Moiré superlattices in transition metal dichalcogenide heterobilayers exhibit various correlated insulating states driven by long-range Coulomb interactions, and these states crucially alter exciton resonances, particularly at fractional fillings. We revisit a theoretical framework to investigate the doping dependence of exciton spectra by extending hydrogenic exciton wave functions, systematically analyzing how the $1s, 2s$, and $3s$ Rydberg states respond to moiré-induced mixing of $s$- and $p$-type orbitals. Notably, while the $1s$ state remains relatively robust against doping, higher Rydberg excitons show strong redshifts and oscillator-strength quenching near specific fractional fillings. We incorporate both defect-induced quasiordering and thermal fluctuations to capture realistic device conditions, employing a large supercell approach. By selectively randomizing a subset of electrons or utilizing classical Monte Carlo simulations, we present direct calculations of exciton spectra under varying defect densities and temperatures. Our results emphasize how even moderate disorder or finite temperature can partially or completely suppress characteristic moiré exciton physics. We show how the $2s$ exciton states respond to the phase transition in correlated electron states. This comprehensive picture not only clarifies recent experimental observations but also provides a framework to guide the design of moiré-based optoelectronic devices.

The coherent spin dynamics of electrons are investigated for ${\mathrm{CsPbI}}_3$ perovskite nanocrystals in a glass matrix using time-resolved Faraday ellipticity. In nanocrystals with a diameter of about 11 nm, the Larmor precession frequency has a linear dependence on the magnetic field corresponding to the electron Landé $g$ factor of 2.07. We find a finite Larmor precession frequency at zero magnetic field, corresponding to the electron spin splitting of 0.8 $\mu \mathrm{eV}$. This splitting is explained by the hyperfine interaction with nuclear spin fluctuations. Our model analysis shows that the hyperfine interaction for the conduction-band electrons is contributed both by the $p$ orbitals of the lead atoms and by the $s$ orbitals of the iodine atoms, with the leading contribution to the hyperfine field fluctuations coming from iodine. This fact agrees well with the 9% iodine contribution to the Bloch amplitude of the conduction band, obtained by density functional theory calculations. From these findings, the atomic hyperfine constant for the $5s$ orbital of iodine is evaluated as 190 $\mu \mathrm{eV}$.

For nontopological quantum materials, introducing defects can significantly alter their properties by modifying symmetry and generating a nonzero analytical index, thus transforming the material into a topological one. We present a method to construct the potential matrix configuration with the purpose of obtaining a nonzero analytical index, akin to a topological invariant like a winding or Chern number. We establish systematic connections between these potentials, expressed in the continuum limit, and their initial tight-binding model description. We apply our method to graphene with an adatom, a vacancy, and both as key examples illustrating our comprehensive description. This method enables analytical differentiation between topological and nontopological zero-energy modes and allows for the construction of defects that induce topology.

Black phosphorene (BP) has emerged as a promising platform for tunable nonlinear photonics due to its layer-dependent band gap, high carrier mobility, and remarkable in-plane anisotropy. In this study, we investigate the second harmonic generation (SHG) of monolayer and bilayer BP under an external static electric field. The electronic states are described by a tight-binding model, and the nonlinear optical conductivities are derived from the semiconductor Bloch equations using perturbation theory. Our results reveal that BP exhibits large second-order nonlinear optical response along the armchair direction, with significant resonant enhancement when the incident photon energy approaches half of its band gap. Under an applied electric field of ${10}^7$ V/m, the effective second-order nonlinear susceptibility of BP can be as large as ${10}^3$ pm/V, surpassing that of the conventional nonlinear crystal ${\mathrm{AgGaSe}}_2$ by more than an order of magnitude. With respect to the static electric field induced by gate voltage, we discuss the relation between the electric-field-induced second harmonic (EFISH) generation and conventional SHG—under lower gate voltage, the EFISH approach agrees well with the SHG solutions, whereas the former is no longer applicable under higher gate voltage. Specifically, as the gate voltage increases, monolayer BP exhibits the band gap expansion and the corresponding blueshift in the SHG resonant peak. In contrast, bilayer BP undergoes a semiconductor-to-semimetal transition, forming a Dirac cone and generating divergent SHG spectra as photon energy goes to zero. Additionally, the chemical potential allows for precise control over interband and intraband nonlinear responses. In this work, we provide important theoretical foundations for the development of BP-based tunable nonlinear photonic devices and expand the application potential of anisotropic two-dimensional materials in nonlinear optics.

