. Our study highlights the critical role of local magnetic moments and EPC in the nickelate.

We discuss the evolution of high-order Van Hove singularities (hoVHSs) that carry faster-than logarithmic divergences over a wide range of parameters in cuprate-like electronic band dispersions. Numerical analysis gives insight into the quantization of the VHS power-law-exponent pV and into transitions between hoVHSs with different values of pV. The cuprates are found to lie in the parameter regime where the amplitude of the hoVHS is not too large. Our study indicates that the occurrence of high-temperature superconductivity requires simultaneous tuning of two different competing orders (antiferromagnetism and the density wave associated with the hoVHS in cuprates), which is why it is so rare.

Emergence of topological states in strongly correlated systems, particularly two-dimensional (2D) transition-metal dichalcogenides, offers a platform for manipulating electronic properties in quantum materials. However, a comprehensive understanding of the intricate interplay between correlations and topology remains elusive. Here we employ first-principles modeling to reveal two distinct 2 × 2 charge density wave (CDW) phases in monolayer 1H-NbSe2, which become energetically favorable over the conventional 3 × 3 CDWs under modest biaxial tensile strain of about 1%. These strain-induced CDW phases coexist with numerous topological states characterized by Z2 topology, high mirror Chern numbers, topological nodal lines, and higher-order topological states, which we have verified rigorously by computing the topological indices and the presence of robust edge states and localized corner states. Remarkably, these topological properties emerge because of the CDW rather than a pre-existing topology in the pristine phase. These results elucidate the interplay between correlations, topology, and geometry in 2D materials and indicate that strain-induced correlation effects can be used to engineer topological states in materials with initially trivial topology. Our findings may be applied in electronics, spintronics, and other advanced quantum devices that require robust and tunable topological states.

Despite extensive investigations, many aspects of charge density waves (CDWs) remain elusive, especially the relative roles of electron-phonon coupling and Fermi surface nesting as the underlying driving mechanisms responsible for the emergence of the CDW vector Q_CDW. It is puzzling that even though electrons interact strongly with optical phonons in many correlated systems, the actual mode softening is of an acoustic mode. Here we consider monolayer 1H-NbSe_2 as an exemplar system, and through an accurate computation of the phonon self-energy, including its off-diagonal components, we provide compelling evidence that the relevant mode is a longitudinal optical phonon that softens by anti-crossing several intervening phonon bands, i.e. a Kohn ladder which has been only observed previously in high temperature superconductors. We also show that Q_CDW is fixed by the convolution of the susceptibility and electron-phonon coupling, and that the softened phonons are circularly polarized.

Recent discovery of superconductivity in infinite-layer nickelates has ignited renewed theoretical and experimental interest in the role of electronic correlations in their properties. Here, using first-principles simulations, we show that the parent compound of the nickelate family, LaNiO_{2}, hosts competing low-energy stripe phases, similar to doped cuprates. The stripe states are shown to be driven by multiorbital electronic mechanisms and Peierls distortions. Our study indicates that both strong correlations and electron-phonon coupling effects play a key role in the physics of infinite-layer nickelates, and sheds light on the microscopic origin of electronic inhomogeneity and the lack of long-range order in the nickelates.

While magnetic fields generally compete with superconductivity, a type II superconductor can persist to very high fields by confining the field in topological defects, namely vortices. We propose that a similar physics underlies the pseudogap phase in cuprates, where the relevant topological defects are the antiphase domain walls of an underlying antiferromagnetic (AFM) order. A key consequence of this scenario is that the termination of the pseudogap phase should be quantitatively described by the underlying AFM model. We demonstrate that this picture can explain a number of key experimentally observed signatures of the pseudogap phase and how it collapses in the cuprates.

The enigmatic mechanism underlying unconventional high-temperature superconductivity, especially the role of lattice dynamics, has remained a subject of debate. Theoretical insights have long been hindered due to the lack of an accurate first-principles description of the lattice dynamics of cuprates. Recently, using the r2SCAN meta-generalized gradient approximation (meta-GGA) functional, we have been able to achieve accurate phonon spectra of an insulating cuprate YBa2Cu3O6 and discover significant magnetoelastic coupling in experimentally interesting Cu-O bond stretching optical modes [Ning et al., Phys. Rev. B 107, 045126 (2023)]. We extend this work by comparing Perdew-Burke-Ernzerhof and r2SCAN performances with corrections from the on-site Hubbard U and the D4 van der Waals (vdW) methods, aiming at further understanding on both the materials science side and the density functional side. We demonstrate the importance of vdW and self-interaction corrections for accurate first-principles YBa2Cu3O6 lattice dynamics. Since r2SCAN by itself partially accounts for these effects, the good performance of r2SCAN is now more fully explained. In addition, the performances of the Tao-Mo series of meta-GGAs, which are constructed in a different way from the strongly constrained and appropriately normed (SCAN) meta-GGA and its revised version r2SCAN, are also compared and discussed.

