The Moore-Read Pfaffian (Pf) state exhibits two distinct neutral excitation modes, the bosonic magnetoroton mode and the neutral fermion mode. These two modes have been conjectured to be supersymmetric (SUSY) partners in the long-wavelength limit. Previous studies on these neutral excitations of the Pf state have shown evidence in favor of SUSY in the vicinity of the second Landau level (SLL) Coulomb interaction. Inspired by that, using the framework of parton theory, we test the SUSY conjecture for a state that lies in the same universality class as the particle-hole conjugate of the Pf, namely the anti-Pf (aPf) state, by constructing explicit wave functions for its magnetoroton and neutral fermion excitations and evaluating them for very large system sizes. As with the previous studies on the Pf state, we find that the long-wavelength gaps of the neutral modes of the parton state belonging to the same topological class as the aPf are close to each other for the SLL Coulomb interaction. Furthermore, using the parton wave functions, we compute the dispersion of various neutral collective excitations, including the magnetoroton, neutral fermion, and parton-excitons, for several notable non-Abelian and Abelian states. Finally, we propose a parton-exciton ansatz for the gapped neutral excitation of the composite fermion Fermi liquid at quarter filling and compute its dispersion for the Coulomb interaction in the lowest Landau level.

Lanthanide (Ln) materials are widely studied using x-ray absorption spectroscopy (XAS), primarily at the Ln $3d$ edge, with less attention given to the $4d$ edge. Spectral features are usually analyzed in relation to bulk properties with surface effects rarely considered. In this study, we explore surface phenomena and their impact on XAS spectra, using as examples the antiferromagnetic (AFM) Kondo lattice ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$, where we thoroughly examine both the $3d$ and $4d$ edges, and AFM ${\mathrm{LnRh}}_2{\mathrm{Si}}_2$ (Ln = Tm, Tb, and Pr), where our focus is primarily on the $3d$ edge. We observe significant contributions from surface effects in the $3d$ XAS spectra, even when measured in the total electron yield regime. We find evidence of Ce $4f$ moment reorientation at the Ce-terminated surface of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$, linked to changes in the crystal electric field at the surface. By modeling the Ce $3d$ and $4d$ XAS spectra, we not only distinguish between surface and bulk properties but also reveal the fine multiplet structure and the characteristic shape of the giant resonance associated with $|M_J\rangle$ states. These findings provide insights into $4f$-derived surface phenomena and their distinction from bulk electronic properties, while also emphasizing the general importance of surface sensitivity in XAS measurements of Ln materials.

Properties of Cu-Ni solid solutions have long been studied in physical and materials sciences. Yet, their many-body properties have not been well understood. Here, we investigate ultrafast luminescence in near-infrared region for ${\mathrm{Cu}}_{1-x}{\mathrm{Ni}}_x$ alloys. The luminescence intensity was the highest in Cu and decreased dramatically by adding Ni, approaching close to the value for pure Ni at $x=0.45$. This composition dependence was well reproduced by calculations assuming two-body scattering of the energetic electrons. The luminescent decay rate was not straightforward, i.e., it decreased first by adding Ni up to $x=0.17$ and then started to increase approaching twice the initial value at $x=0.45$. This behavior was in good agreement with ab initio calculations of electron-phonon (e-ph) coupling strength. This work provides a new perspective on the electron relaxation dynamics in solid solution systems.

Two-dimensional (2D) magnetic materials provide a unique platform for exploring quantum phases from magnetic order in reduced dimensions. While there have been extensive studies on 2D magnetic materials based on $3d$ electrons, experimental studies on $4f$-electron counterparts are far fewer, particularly on their electronic structure. In this study, we report the successful synthesis of ultrathin ${\mathrm{SmC}}_6$ films using molecular beam epitaxy. Utilizing in situ angle-resolved photoemission spectroscopy (ARPES), we uncover a large band splitting in the valence bands, which we attribute to the ferromagnetic order driven by exchange couplings between Sm $4f$ moments and conduction electrons. Despite the small magnetic moment of Sm, the observed splitting is comparable to those of Eu- and Gd-based systems with much larger local moments. Interestingly, the surface state also exhibits splitting with similar magnitude and can be eliminated by overannealing, while the valence bands with ferromagnetic-like splittings remain robust. Our work provides spectroscopic insight to understand the electronic origin of magnetic order in Sm-based compounds. Our study also offers a platform to study 2D magnetic materials based on $4f$ electrons.

