The fractional quantum anomalous Hall (FQAH) phase, featuring unique fractionally quantized states, has garnered substantial experimental progress in recent years. To unlock its full potential for applications in advanced electronics, integrating the FQAH phase with nontrivial higher-order topological states hosting fractional corner states is highly promising. Here, we establish a theoretical model on a generic $s{p}^2$ hybridized honeycomb lattice with a second-order topological insulating (SOTI) index that can give rise to the appealing FQAH state. Two topological flat bands carrying opposite nonzero Chern numbers emerge around the Fermi level, separated by an SOTI band gap. Exact-diagonalization calculations reveal that electron correlations drive the topological flat bands into rare FQAH states at fractional fillings of 1/3 and 2/5. These prominent fractional topological states persist across a wide parameter range, demonstrating exceptional resilience to variations in band dispersion and orbital composition. The coexistence of FQAH and SOTI states is anticipated to be realized in a practical silicene nanomesh material from first-principles calculations. Our work provides a different pathway for the fabrication of multifunctional and highly miniaturized topological quantum devices in pursuit of the topological quantum computing.

Exploring novel topological matters with exotic quantum states has always been a core issue in the field of condensed matter physics, which can update the understanding of topological phases and broaden the classification of topological materials. Here, we report a class of unconventional hybrid-order topological insulators (HyOTIs), which simultaneously host various higher-order topological states in a single band gap. Such topological states exhibit a unique bulk-boundary correspondence that is different from the well-known first-order topological states, higher-order topological states, and the coexistence of both. We develop a generic surface theory to precisely capture them and discover a three-dimensional unconventional HyOTI protected by inversion symmetry, which renders both helical and corner topological states and exhibits an excellent bulk-edge-corner correspondence. By adjusting the parameters of the system, we also observe the nontrivial phase transitions between the inversion-symmetric HyOTI and other conventional phases. We further propose a circuit-based experimental scheme to detect these interesting results. Particularly, we demonstrate that a modified tight-binding model of bismuth can support the unconventional HyOTI, suggesting a possible route for its material realization. This work significantly advances the research of hybrid topological states in both theory and experiment.

Quantum integrability emerging near a quantum critical point (QCP) is manifested by an exotic excitation spectrum that is organized by the associated algebraic structure. A well-known example is the emergent $E_8$ integrability near the QCP of a transverse field Ising chain (TFIC), which was long predicted theoretically and initially proposed to be realized in the quasi-one-dimensional (q1D) quantum magnet ${\mathrm{CoNb}}_2{\mathrm{O}}_6$. However, later measurements on the spin excitation spectrum of this material revealed a series of satellite peaks in low energies that go beyond the description of the $E_8$ Lie algebra. Motivated by this experimental progress, we hereby revisit the spin excitations of ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ by combining numerical calculation and analytical analysis. We show that, as effects of strong interchain fluctuations, the spectrum of the system near the 1D QCP is characterized by an emergent $D_8^{\left(1\right)}$ Lie algebra instead of the $E_8$ one. We further show that the $D_8^{\left(1\right)}$ spectrum can be realized in a broad class of interacting quantum systems. Our results advance the exploration and manipulation of integrability in quantum critical systems.

The magneto-optical response of excitons in monolayer transition metal dichalcogenides is governed by a complex interplay of Bloch-state quantum geometry—reflected in the electronic magnetic moment—coupled with interband mixing and many-body interactions. Here, we develop a robust and general first-principles framework for many-body exciton $g$ factors (magnetic moments) by incorporating off-diagonal terms for the spin and orbital angular momenta of single-particle bands and many-body states for magnetic fields pointing in arbitrary spatial directions. We implement our framework using many-body perturbation theory via the GW-Bethe-Salpeter equation  and supplement our analysis with robust symmetry-based models. Focusing on the archetypal monolayer ${\mathrm{WSe}}_2$, we accurately reproduce the known results of the low-energy excitons including the Zeeman splitting and the dark/gray exciton brightening. Furthermore, our theory naturally reveals the magnetic-field hybridization of higher-energy excitons ($s, p$, and $d$ like) and shows that the magnetic moments of nodal excitons ($p$ and $d$ like) do not acquire additional contributions of $\pm m_j{\mu }_B$ ($m_j=1,2$), characteristic of the hydrogenic picture. Our general approach also allows us to resolve the long-standing puzzle of the experimentally measured nonmonotonic Rydberg series ($1s-4s$) of exciton $g$ factors. Our framework offers a comprehensive approach to investigate, rationalize, and predict the nontrivial interplay between magnetic fields, angular momenta, and many-body exciton physics in van der Waals systems, offering different opportunities to probe signatures of quantum geometry within many-body states.