Unidirectional modes in magnetically biased electromagnetic systems have long been associated with a thermodynamic paradox: the absence of counterpropagating channels may produce field “hotspots” that can act as unphysical sinks of thermal radiation. Here we revisit this problem and show that, surprisingly, material dissipation alone cannot fully regularize the singular behavior of the normal modes of a nonreciprocal cavity. We demonstrate that the paradox is resolved by nonlocal effects, which suppress the material response at short wavelengths and eliminate field singularities altogether. Our analysis reveals a fundamental link between nonlocality, topology, and thermodynamic consistency, showing that real-space singularities and ill-defined topologies go hand in hand, even in strongly dissipative platforms. These findings clarify the physical origin of the paradox and establish nonlocality as a natural and robust mechanism for its resolution, opening new avenues to explore the intertwined roles of topology and nonlocality in passive nonreciprocal photonics.

Multiparticle correlations of exciton polaritons and reservoir excitons in the strong light-matter coupling regime dictate the quantum dynamics of optical microcavities. In this work, we examine the many-body exciton-polariton dynamics in a Fabry-Pérot microcavity of a two-dimensional metal-halide semiconductor over timescales involving polariton $(\ll 1\mathrm{ps})$ and exciton $(\gg 1\mathrm{ps})$ scattering. We find enhanced exciton nonlinear dynamics in the microcavity versus the bare semiconductor, concomitant with ultrafast polariton scattering dynamics. We measure, by means of coherent spectroscopy, the coupling between exciton polaritons, bright excitons, and reservoir excitons that highlight the complex scattering landscape that fundamentally drives polariton condensation.

Andreev molecule states arise from hybridization of Andreev bound states in different Josephson junctions. Extensive theoretical and experimental research concentrates on direct coherent electron coupling between the junctions: this implies the distance between the junctions is of the order of the superconducting coherence length, that is, short. We propose and discuss the possibility to create Andreev molecules at long (in principle, arbitrary long) distance between the junctions. In this case, the hybridized states are excited quasiparticle singlets and the coupling is provided by an embedding electric circuit. To achieve a strong hybridization, one aligns the energies of the Andreev bound states by tuning the associated phase drops. In fact, a recent experiment realizes such setup. With circuit theory we derive the hybridization level splitting and estimate the scale of the effect. Since the phenomenon encompasses excited states, we derive and solve the associated Lindblad equation under condition of persistent resonant excitation. By analyzing the resulting dissipative dynamics, we identify relevant regimes where the hybridization and resonant excitation peaks are most pronounced. The low-frequency mutual inductance of the Josephson junctions is an important signature of the molecular state and the associated nonlocal Josephson effect. We demonstrate the peak structures for both mutual and self-inductance, and compute them in various frequency regimes. In an interesting common case, the embedding circuit includes an oscillator, which can be used both to enhance hybridization and to read out the quantum states with two-tone spectroscopy. We derive and solve the Lindblad equation for the two-tone spectroscopy setup to demonstrate the readout of the molecular states. If the readout and enhancement of the hybridization are provided by different oscillators, we demonstrate that the states can be immediately identified from the oscillator response. However, in a more restricted setup where the same oscillator is used, the oscillator response manifests more resonant peaks, indicating all transitions between states with different photon numbers.

