We explore the consequences of disorder on phase coherence in the Mott insulator phases in an optical lattice. Few bosons with contact interaction in small optical lattice can feature varieties of insulating phases—weakly interacting Mott in deep lattice, maximally fragmented and strongly interacting Mott in intermediate lattice, weak Mott with double filling and intrawell coherence, fermionized Mott with strong intrawell coherence. Utilization of the multiconfigurational time-dependent Hartree method for bosons to solve the many-boson Schrödinger equation, facilitates to understand the microscopic effect of disorder on the different kinds of Mott phases in the primary lattice. The many-body properties are analyzed by distinct measures of the reduced one-body density in real and momentum space, fragmentation, order parameter, variance of spatial single-shot measurements, compressibility, and the Glauber normalized correlation functions. We find very complex competition of localization due to disorder and Mott correlation. We observe distinct response of four different Mott phases in the disordered lattice. When the weakly interacting Mott exhibits the Bose glass phase, the strongly correlated and fully fragmented Mott exhibits leakage, melting and central localization. In contrast, weak Mott with double filling which is a spatially separated dimer in each site, exhibits only some dissociation of intrawell coherence and assist in the development of interwell coherence in the presence of strong disorder. For the fermionized Mott, when the density in each well is fragmented, strong disorder interferes with the intrawell correlation and the characteristic dip in each site starts to disappear leading to simple Mott localization with a pair of bosons.

We study the algebraic structure of electron density operators in gapless Weyl fermion systems in $d=3,5,7,\cdots$ spatial dimensions and in topological insulators (without any protecting symmetry) in $d=4,6,8,\cdots$ spatial dimensions. These systems are closely related by the celebrated bulk-boundary correspondence. Specifically, we study the higher bracket—a generalization of commutator for more than two operators—of electron density operators in these systems. For topological insulators, we show that the higher-bracket algebraic structure of density operators structurally parallels with the Girvin-MacDonald-Platzman algebra (the $W_{1+\infty }$ algebra), the algebra of electron density operators projected onto the lowest Landau level in the quantum Hall effect. By the bulk-boundary correspondence, the bulk higher-bracket structure mirrors its counterparts at the boundary. Specifically, we show that the density operators of Weyl fermion systems, once normal-ordered with respect to the ground state, their higher bracket acquires a $c$-number part. This part is an analog of the Schwinger term in the commutator of the fermion current operators. We further identify this part with a cyclic cocycle, which is a topological invariant and an element of Connes' noncommutative geometry.

We investigate the quantum Hall effect in a single Landau level in the presence of a square superlattice of $\delta$-function potentials. The interplay between the superlattice spacing $a_s$ and the magnetic length ${\ell }_B$ in a clean system leads to three interesting characteristic regimes corresponding to $a_s<{\ell }_B, a_s\gg {\ell }_B$, and the intermediate one where $a_s\sim {\ell }_B$. In the intermediate regime, the continuous magnetic translation symmetry breaks down to discrete lattice symmetry. In contrast, we show that, in the other two regimes, the same is hardly broken in the topological band despite the presence of the superlattice. In the presence of weak disorder (white-noise) one typically expects a tiny fraction of extended states due to topological protection of the Landau level. Interestingly, we obtain a large fraction of extended states throughout the intermediate regime which maximizes at the special point $a_s=\sqrt{2\pi }{\ell }_B$. We argue the superlattice induced percolation phenomenon requires both the breaking of the time reversal symmetry and the continuous magnetic translational symmetry. It could have a direct implication on the integer plateau transitions in both continuous quantum Hall systems and the lattice based anomalous quantum Hall effect.

“Half moons,” distinctive crescent patterns in the dynamical structure factor, have been identified in inelastic neutron scattering experiments for a wide range of frustrated magnets. In an earlier paper [H. Yan et al., Phys. Rev. B 98, 140402(R) (2018)] we have shown how these features are linked to the local constraints realized in classical spin liquids. Here, we explore their implication for the topology of magnon bands. The presence of half moons indicates a separation of magnetic degrees of freedom into irrotational and incompressible components. Where bands satisfying these constraints meet, it is at a singular point encoding Berry curvature of $\pm 2\pi$. Interactions which mix the bands open a gap, resolving the singularity, and leading to bands with finite Berry curvature, accompanied by characteristic changes to half-moon motifs. These results imply that inelastic neutron scattering can, in some cases, be used to make rigorous inference about the topological nature of magnon bands.