We propose an innovative strategy to integrate $d$-wave altermagnetism with intrinsic second-order topological phases in two-dimensional bilayer Chern insulators. Using bilayer ${\mathrm{V}}_2{\mathrm{WS}}_4$ as a case study, our first-principles calculations reveal that the A-type antiferromagnetic interlayer configuration transforms the system into a $d$-wave altermagnet, resulting in four topological corner states localized at the corners of a square flake. Notably, interlayer sliding disrupts the symmetry between diagonal and antidiagonal corners, leading to a controlled splitting of the corner state into two doubly degenerate sets. An effective lattice model successfully captures the essential features observed in our first-principles calculations, providing insights into the interplay between stacking geometry, interlayer interactions, and higher-order topology. Our findings position $d$-wave altermagnets as a promising platform for engineering tunable higher-order topological states, paving the way for their integration into van der Waals heterostructures.

Chern insulators, distinguished by a nonzero Chern number in topological phases, exhibit a quantum Hall effect without requiring Landau levels. Although acoustic counterparts of Chern insulators were created via engineered nonreciprocity with vortex flows, the concerning studies primarily relied on quantum-mechanical analogies, and full-wave simulations and experiments, which lack a theoretical model on the basis of the acoustic foundation. Thus, in this work, we present a theory to study acoustic Chern insulators (ACIs) created by introducing vortex flows into honeycomb lattices and derive an analytic solution for the Hamiltonian of the system from fundamental acoustic wave equations. The frequency band calculated using our theoretical model is in good agreement with that obtained using full-wave simulations, which demonstrates the accuracy of the theory. According to the theory, a different edge state is observed. Furthermore, the theory can also be applied to study the frequency band of deformed lattices, which exhibit distinct symmetry from the band structure of regular lattices. The theoretical model provides a way to further understand the physical mechanism of an ACI in terms of acoustic waves, which demonstrates that the breaking of time-reversal symmetry in the ACI originates from the Doppler effect induced by the vortex flows. The theoretical framework also presents a method to achieve the Hamiltonian from fundamental acoustic wave equations and can also be applied in the research of other acoustic topological materials, which provides a universal way to reveal the mechanism of acoustic wave manipulation with topological materials.

A second-principles effective interatomic potential is introduced for the prototypical perovskite ${\mathrm{CaTiO}}_3$ (CTO), relying on a Taylor polynomial expansion of the Born-Oppenheimer energy surface around the cubic reference structure, in terms of atomic displacements and macroscopic strains. This model captures various phases of bulk CTO and successfully reproduces, in particular, the structure, energy, and dynamical properties of the nonpolar $Pbnm$ ground state as well as of the hidden ferroelectric $R3c$ phase. Finite-temperature simulations suggest that the still debated sequence of structural phase transitions over heating is $Pbnm\left(a^{-}{a}^{-}{c}^{+}\right)\to C2/m\left(a^{-}{b}^{-}{c}^0\right)\to I4/mcm\left(a^{-}{c}^0{c}^0\right)\to Pm\overline{3}m\left(a^0{a}^0{a}^0\right)$, a sequence during which the oxygen octahedra rotations around the three pseudocubic axes vanish successively. Although never experimentally observed in bulk, the ferroelectric $R3c$ phase appears to be metastable and at an energy only slightly above the $Pbnm$ ground state at 0 K. The simulations confirm that, if induced in some way, the $R3c$ phase remains stable up to about 300 K and shows ferroelectric properties. Furthermore, we find that the minimum energy path connecting the $Pbnm$ and $R3c$ phases involves localized layer by layer flipping of octahedral rotations, a mechanism which is shown to be at play during the thermal destabilization process of the $R3c$ phase toward the $Pbnm$ ground state. The proximity of the $R3c$ phase with the $Pbnm$ ground state suggests that the former could be stabilized under electric field. However, due to the large energy barrier, the field required for the $Pbnm$ to $R3c$ transition appears to be extremely large, consistent with the fact that bulk CTO was never reported to be ferroelectric nor antiferroelectric.