A key insight of Einstein's theory of the photoelectric effect is that a minimum energy is required for photoexcited electrons to escape from a material. For the past century it has been assumed that photoexcited electrons of lower energies make no contribution to the photoemission spectrum. Here we demonstrate the conceptual possibility that the energy of these 'failed' photoelectrons-primary or secondary-can be partially recycled to generate new 'tertiary' electrons of energy sufficient to escape. Such a 'recycling' step goes beyond the traditional three steps of the photoemission process (excitation, transport, and escape), and, as we illustrate, it can be realized through a novel Auger mechanism that involves three distinct minority electronic states in the material. We develop a phenomenological three-band model to treat this mechanism within a revised four-step framework for photoemission, which contains robust features of linewidth narrowing and population inversion under strong excitation, reminiscent of the lasing phenomena. We show that the conditions for this recycling mechanism are likely satisfied in many quantum materials with multiple flat bands properly located away from the Fermi level, and elaborate on the representative case of SrTiO3 among other promising candidates. We further discuss how this mechanism can explain the recent observation of anomalous intense coherent photoemission from a SrTiO3 surface, and predict its manifestations in related experiments, including the 'forbidden' case of photoemission with photon energies lower than the work function. Our study calls for paradigm shifts across a range of fundamental and applied research fields, especially in the areas of photoemission, photocathodes, and flat-band materials.

Evidence is growing that a second dome of high-$T_\mathrm{c}$ superconductivity can be accessed in the cuprates by increasing the doping beyond the first dome. Here we use \emph{ab initio} methods without invoking any free parameters such as the Hubbard $U$, to reveal that pressure could turn YBa$_2$Cu$_3$O$_7$ into an ideal candidate for second-dome-superconductivity, displaying the predicted signature of strongly hybridized $d_{x^2-y^2}$ and $d_{z^2}$ orbitals. Notably, pressure is found to induce a phase transition replacing the antiferromagnetic phases with an orbitally-degenerate $d$-$d$ phase. We find an interesting doping-dependence of the oxygen-hole fraction in the CuO$_2$ planes, which suggests the presence of a second dome.

Photocathodes-materials that convert photons into electrons through a phenomenon known as the photoelectric effect-are important for many modern technologies that rely on light detection or electron-beam generation1-3. However, current photocathodes are based on conventional metals and semiconductors that were mostly discovered six decades ago with sound theoretical underpinnings4,5. Progress in this field has been limited to refinements in photocathode performance based on sophisticated materials engineering1,6. Here we report unusual photoemission properties of the reconstructed surface of single crystals of the perovskite oxide SrTiO3(100), which were prepared by simple vacuum annealing. These properties are different from the existing theoretical descriptions4,7-10. In contrast to other photocathodes with a positive electron affinity, our SrTiO3 surface produces, at room temperature, discrete secondary photoemission spectra, which are characteristic of efficient photocathode materials with a negative electron affinity11,12. At low temperatures, the photoemission peak intensity is enhanced substantially and the electron beam obtained from non-threshold excitations shows longitudinal and transverse coherence that differs from previous results by at least an order of magnitude6,13,14. The observed emergence of coherence in secondary photoemission points to the development of a previously undescribed underlying process in addition to those of the current theoretical photoemission framework. SrTiO3 is an example of a fundamentally new class of photocathode quantum materials that could be used for applications that require intense coherent electron beams, without the need for monochromatic excitations.

Spin-momentum locking is a unique intrinsic feature of strongly spin-orbit coupled materials and a key to their promise of applications in spintronics and quantum computation. Much of the existing work, in topological and non-topological pure materials, has been focused on the orthogonal locking in the vicinity of the Γ point where the directions of spin and momentum vectors are locked perpendicularly. With the orthogonal case, enforced by the symmetry in pure systems, mechanisms responsible for non-orthogonal spin-momentum locking (NOSML) have drawn little attention, although it has been reported on the topological surface of α-Sn. Here, we demonstrate that, the presence of the spin-orbit scattering from dilute spinless impurities can produce the NOSML state in the presence of a strong intrinsic spin-orbit coupling in the pristine material. We also observe an interesting coupling threshold for the NOSML state to occur. The relevant parameter in our analysis is the deflection angle from orthogonality which can be extracted experimentally from the spin-and-angle-resolved photoemission (S-ARPES) spectra. Our formalism is applicable to all strongly spin-orbit coupled systems with impurities and not limited to topological ones. The understanding of NOSML bears on spin-orbit dependent phenomena, including issues of spin-to-charge conversion and the interpretation of quasiparticle interference (QPI) patterns as well as scanning-tunneling spectra (STS) in general spin-orbit coupled materials.