We study two-dimensional superconductivity mediated by magnetic fluctuations at the interface between a ferromagnetic insulator and the nonsymmorphic topological crystalline insulator with a fourfold-degenerate Dirac point wallpaper fermion. We demonstrate that BCS pairing with zero center-of-mass momentum induces chiral $p$-wave superconductivity, and the Amperean pairing with center-of-mass momentum $2k_{\mathrm{F}}$ can give rise to a parity-mixed superconducting state. We find that the Amperean pairing exhibits a mixture of $s$-wave and $p$-wave components due to the multiband nature of the wallpaper fermion and the easy-axis anisotropy of the ferromagnetic insulator. Additionally, we find that the stability of the superconducting state with BCS and the Amperean pairing is governed by the easy-axis anisotropy.

Exploring the coupling between layer, magnetism, valley, and topology in two-dimensional (2D) materials is an important approach to deepen our understanding of materials properties. We propose 27 stable ferromagnetic monolayers of Janus XYZH $(X=\mathrm{Sc},\mathrm{Y},\mathrm{La},Y\mathrm{=}\mathrm{Cl},\mathrm{Br},\mathrm{I},\text{and} Z=\mathrm{S},\mathrm{Se},\mathrm{Te})$. All these monolayers exhibit spontaneous valley polarization, forming ferromagnetic valley (FV) monolayers, showing the anomalous valley Hall (AVH) effect. By applying external strain, the topological phase transitions including quantum anomalous Hall (QAH) effect can be introduced. In the ScBrSH bilayer system, AA and AB stacking configurations were constructed through interlayer sliding and rotating operations. The bilayer system exhibits interlayer antiferromagnetic ordering with spontaneous valley polarization differing from the FV observed in monolayers. The sliding ferroelectricity in the AA stacking bilayer indicates that the system exhibits pronounced multiferroic characteristics. Further analysis shows that interlayer sliding can introduce a layer polarization anomalous valley Hall (LPAVH) effect, which can be precisely controlled by tuning the direction of the ferroelectric polarization. Upon applying external strain, the quantum layer spin Hall effect observed during the topological phase transition in the bilayer can be regarded as the superposition of two QAH monolayers. Furthermore, applying a twisting operation to the bilayer induces unexpected altermagnetism. Our study systematically reveals the rich physical properties of 2D XYZH materials, providing important theoretical foundations and guidance for the design and development of next-generation quantum devices.

This study investigates the nuclear quantum effects (NQEs) in graphene/hexagonal boron nitride (G/hBN) heterostructures at low temperatures and explores the modulation of these effects through mechanical tensile strain. By employing path integral molecular dynamics simulations to account for the quantum nature of atomic nuclei in conjunction with density functional theory and machine learning potential models, we enable the simulation of large-scale systems over extended timescales. Our findings reveal that significant, albeit transient, NQEs are present during the transition from AA to AB stacking. We demonstrate that the application of appropriate mechanical tensile strain can effectively prolong the duration of this quantum state and, in certain cases, stabilize NQEs in an intermediate state, preventing their evolution into a classical state. This work provides insights into the stacking transition mechanisms and NQEs in G/hBN heterostructures, proposing potential methods for regulating these quantum properties. These findings have considerable significance for the understanding and control of quantum characteristics in two-dimensional material heterostructures.

Experimental realizations of Abelian fractional Chern insulators have demonstrated the potentials of moiré systems in synthesizing exotic quantum phases. Remarkably, a twisted multilayer graphene system may also host non-Abelian states competing with charge density waves under Coulomb interactions. Here, through larger-scale exact diagonalization simulations, we map out the quantum phase diagram for a $\nu =1/2$ system with electrons occupying the lower moiré band of a double twisted bilayer graphene. By increasing the system size, we find the ground state has sixfold near degeneracy and with a finite spectral gap separating the ground states from the excited states across a broad range of parameters. Further computation of many-body Chern numbers establish the topological order of the state, and we rule out the possibility of charge density wave orders based on a featureless density structure factor. Furthermore, we inspect the particle-cut entanglement spectrum to identify the topological state as a non-Abelian Moore-Read state. Combining all the above evidence, we conclude that the Moore-Read ground state dominates the quantum phase diagram for a double twisted bilayer graphene system for a broad range of coupling strengths with realistic Coulomb interactions.