Recently, a first-order phase transition associated with charge density wave (CDW) has been observed at low temperatures in intermetallic compound ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$. However, this transition is absent in its isostructural sister compound ${\mathrm{BaCo}}_2{\mathrm{Al}}_9$. Consequently, an intriguing question arises as to the underlying factors that differentiate ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$ from ${\mathrm{BaCo}}_2{\mathrm{Al}}_9$ and drive the CDW transition in ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$. Here, we set out to address this question by conducting a comparative ab initio study of the electronic structures, lattice dynamics, and electron-phonon interactions of their high-temperature phases. We find that both compounds are dynamically stable with similar phonon dispersions. The electronic structure calculations reveal that both compounds are nonmagnetic metals; however, they exhibit distinct band structures around the Fermi level. In particular, ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$ exhibits a higher density of states at the Fermi level with dominant partially filled Fe-$3d$ states and a more intricate Fermi surface. This leads to an electronic instability of ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$ toward the CDW transition, which is manifested by the diverged electronic susceptibility at the CDW wave vector ${\mathbf{q}}_{\mathrm{CDW}}=(0.5,0,0.3)$, observable in both the real and imaginary parts. Conversely, ${\mathrm{BaCo}}_2{\mathrm{Al}}_9$ does not display such behavior, aligning well with experimental observations. Although the electron-phonon interactions in ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$ surpass those in ${\mathrm{BaCo}}_2{\mathrm{Al}}_9$ by two orders of magnitude, the strength is relatively weak at the CDW wave vector, suggesting that the CDW in ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$ is primarily driven by electronic factors.

Recent theoretical work has shown that higher-order moments of the Berry curvature, e.g., Berry curvature quadrupole and hexapole moments, can produce the leading order nonlinear anomalous Hall response (NLAH) in systems with special magnetic point group symmetry. Recent experimental work has reported the observation of the Berry curvature quadrupole-induced third-order NLAH (i.e., Hall voltage proportional to the third power of the external electric field) from cryogenic conditions to room temperature in an epitaxially grown material platform with broken time-reversal symmetry. In this paper, using semiclassical Boltzmann formalism in the relaxation time approximation, we compute the Berry curvature quadrupole-induced nonlinear anomalous thermal Hall and Nernst coefficients in time-reversal broken systems. In systems where Berry curvature monopole and dipole moments vanish by symmetry, our results predict the behavior of the leading order anomalous thermal Hall and Nernst coefficients proportional to the third power of the applied longitudinal temperature gradient. They are guaranteed to exist in systems that have already exhibited the third-order nonlinear anomalous Hall effect in recent experiments.

We analyze the quasiparticle interaction function (the fully dressed and antisymmetrized interaction between fermions) for a two-dimensional Fermi liquid at zero temperature close to a q=0 charge quantum critical point (QCP) in the $s\text{−}\mathrm{wave}$ channel (the one leading to phase separation). By the Ward identities, this vertex function must be related to quasiparticle residue $Z$, which can be obtained independently from the fermionic self-energy. We show that to satisfy these Ward identities, one needs to go beyond the standard diagrammatic formulation of Fermi-liquid theory and include a series of additional contributions to the vertex function. These contributions are not present in a conventional Fermi liquid, but do emerge near a QCP, where the effective 4-fermion interaction is mediated by a soft dynamical boson. We demonstrate explicitly that including these terms restores the Ward identity. Our analysis is built on previous studies of the vertex function near an antiferromag netic QCP [Phys. Rev. B 89, 045108 (2014)] and a $d$-wave charge-nematic QCP [Phys. Rev. B 81, 045110 (2010)]. We show th at for $s\text{−}\mathrm{wave}$ charge QCP the analysis is more straightforward and allows one to obtain the full quasiparticle interaction function (the Landau function) near a QCP. We show that all partial components of this function (Landau parameters) diverge near a QCP, in the same way as the effective mass $m^{*}$, except for the $s$-wave charge component, which approaches $-1$. Consequently, the susceptibilities in all channels, except for the critical one, remain finite at a QCP, as they should.

Here we show that, in contrast to the observed surface states in well studied pnictogen chalcogenide van der Waals (vdW) topological insulators with quintuple layer (QL) or septuple layer (SL) structure, in superlattices, comprising the alternating QL and SL vdW blocks, the Dirac state becomes accompanied by emergent spin-polarized states of the Rashba type. This specific feature is caused by an inequivalence of the surface and subsurface structural blocks and an electrostatic potential bending near the surface. Within density functional theory and ab initio tight-binding calculations we analyze peculiarities of these states depending on the surface termination, structural parameters, and chemical composition. It is found that their possible hybridization with the Dirac state significantly affects its dispersion and spatial localization. We analyze the influence of intrinsic magnetism on behavior of the termination-dependent surface states for magnetic QL/SL superlattices. These findings provide a better understanding of the existing experimental observations of such QL/SL alternating superlattices.