The magnetic control by acoustically induced strain has driven significant research to pursue novel, ultrafast, compact, and energy-efficient electronic and spintronic devices. In this regard, magnetoelastic antiferromagnets have been highlighted as promising functional materials for this purpose. In this work, we report an experimental and phenomenological study of acoustic resonances in the two magnetic sublattices antiferromagnet ${\mathrm{NdFeO}}_3$, which exhibits strong interplay between magnetic and lattice degrees of freedom. The elastic properties of ${\mathrm{NdFeO}}_3$ are characterized through resonant ultrasound spectroscopy in the 2–300 K range. Domain-wall dynamics were studied by temperature-dependent Faraday magneto-optical imaging and AC magnetic susceptibility measurements. The results evidence the magnetoelastic coupling in ${\mathrm{NdFeO}}_3$, for which two different mechanisms contribute. The continuous spin reorientation transition is mirrored by the rather high acoustic losses, which correlate with the dispersion of the complex magnetic susceptibility and magnetic domain-wall dynamics. The results are compatible with the expected symmetry lowering during the spin reorientation transition and follow what is expected from a phenomenological approach. The paramagnetic ordering of the Nd sublattice under the influence of the Fe-sublattice magnetic field is found to influence the magnetoelastic properties just below the spin reorientation transition interval. This study highlights the elastic properties of ${\mathrm{NdFeO}}_3$, an interesting material for domain-wall motion control and local properties tailoring, which are the key for future applications in nanoscale devices.

Coherent Raman scattering techniques as coherent anti-Stokes Raman scattering (CARS), offer significant advantages in terms of pixel dwell times and speed as compared to spontaneous Raman scattering for investigations of crystalline materials. However, the spectral information in CARS is often hampered by the presence of a nonresonant contribution to the scattering process that shifts and distorts the Raman peaks. In this work, we apply a method to obtain nonresonant background-free spectra based on time-delayed, broadband CARS (TD-BCARS) using an intrapulse excitation scheme. In particular, this method can measure the phononic dephasing times across the full phonon spectrum at once. We test the methodology on amorphous ${\mathrm{SiO}}_2$ (glass), which is used to characterize the setup-specific and material-independent response times, and then apply TD-BCARS to the analysis of single crystals of diamond and ferroelectrics of potassium titanyl phosphate (KTP) and potassium titanyl arsenate (KTA). For diamond, we determine a dephasing time of $\tau =7.81$ ps for the single ${sp}^3$ peak.

Rydberg lattice under facilitation conditions can feature kinetic constraints, leading to ballistic and nonergodic behavior at different detuning intensities. Here, we demonstrate that a resonant driving field can achieve effects similar to those under facilitation conditions. We focus on the relaxation dynamics of spin clusters in a periodically driven Rydberg spin lattice. Through an effective Hamiltonian for the domain walls of the spin cluster, it is shown that when the driving frequency is resonant with the Rydberg interaction, the spin cluster exhibits ballistic expansion with half the spreading rate compared to the case of facilitation conditions. However, near the resonant point, the spin cluster displays confinement behavior of the Bloch-like oscillations. These results demonstrate the rich dynamic behaviors in the driven Rydberg spin lattices and may find applications in quantum state manipulation.

Magnetoresistance (MR) provides a crucial tool for experimentally studying spin torques. While MR is well established in the device geometry of the spin Hall effect (SHE), as exemplified by the magnet/heavy-metal heterostructures, its role and manifestation beyond the SHE paradigm remain elusive. We propose a general form of MR where the underlying charge-to-spin conversion and its inverse process could violate the simple geometry of the SHE, calling for tensorial descriptions. This MR can generate a series of unique harmonic responses essential for the experimental characterization of unconventional spin-orbit torques in non-SHE materials. We demonstrate these harmonic signals with semimetal ${\mathrm{WTe}}_2$ in mind but the results are not restricted to specific materials.

Collective excitations in superconductors provide essential insights into the symmetry of the broken phase, acting as indicators for identifying the ground state gap symmetry. Time-reversal symmetry breaking (TRSB) superconductors exhibit a rich spectrum of collective modes due to the complexity of their order parameters. These modes, known as “generalized clapping modes,” draw analogies to the clapping modes of helium-3 phase A. This study investigates two-dimensional TRSB superconductors with an order parameter of the form $\mathrm{\Delta }={\mathrm{\Delta }}_1+i{\mathrm{\Delta }}_2$, exploring the characteristics of their collective mode spectrum. We begin with a phenomenological Ginzburg-Landau approach to build intuition, then develop a dynamical theory by deriving linearized equations of motion using the pseudospin formalism. Beyond the linear regime, we propose a classification scheme based on the potential to induce (an)isotropic oscillations in the superconducting condensate. By perturbing the system in symmetry channels distinct from the ground state, we aim to selectively enhance or suppress different mode responses. This study analyzes the features of these generalized clapping modes as a function of the ratio between the order parameter components under various excitation schemes. We believe that our findings could help distinguish between different order parameter symmetries in TRSB superconducting condensates and estimate the magnitude of their components.