The role of lattice dynamics in unconventional high-temperature superconductivity is still vigorously debated. Theoretical insights into this problem have long been prevented by the absence of an accurate first-principles description of the combined electronic, magnetic, and lattice degrees of freedom. Utilizing the recently constructed r^2SCAN density functional that stabilizes the antiferromagnetic (AFM) state of the pristine oxide YBa_2Cu_3O_6, we faithfully reproduce the experimental dispersion of key phonon modes. We further find significant magnetoelastic coupling in numerous high energy Cu-O bond stretching optical branches, where the AFM results improve over the soft non-magnetic phonon bands.

The recently discovered infinite-layer nickelates show great promise in helping to disentangle the various cooperative mechanisms responsible for high-temperature superconductivity. However, lack of antiferromagnetic order in the pristine nickelates presents a challenge for connecting the physics of the cuprates and nickelates. Here, by using a quantum many-body Green’s function-based approach to treat the electronic and magnetic structures, we unveil the presence of many two- and three-dimensional magnetic stripe instabilities that are shown to persist across the phase diagram of LaNiO 2 . Our analysis indicates that the magnetic properties of the infinite-layer nickelates are closer to those of the doped cuprates, which host a stripe ground state, rather than the undoped cuprates. The computed longitudinal-spin, transverse-spin, and charge spectra of LaNiO 2 are found to contain an admixture of contributions from localized and itinerant carriers. Theoretically obtained dispersion of magnetic excitations (spin-flip) is found to be in good accord with the results of recent resonant inelastic X-ray scattering experiments. Our study gives insight into the origin of strong magnetic competition in the infinite-layer nickelates and their relationship with the cuprates.

We generalize the concept of vortex phase in a type II superconductor to textured phases, where certain phases can persist over an extended range of perturbations by confining competing phases on topological defects (the vortices in a superconductor). We apply this model to the pseudogap phase in cuprates, where the relevant topological defects are the antiphase domain walls of an underlying antiferromagnetic (AFM) order. We demonstrate that this model can describe many key features of intertwined orders in cuprates, and most importantly provide the first clear evidence for the Mott-Slater transition in cuprates.

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other's energy-momentum dispersion cones-analogous to two events that can only have a causal connection if they lie in each other's light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated 'thick horizon' in the emergent causal structure.

Beyond the two-dimensional saddle-point Van Hove singularities (VHSs) with logarithmic divergences in the density of states, recent studies have identified higher-order VHSs with faster-than-logarithmic divergences that can amplify electron correlation effects. Here we show that the cuprate high-Tc superconductors harbor high-order VHSs in their electronic spectra and unveil a new correlation that the cuprates with high-order VHSs display higher T c ’s. Our analysis indicates that the normal and higher-order VHSs can provide a straightforward new marker for identifying propensity of a material toward the occurrence of correlated phases such as the excitonic insulators and supermetals. Our study suggests cuprates and related high-T c superconductors as materials for exploring the interplay between high-order VHSs, superconducting transition temperatures, and electron correlation effects.

Flat bands coupled with magnetism and topological orders near or at the Fermi level are well known to drive exotic correlation physics and unconventional superconductivity. Here, based on first-principles modeling combined with an in-depth symmetry analysis, we reveal the presence of topological flat bands involving low-energy Ni-$3d_{z^2}$ states in the recently discovered superconductor LaNiO$_{2}$. Our analysis demonstrates that LaNiO$_2$ is an Axion insulator with $\mathbb{Z}_{4} = 2$ and that it supports topological crystalline insulating states protected by the glide mirror symmetries. The topological flat bands in LaNiO$_{2}$ are also shown to host odd-parity superconductivity. Our study indicates that the nickelates would provide an interesting materials platform for exploring the interplay of flat bands, topological states, and superconductivity.

The intersections of topology, geometry and strong correlations offer many opportunities for exotic quantum phases to emerge in condensed matter systems. Weyl fermions, in particular, provide an ideal platform for exploring the dynamical instabilities of single-particle physics under interactions. Despite its fundamental role in relativistic field theory, the concept of causality and the associated spacetime light cone and event horizon has not been considered in connection with interacting Weyl fermionic excitations in quantum matter. Here, by using charge-density wave (CDW) as an example, we unveil the behavior of interacting Weyl fermions and show that a Weyl fermion in a system can open a band gap by interacting only with other Weyl fermions that lie within its energy-momentum dispersion cone. In this sense, causal connections or interactions are only possible within overlapping dispersion cones and each dispersion cone thus constitutes a solid-state analogue of the more conventional `event horizon' of high-energy physics. Our study provides a universal framework for considering interacting relativistic quasiparticles in condensed matter by separating them into energy-like and momentum-like relationships in analogy with the time-like and space-like events in high-energy physics. Finally, we consider two different candidate materials for hosting the Weyl CDW phase: (TaSe$_4$)$_2$I and Mo$_3$Al$_2$C. Our study greatly enriches the phenomenology and unveils new connections between condensed matter and high-energy physics.