We investigate the Friedel oscillations of the local density of states (LDOS) induced by a single impurity with both a spin-independent potential and an exchange coupling to the electrons in altermagnets and unconventional $p$-wave magnets. We identify features that make the Friedel oscillations and magnetization distinct from other materials with nontrivial spin texture such as Rashba metals. Because time-reversal symmetry is broken in altermagnets, both magnetic and nonmagnetic impurities lead to local magnetization with the spatial pattern that reflects the symmetry of the altermagnetic splitting. The period of the corresponding oscillations provides an alternative way to quantify the altermagnetic spin splitting and the shape of the altermagnetic bands. The LDOS pattern in $p$-wave magnets, which respect combined time-reversal and translation symmetries, is rich. It reveals anisotropy related directly to the spin splitting, but surprisingly also features LDOS oscillations with a doubled period in the proximity of the impurity. The latter effect is also observed in a Rashba metal with an exchange field and originates from the interplay of propagating and evanescent waves. The obtained results are instrumental for investigating altermagnets and unconventional $p$-wave magnets via tunneling probes.

Previous studies of metal nanoparticle plasmonic properties yielded various nontrivial effects beyond the simple dipole response to light, such as the higher-order plasmon modes and dark and bright localized surface plasmons. Another intriguing plasmonic effect is the reduction of bulk plasmon (BP) resonances strength due to the Begrenzung effect, a phenomenon of the BP resonance modifications at the surface, which has been experimentally observed before and mathematically derived. In this work the LSP and BP resonances of tin nanoparticles were studied with electron energy loss spectroscopy (EELS) up to 45 eV. The effect of the Begrenzung effect on the plasmon resonances is here determined by reduced experimental EELS signals on $\mathrm{S}{\mathrm{i}}_3{\mathrm{N}}_4$ encapsulated tin nanoparticles, which is explained by a detailed analysis of simulations. These simulations reveal an ubiquitous manifestation of the Begrenzung effect at multiple energies. The disentanglement of the multiple plasmon resonances in the $\mathrm{Si}{\mathrm{N}}_{\mathrm{x}}$ covered tin nanoparticles give evidence of a rich plasmon occurrence which has been comprehensively mapped, that could lead to precise tailoring of plasmon properties up to extreme ultraviolet energies.

We construct a broad class of frustration-free quantum vertex models in $3+1$ dimensions ($3+1\mathrm{D}$) whose ground states are weighted superpositions of classical 3D vertex model configurations. Our results are illustrated for diamond, cubic, and BCC lattices, but hold in general for 3D lattices with even coordination number. The corresponding classical vertex models have a ${\mathbb{Z}}_2$ gauge constraint enriched with a ${\mathbb{Z}}_2$ global symmetry. We study the interplay between these symmetries by exploiting exact wave function dualities and effective field theories. We find an exact gapless point which by duality is related to the Rokhsar-Kivelson (RK) point of $U\left(1\right)$ spin liquids. At this point, both the symmetry breaking and deconfinement order parameters exhibit long range order. The gapless point is additionally a self-dual point of a second duality that maps the ${\mathbb{Z}}_2$ deconfined and ${\mathbb{Z}}_2$ symmetry-broken phases to one another. For the BCC lattice vertex model, we find that gapless point is proximate to an unusual intermediate phase where symmetry breaking and deconfinement coexist.

Recently, a new exciton species of quadrupole exciton (QX) has been discovered in two-dimensional (2D) transition-metal dichalcogenide (TMD) heterotrilayers, which has attracted increasing attention for its fascinating properties. Theoretically, it is predicted that QXs will be squeezed into energetically favored staggered dipole excitons (Stg-DXs) as the exciton density increases. Here, we report photoluminescence spectroscopy studies of this exciton transition between QXs and Stg-DXs in ${\mathrm{WSe}}_2/{\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterotrilayers. As the exciton density increases, we observe that the Stark effect curve gradually deforms from a hyperbola to a piecewise linear function, providing the first sign of the transition. At the same time, the initially dark QXs become radiative, reaffirming the transition from QXs to Stg-DXs, as the optical selection rules are lifted by breaking the mirror symmetry. Remarkably, we find that this transition can be tuned by introducing doping to change the screening and thus the interactions between excitons. Our results provide observations and understanding of QXs and Stg-DXs in TMD heterotrilayers.