Two-dimensional materials with intrinsic superconductivity and nontrivial topology represent a frontier for discovering exotic quantum states and potential applications in quantum devices. Here, we report the first comprehensive theoretical investigation of superconductivity in monolayer and bilayer ${\mathrm{Cu}}_2\mathrm{N}$. The monolayer ${\mathrm{Cu}}_2\mathrm{N}$ has been recently synthesized experimentally and features a unique checkerboard lattice with topological nodal lines. Following this experimental breakthrough, we predict phonon-mediated superconductivity with transition temperatures ($T_c$) of 3.8 K (monolayer) and 7.9 K (bilayer) arising from strong electron-phonon coupling ($\lambda =0.76$ and 0.84, respectively) mediated primarily by Cu $d$-orbitals and low-frequency phonon modes. The bilayer shows 84% $T_c$ enhancement through additional interlayer vibrational modes that strengthen Cu $d$-orbital coupling via enhanced out-of-plane vibrations. Strain engineering enhances monolayer $T_c$ to 4.5 K under 0.2% compressive strain through optimized electronic density of states and phonon softening. We identify a practical synthesis pathway involving multilayer growth followed by controlled exfoliation with moderate energy cost ($0.97{\mathrm{J}/\mathrm{m}}^2$). Our results demonstrate that ${\mathrm{Cu}}_2\mathrm{N}$, featuring coexisting topological nodal lines and phonon-mediated superconductivity, represents a promising experimental platform for investigating potential topological superconducting behavior in accessible two-dimensional systems.

We present a matrix-product state (MPS) based band Lanczos method as solver for quantum cluster methods such as the variational cluster approximation. While a naïve implementation of MPS as cluster solver would barely improve its range of applicability, we show that our approach makes it possible to treat cluster geometries well beyond the reach of exact diagonalization methods. The key modifications we introduce are a continuous energy truncation combined with a convergence criterion that is more robust against approximation errors introduced by the MPS representation and provides a bound to deviations in the resulting Green's function. The potential of the resulting cluster solver is demonstrated by computing the self-energy functional for the single-band Hubbard model at half filling in the strongly correlated regime, on different cluster geometries. Here, we find that only when treating large cluster sizes, observables can be extrapolated to the thermodynamic limit, which we demonstrate at the example of the staggered magnetization. Treating clusters sizes with up to $6\times 6$ sites we obtain significant improvement over the extrapolation accessible with exact diagonalization solvers when comparing with quantum Monte Carlo results. Finally, we illustrate the applicability of the MPS cluster solver to more complex models by calculating spectral properties as relevant for the electron-doped cuprate ${\mathrm{CaCuO}}_2$.

Utilizing ultrafast optical pump-probe spectroscopy, we investigate the coexistence and competition of electronic orders in the bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Our results reveal two coexisting density waves that can be selectively manipulated with light. We directly identify a spin-density wave (SDW) with electronic nematicity emerging below $T_{\mathrm{SDW}}$ $\approx 140$ K by measuring its spin dynamics, and discover a distinct, nonmagnetic charge order appearing below $T_{\mathrm{DW}}$ $\approx 115$ K. The central finding is the demonstration of differential optical control: the charge order is fragile, completely suppressed by a pump fluence of approximately 40 $\mu \mathrm{J}/{\mathrm{cm}}^2$, while the SDW is remarkably robust, persisting to 200 $\mu \mathrm{J}/{\mathrm{cm}}^2$. This work establishes a clear hierarchy in the stability of competing electronic orders and provides a powerful method for disentangling their interplay in quantum materials.

It is common in condensed matter systems for reflection ($R$) and time-reversal ($T$) symmetry to both be broken while the combination $RT$ is preserved. In this paper, we study invariants that arise due to $RT$ symmetry. We consider many-body systems of interacting fermions with fermionic symmetry groups $G_f={\mathbb{Z}}_2^f\times {\mathbb{Z}}_2^{RT}$, $\mathrm{U}{\left(1\right)}^f⋊{\mathbb{Z}}_2^{RT}$, and $\mathrm{U}{\left(1\right)}^f\times {\mathbb{Z}}_2^{RT}$. We show that (2+1)D invertible fermionic topological phases with these symmetries have a $\mathbb{Z}\times {\mathbb{Z}}_8$, ${\mathbb{Z}}^2\times {\mathbb{Z}}_2$, and ${\mathbb{Z}}^2\times {\mathbb{Z}}_4$ classification, respectively, which we compute using the framework of $G$-crossed braided tensor categories. We provide a many-body $RT$ invariant in terms of a tripartite entanglement measure, and which we show can be understood using an edge conformal field theory computation in terms of vertex states. For $G_f=\mathrm{U}{\left(1\right)}^f⋊{\mathbb{Z}}_2^{RT}$, which applies to charged fermions in a magnetic field, the nontrivial value of the ${\mathbb{Z}}_2$ invariant requires strong interactions. For symmetry-preserving boundaries, the phases are distinguished by zero modes at the intersection of the reflection axis and the boundary. Additional invariants arise in the presence of translation or rotation symmetry.