The attention mechanism has transformed artificial intelligence research by its ability to learn relations between objects. In this work, we explore how a many-body wave-function Ansatz constructed from a large-parameter self-attention neural network can be used to solve the interacting electron problem in solids. By a systematic neural-network variational Monte Carlo study on a moiré quantum material, we demonstrate that the self-attention Ansatz provides an accurate and efficient solution without human bias. Moreover, our numerical study finds that the required number of variational parameters scales roughly as $N^2$ with the number of electrons, which opens a path towards efficient large-scale simulations.

We study the correlated Haldane-Hubbard model with single-particle gain and loss, focusing on its non-Hermitian phase diagram and the ensuing nonunitary dynamic properties. The interplay of interactions and nonhermiticity results in insulating behavior with a phase diagram divided into three distinct regions, exhibiting either topologically gapped or (real) gapless regimes and a trivial phase. The latter is mapped by the emergence of a local order parameter associated with a charge density wave. A $\mathcal{P}T$-symmetry breaking at the low-lying spectrum occurs when increasing the gain-loss magnitude at a fixed interaction strength, marking the transition from gapped to gapless topological behavior. Further increase leads to the onset of charge ordering in a first-order phase transition in which level crossing takes place in the spectrum's real part. The support that the staggered gain and loss display to robust charge density wave in equilibrium is confirmed in the real-time dynamics in the presence of nonhermiticity, suggesting that engineered gain and loss can be used to tailor an ordered many-body state in experiments.

The $T^2$-scaling of resistivity with temperature is often viewed as a classic hallmark of a Fermi-liquid (FL) behavior in metals. However, if umklapp scattering is suppressed, this scaling is not universally guaranteed to occur. In this case, the resistivity behavior is influenced by several factors, such as dimensionality (two vs three), topology (simply- vs multiply-connected Fermi surfaces), and (in two dimensions) the shape (convex vs concave) of the Fermi surface (FS). Specifically for an isotropic spectrum, as well as for a two-dimensional (2D) convex FS, the $T^2$ term is absent, and the first nonzero contribution scales as $T^{4}lnT$ in 2D and as $T^4$ in 3D. In this paper, we study the $T$-dependence of the resistivity, arising from electron-electron interactions, in the presence of a weak magnetic field. We show that, for an isotropic FS in any dimensions and for a convex 2D FS, the $T^2$ term is also absent in both Hall and diagonal components of the magnetoconductivity, which instead scale as $B{T}^{4}lnT$ and $B^2{T}^{4}lnT$, respectively, in 2D and as $B{T}^4$ and $B^2{T}^4$ in 3D. The FL-like scaling, i.e., $B{T}^2$ and $B^2{T}^2$ of the Hall and diagonal conductivities is recovered for a concave FS in 2D. Furthermore, we show that, for an isotropic spectrum, magnetoresistance is absent even in the presence of electron-electron interactions. Additionally, we examine the high-temperature limit, when electron-electron scattering prevails over the electron-impurity one, and show that all the components of the conductivity tensor saturate in this limit at values that are determined by impurity scattering but, in general, differ from the corresponding values at $T=0$.

We present a numerical implementation, based on Wannier interpolation, of a Kubo-Greenwood formalism for computing the spatially dispersive optical conductivity in crystals at first order in the wave vector of light. This approach is more efficient than direct $\mathit{ab}\mathit{initio}$ methods because, with less computational cost, it allows for a much finer sampling of reciprocal space, resulting in better-resolved spectra. Moreover, Wannier interpolation avoids errors arising from truncation of the sums over conduction bands when evaluating the spatially dispersive optical matrix elements. We validate our method by computing the optical activity spectrum of selected crystals, both polar (GaN) and chiral (trigonal Te, trigonal Se, and $\alpha$-quartz), and comparing it with existing literature.