The phase transitions of ferroelectric ceramics under dynamic compressions are of importance for materials and applications design. However, there are very few effective methods for describing the shock-induced phase transition process in ferroelectric ceramics, due to the tiny structural volume change during compression. Here the phase transition behaviors of $\mathrm{KNb}{\mathrm{O}}_3$ ceramics under compression are studied by measuring electrical responses. A model describing the phase variation in ferroelectric ceramics under uniaxial compressions with respect to pressures has been established, which may provide a reference for studying dynamic phase transitions in ferroelectrics under shock waves. Unlike hydrostatic high-pressure processes, the shock-induced phase transition initiates at relatively low pressures and increases progressively as the pressure rises. Random orientations of the grains in ceramics lead to different pressure conditions of each grain, which is responsible for the gradual phase transition processes. The proportion of phase transitions in three-dimensional space can be visualized using ab initio density functional theory. These findings have significant implications for material design and optimization.

Considerable attention has been devoted to $\mathrm{CaA}{\mathrm{l}}_2\mathrm{S}{\mathrm{i}}_2$-type Zintl-phase compounds for their intriguing physical properties, particularly the complex interplay between band structures and magnetism. Herein we grow high-quality single crystals of nonmagnetic $\mathrm{YbA}{\mathrm{l}}_2\mathrm{S}{\mathrm{i}}_2$ and examine the physical properties, including resistivity, magnetoresistance, angular magnetoresistance, Hall resistivity, and band structures. This compound shows metallic properties and Fermi-liquid behaviors. Its resistivity under magnetic fields increases as per Kohler rule, with normalized magnetoresistance curves merging into one, ruling out potential metal-insulator-like transitions. Colossal magnetoresistance is observed at low temperatures. Hall resistivity analysis categorizes this compound as an uncompensated semimetal. Its angle dependence of the magnetoresistance and quantum oscillation frequencies demonstrate an anisotropy ratio of ∼1.26 for the Fermi surface. Theoretical calculations corroborate these findings, mapping Fermi surfaces with three hole pockets and an electron pocket. Considering both the experimental and theoretical results, the colossal and angle-dependent magnetoresistance may be ascribed to unequal carrier densities coupled with large differences in carrier mobilities and Fermi-surface anisotropy, respectively. These results imply $\mathrm{YbA}{\mathrm{l}}_2\mathrm{S}{\mathrm{i}}_2$ is a promising candidate to study the crucial effect of electronic properties on its charge transport.

Superconductivity in two dimensions has attracted renewed interest in the context of two-dimensional (2D) van der Waals materials. Key questions remain regarding the nature and manifestations of the superconductivity in these materials. One open question is whether superconducting fluctuations in such 2D systems can be described by the classic Aslamazov-Larkin (A-L) equation. While the A-L model has long been found to accurately describe the paraconductivity of some conventional 2D superconductors, its applicability in ultrathin limit near the superconductor-insulator transition (SIT) has not been established. Here, we report a systematic study of superconducting fluctuation and paraconductivity in ultrathin 2D amorphous Pb films near the SIT. Pb films were incrementally deposited, and the electrical measurements were performed in situ at each thickness in a dilution refrigerator, resulting in a series of sheet resistance curves $\left[R_{\square }\left(T\right)\right]$ across the SIT. Paramagnetic impurities (Cr) were then deposited on the same superconducting film, driving it back to the insulating state and yielding another set of $R_{\square }$($T$). Both types of $R_{\square }$($T$) curves were analyzed with the A-L equation. At all film thicknesses (and $T_C$'s), we observed a background paraconductivity significantly greater than the A-L value. As the film thickness decreases and the SIT is approached, the paraconductivity increases precipitously, reaching more than an order of magnitude higher than that of the A-L value at the immediate vicinity of the SIT. Accompanying the presence of excess paraconductivity and its increase with decreasing thickness, the paraconductivity exhibits exponential scaling with $T$ above $T_C$, whose temperature range and slope show concomitant variations with decreasing film thickness. In contrast, suppression of $T_C$ by magnetic impurity results in much weaker increase of the excess paraconductivity and little change in the temperature range and slope of the exponential $T$ scaling. These observations are consistent with the presence of emergent localized superconducting pairing above $T_C$ in the strongly disordered, morphologically nominally uniform amorphous films. The spatially localized superconductivity likely causes excess paraconductivity beyond the A-L theory and percolative superconducting transitions. Such electronic inhomogeneities proliferate with decreasing film thickness, especially near the SIT.