Our study aims to provide a theoretical paradigm for a Λ-type negative differential resistance (NDR) device and to discover the general properties and mechanisms. In this study, we construct a NDR device named a metal-insulator interface reflecting electronic grid, which is made from rutile-$\mathrm{Ru}{\mathrm{O}}_2$ and $\mathrm{Ti}{\mathrm{O}}_2$, and the central region including an extension region with $\mathrm{Ru}{\mathrm{O}}_2\text{−}\mathrm{Ti}{\mathrm{O}}_2$ and a scattering region with pure $\mathrm{Ru}{\mathrm{O}}_2$. The device exhibits a Λ-type NDR phenomenon, which is robust in different crystallographic geometries for both nonmagnetic and altermagnetic ordering for $\mathrm{Ru}{\mathrm{O}}_2$. The NDR phenomenon also shows anisotropy for different magnetic states for $\mathrm{Ru}{\mathrm{O}}_2$, which can be used to distinguish the magnetic ground state of $\mathrm{Ru}{\mathrm{O}}_2$. To explain the Λ-type NDR phenomenon, we propose a general transmission channel selection mechanism in the interface of $\mathrm{Ru}{\mathrm{O}}_2$ and $\mathrm{Ti}{\mathrm{O}}_2$, which can be described by Bragg's law, and we believe that this mechanism is the main source of Λ-type NDR. This effect occurs at the interface, so it has the opportunity to exist in other devices with similar configurations. Our designed NDR device has a broad application in high-frequency oscillators and memory devices.

We report the quantization, quantum oscillations, and singular behavior of sublattice symmetry-breaking sublattice charge order (SCO) in two-dimensional Dirac insulators at charge neutrality under perpendicular magnetic fields $B$. SCO is induced by staggered sublattice potentials, such as those originating from substrates, strains, hydrogenation, and chemical doping. In small nonquantizing magnetic fields that result in less than a flux quantum threading the system, and small sublattice symmetry breaking potentials, SCO exhibits perturbative singular magnetic field dependence, $\sim \left|B\right|$, originating from hopping between neighboring sites of the same sublattice. At intermediate magnetic fields, when the cyclotron gap between the zeroth Landau level and the first Landau level, ${\omega }_c$, is smaller than the sublattice potential, ${\omega }_c\lesssim \mathrm{\Delta }$, SCO shows universally quantized plateaus owing to discrete Landau-level degeneracy. As the magnetic flux increases by one flux quantum, one electron (per spin) is transferred from the sublattice with a higher chemical potential to the sublattice with a lower chemical potential. One electron transfer between sublattices per flux quantum results from the sublattice polarization of the zeroth Landau level in gapped Dirac materials, realizing the topological Thouless pump effect. At stronger magnetic fields, ${\omega }_c\gtrsim \mathrm{\Delta }$, corresponding to integer quantum Hall regimes, SCO displays singularities based on the physics of quantum magneto-oscillations. Our findings suggest new ways to experimentally detect the presence of the energy gap in Dirac materials, irrespective of the gap size.

Electrides provide a unique opportunity to study electron localization and emergent magnetism in systems where the Fermi surface is formed by interstitial electronic states. This work introduces “magnetrides” as electrides where nonatomic electrons develop correlated magnetic order while maintaining a spatially and electronically distinct subsystem from atomic states—a paradigm enabling pristine electron spin systems. This concept is realized in novel monolayer XF $(X=\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba})$ electrenes, with BaF emerging as a prototypical example of “magnetrene” through its intrinsic interstitial moments, absent in the isoelectronic CaF and SrF. First-principles calculations trace this behavior to strain-tunable competition between cation $s$, $p$, and $d$ orbital contributions that shape the electride molecular orbital's topology at the Fermi level. The resulting system combines metallicity, robust in-plane ferromagnetism, strongly correlated localization $(U=2.9\mathrm{eV})$ confirmed by DMFT, and orbital-controlled magnetic transitions, establishing 2D magnetrenes as a versatile platform for designing nonatomic magnetic quantum phases.