Topological lasers, known for their robustness and unique features originating from nontrivial topology, have recently become a focal point of research in photonics. In this work, we propose a topological laser based on two-dimensional Su-Schrieffer-Heeger photonic lattices as induced by artificial gauge flux insertion. The underlying effect, called the topological Wannier cycles, is characterized by topological local modes with continuously tunable frequency and orbital angular momentum emerging in two photonic band gaps. These topological local modes enable single-mode large-area lasing in each photonic band gap with both topological robustness and exceptional tunability in frequency and orbital angular momentum properties, setting a notable contrast with previous topological lasers. We further discuss both localized and extended artificial gauge flux insertion and compare their properties. We find that extended gauge flux achieves significantly higher laser output intensity and larger single-mode area under laser-gain conditions, outperforming the local gauge flux configuration in both output intensity and resilience against disorders. We also elucidate the precise mechanisms by which nonlinear gain and gauge flux govern the photon dynamics in various regimes. These results provide crucial theoretical insights for orbital angular momentum control in topological lasers and pave the way for advancements in high-precision engineering of lasers and optical systems.

We investigate the supercurrent flowing in a spin-triplet superconductor (TS) junction with an unconventional $p$-wave magnet (UPM) sandwiched between TS electrodes. It is demonstrated that the UPM functions as a normal metal and supercurrents are hardly affected when the magnetization is aligned with the $\mathbf{d}$ vectors of the TS. In contrast, the supercurrent can be drastically modulated when they are misaligned. A spin supercurrent can be induced due to the $\mathbf{d}$ vector rotated by the UPM and the charge supercurrent can exhibit an abrupt current-reversal effect when the UPM strength vector $\mathit{\alpha }$ is along the longitudinal current direction. The slight deviation of $\mathit{\alpha }$ from the current direction leads to rapid suppression of supercurrents, which is attributed to the different-period oscillation of the momentum-resolved supercurrent induced by the UPM.

We consider the nonlinear response of a disordered two-dimensional electronic system, lacking inversion symmetry, to an external alternating electric field. The application of an in-plane static magnetic field induces local contributions to the current density that are quadratic in the electric field and linear in the magnetic field. This current oscillates at twice the frequency of the external irradiation and there are two linearly independent vector combinations that contribute to the current density. This particular mechanism coexists with the topological Berry-dipole contribution to the second harmonic of the current density, which can be generated by quantum confinement. Additional nonlocal terms in the current density are possible in the regime away from the normal incidence. The total current exhibits a nonreciprocal character upon reversal of the magnetic field direction. We evaluate the magnitude of this effect by computing its dependence on the strength of spin-orbit coupling and the disorder scattering rate. Importantly, we show that these local second-harmonic contributions can be resonantly excited when the frequency of the external radiation approaches the energy separation between the spin-orbit split bands.

Scaling the thickness of a material to an atomically thin limit leads to the emergence of distinct physical properties that are unachievable in its bulk counterpart. Here, we predict the existence of superconducting state with a critical temperature $\left(T_{\mathrm{c}}\right)$ of 1.50 K in a stable atomically thin two-dimensional (2D) crystal of scandium (Sc), referred to as “scandiene.” Unlike its metallic bulk counterpart, the emergence of superconductivity in scandiene is driven by an overall softening of phonons and an increased electronic density of states at the Fermi level. Hydrogenation of scandiene can give rise to the formation of two phases, i.e., electride and nonelectride ${\mathrm{Sc}}_2\mathrm{H}$. The $T_{\mathrm{c}}$ of both electride and nonelectride ${\mathrm{Sc}}_2\mathrm{H}$ remains measurable, with approximate values of 1.76 and 1.54 K, respectively. Notably, in the ${\mathrm{Sc}}_2\mathrm{H}$ electride, strong electron-phonon coupling between interstitial anionic electrons and low-frequency acoustic modes dominated by Sc atoms significantly enhances the $T_{\mathrm{c}}$ up to 15.0 K under 8% biaxial tensile strain. These findings not only expand the family of 2D monoelemental materials but also establish avenues for exploring superconductivity in the 2D limit.