${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ superconductors are commonly considered layered van der Waals materials with negligible interlayer coupling. Here, using inelastic neutron scattering to study spin excitations in single-crystal samples, we reveal that the magnetic coupling between adjacent Fe layers is ferromagnetic in nature, making the system different from most unconventional superconductors including iron pnictides. The weak interlayer coupling is estimated to be $J_c\sim$ 0.2 meV, in agreement with the short spin-spin correlation length ${\xi }_c\sim 0.2c$ along the $c$ axis. The results provide an experimental basis for establishing a microscopic theoretical model to describe the absence of magnetic order in ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$.

A recent experiment by P. F. Shan et al. (arXiv:2304.09011) found that rhenium trioxide ${\mathrm{ReO}}_3$, a simple metal at ambient pressure, becomes superconducting with a transition temperature as high as 17 K at 30 GPa. In this paper, we analyze the electron-phonon origin of superconductivity in rhombohedral ${\mathrm{ReO}}_3$ in detail. In addition, we also conduct a high-throughput screening of isostructural transition metal trioxides $X{\mathrm{O}}_3$ in searching for potential pressure-induced superconductors. In total, 28 $X{\mathrm{O}}_3$ compounds have been studied, of which four candidates ${\mathrm{RuO}}_3, {\mathrm{OsO}}_3, {\mathrm{IrO}}_3$, and ${\mathrm{PtO}}_3$ are predicted superconducting with the transition temperatures of 26.4, 30.3, 0.9, and 2.8 K at 30 GPa, respectively. Both ${\mathrm{IrO}}_3$ and ${\mathrm{PtO}}_3$ stay superconducting even at ambient pressure. In ${\mathrm{ReO}}_3, {\mathrm{RuO}}_3,{\mathrm{OsO}}_3$, and ${\mathrm{IrO}}_3$, the conduction electrons around the Fermi level are dominantly from the X-d and the O-$2p$ orbitals, and their electron-phonon coupling originates from the lattice dynamics of both the heavier transition metal atom and the oxygen atom. Inclusion of spin-orbital coupling would mildly suppress the transition temperatures of these transition metal trioxide superconductors except ${\mathrm{RuO}}_3$.

Machine-learning models can be trained to predict the converged electron charge density of a density functional theory (DFT) calculation. In general, the value of the density at a given point in space is invariant under global translations and rotations having that point as a center. Hence, one can construct locally invariant machine-learning density predictors. However, the widely used projector augmented wave (PAW) implementation of DFT requires the evaluation of the one-center augmentation contributions that are not rotationally invariant. Building on our recently proposed Jacobi-Legendre charge-density scheme, we construct a covariant Jacobi-Legendre model capable of predicting the local occupancies needed to compose the augmentation charge density. Our formalism is then applied to the prediction of the energy barrier for the 1H-to-1T phase transition of two-dimensional ${\mathrm{MoS}}_2$. With extremely modest training, the model is capable of performing a non-self-consistent nudged elastic band calculation at virtually the same accuracy as a fully DFT-converged one, thus saving thousands of self-consistent DFT steps. Furthermore, at variance with machine-learning force fields, the charge density is here available for any nudged elastic band image, so that we can trace the evolution of the electronic structure across the phase transition.

We construct a fast, transferable, general purpose, machine-learning interatomic potential suitable for large-scale simulations of ${\mathrm{N}}_2$. The potential is trained only on high quality quantum chemical molecule-molecule interactions; no condensed phase information is used. Although there are no explicit or implicit many-molecule interaction terms, the potential reproduces the experimental phase diagram including the melt curve and the molecular solid phases of nitrogen up to $10\mathrm{GPa}$. This demonstrates that many-molecule interactions are unnecessary to explain the condensed phases of ${\mathrm{N}}_2$. With increased pressure, transitions are observed from cubic $\left(\alpha \right)$, which optimizes quadrupole-quadrupole interactions, through tetragonal $\left(\gamma \right)$, which allows more efficient packing, to monoclinic $\left(\lambda \right)$, which packs still more efficiently. On heating, we obtain the hcp three-dimensional (3D) rotor phase $\left(\beta \right)$ and, at pressure, the cubic $\delta$ phase which contains both 3D and 2D rotors, tetragonal ${\delta }^{*}$ phase with 2D rotors, and the rhombohedral $\epsilon$. Molecular dynamics demonstrates where these phases are indeed rotors, rather than frustrated order. The model supports the metastability of the complex $\iota$ phase, but not the reported existence of the wide range of bond lengths. The thermodynamic transitions involve both shifts of molecular centers and rotations of molecules: the onset of rotation is rapid, whereas motion of molecular centers is inhibited and we suggest that this is the cause of the experimentally observed sluggishness of transitions. Routine density functional theory calculations give a similar picture to the potential.