This work presents a method to quantize low energy excitations of systems whose ground state is best represented by a matrix product state (MPS) such as the Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The approach is similar to the spin-wave model of excitations in typical magnetic materials, but includes a more general set of fluctuations in entanglement structure. We argue that the quasilocal action of tensor fluctuations facilitates a description in terms of bosonic modes. We apply this approach to compute fluctuation corrections to the bilinear-biquadratic Heisenberg model, whose ground state we expect to be close to the exact bond dimension 2 AKLT state in a certain parameter range. Our results show significant improvements in energy approximations, highlighting both the qualitative and quantitative potential of this paradigm for studying complex entangled systems. This approach paves the way for new insights into the low-energy physics of correlated materials and the development of effective field theories beyond traditional semiclassical methods.

Transition metal spinels, particularly those containing chromium $3+$ ions $\left({\mathrm{Cr}}^{3+}\right)$, display a rich variety of low-temperature magnetostructural states. Here, we present a combined neutron scattering, synchrotron x-ray diffraction, and density functional theory study of the frustrated “breathing pyrochlore” chromium spinel ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$, where the adjacent ${\mathrm{Cr}}^{3+}$ tetrahedra alternate in magnetic interaction strength. We first establish the low-temperature tetragonal structure from the diffraction measurements. Considering the magnetic structure in light of the distortions generated by this structure, the short magnetic correlation length found in a previous study can be explained by dimensional reduction due to residual frustration. The Heisenberg Hamiltonian for the low-temperature structure is extracted using density functional theory-based energy mapping and clearly shows the partial release of frustration due to the structural transition. The first four exchanges terms dominate, and the two nearest-neighbor exchanges $J$ and $J^{\prime }$ in the high-temperature structure both split substantially. The full magnetic excitation spectrum obtained by inelastic neutron scattering can be accurately reproduced by a linear spin-wave theory model using the density functional exchange parameters as a starting point. However, it is found that multiple parameter sets that obey the relation $(J_1+J_4)/(J_2+J_3)\sim 1.24$, $J_1>J_2$, and $J_3>J_4$ provide an equally good description of the data. This ratio, along with the low-temperature structure, suggests that it is the distortion of the small tetrahedra that drives the magnetostructural transition.

The structure factor is a useful observable for probing charge density correlations in real materials, and its long-wavelength behavior encapsulated by “quantum weight” has recently gained prominence in the study of quantum geometry and topological phases of matter. Here, we employ the full static structure factor $S\left(\mathbf{q}\right)$ to explore the phase diagram of twisted transition metal dichalcogenides (TMDs), specifically $t{\mathrm{MoTe}}_2$, at filling factors $\nu =1/3$, $2/3$ under varying displacement fields. Our results reveal a topological phase transition between a fractional Chern insulator (FCI) and a generalized Wigner crystal. This transition is marked by the appearance of Bragg peaks at charge-density-wave vectors, and simultaneously, a large decrease of $S\left(\mathbf{q}\right)$ at small $\mathbf{q}$ which lowers the interaction energy. We further calculate the quantum weight of various FCI states, verifying the universal topological bound for interacting systems. Our findings provide insights into the phase diagram of twisted TMDs and establish a general framework for characterizing topological phases through structure factor analysis.

Moiré engineering offers new pathways for manipulating emergent states in twisted layered materials and lattice mismatched heterostructures. With the key role of the geometry of the underlying lattice in mind, here we introduce the watermill lattice, a two-dimensional structure with low-energy states characterized by massless pseudospin-$3/2$ fermions with high winding numbers. Its twisted bilayer is shown to exhibit magic angles, where four isolated flat bands emerge around the Fermi level, featuring elevated Wilson-loop windings and enhanced quantum geometric effects, such as an increase in the ratio of the Berezinskii-Kosterlitz-Thouless transition temperature to the mean-field critical temperature under a weak Bardeen-Cooper-Schrieffer pairing. We discuss how the watermill lattice could be realized in the MXene and group-IV materials. Our Letter highlights the potential of exploiting lattice geometry in moiré engineering to uncover novel quantum phenomena and tailor emergent electronic properties in materials.