The tetragonal $4f$-electron intermetallic ${\mathrm{ErB}}_4$ is characterized by strong Ising anisotropy along the tetragonal $c$ axis. The magnetic moments on the erbium sites can be mapped onto a Shastry-Sutherland lattice, resulting in geometrical frustration. At zero magnetic field ${\mathrm{ErB}}_4$ exhibits collinear columnar antiferromagnetic (CAFM) order below $T_{\text{N}}=15.4\mathrm{K}$. In the presence of a magnetic field parallel to the $c$ axis, ${\mathrm{ErB}}_4$ exhibits a plateau at $1/2$ of the saturation magnetization $M_{\text{S}}$, which arises at a spin-flip transition at $H_1$ $=$ 1.9 T. Fractional magnetization plateaus and other exotic spin phases are a well-established characteristic feature of frustrated spin systems. Monte Carlo simulations propose that ${\mathrm{ErB}}_4$ is an ideal candidate to feature a spin supersolid phase in close vicinity of $H_1$ between the CAFM and $M/M_{\text{S}}=1/2$ plateau (HP) phase. Here, we combine single-crystal neutron diffraction and inelastic neutron scattering to study the magnetic phase diagram and the crystal electric-field (CEF) ground state of ${\mathrm{ErB}}_4$. Our measurements as a function of magnetic field find no signature of the spin supersolid phase but allow us to determine the magnetic structure of the HP phase to be of the up-up-up-down (uuud) type consistent with an Ising material. The magnetic moment ${\mu }_{\mathrm{CEF}}$ $=$ $8.96{\mu }_B$ expected from the CEF configuration determined by our inelastic neutron-scattering measurements is also consistent with the ordered moment observed in neutron diffraction, showing that the moments are fully ordered and close to the ${\mathrm{Er}}^{3+}$ free ion moment (9.6 ${\mu }_B$).

We investigate the intrinsic nonlinear valley Nernst effect, which induces a transverse valley current via a second-order thermoelectric response to a longitudinal temperature gradient. The effect arises from the Berry connection polarizability dipole of valley electrons and is permissible in both inversion-symmetric and inversion-asymmetric materials. We demonstrate that the response tensor is connected to the intrinsic nonlinear valley Hall conductivity through a generalized Mott relation, with the two being directly proportional at low temperatures, scaled by the Lorenz number. We elucidate the symmetry constraints governing this effect and develop a theory for its nonlocal measurement, revealing a nonlocal second-harmonic signal with a distinct ${\rho }^2$ scaling. This signal comprises two scaling terms, with their ratio corresponding to the square of the thermopower normalized by the Lorenz number. Key characteristics are demonstrated using a tilted Dirac model and first-principles calculations on bilayer ${\mathrm{WTe}}_2$. Possible extrinsic contributions and alternative experimental detection methods, e.g., by valley pumping and by nonreciprocal directional dichroism, are discussed. These findings underscore the significance of band quantum geometry on electron dynamics and establish a theoretical foundation for nonlinear valley caloritronics.

We report the results of high-resolution dc magnetization and specific-heat measurements at very low temperatures for a single crystal of ${\mathrm{UBe}}_{13}$ in magnetic fields applied along the [001] and [111] directions, in both the normal and superconducting states. In the normal state, magnetic susceptibility $\chi \left(T\right)=M/H$ exhibits a logarithmic temperature dependence over a wide temperature range (1–20 K). However, with increasing field, this non-Fermi-liquid (NFL) behavior of $\chi \left(T\right)$ at low temperatures is suppressed. Moreover, a susceptibility maximum occurs below 4 T, whereas Fermi-liquid coherence is recovered above 8 T. In addition, thermodynamic anomalies ($T_{\mathrm{A}}$ and $H_{\mathrm{A}}$) occur in both magnetic susceptibility and specific heat at intermediate fields (6–10 T) along the [111] direction. Furthermore, a nontrivial fifth-order nonlinear susceptibility is observed in the normal-state magnetization of ${\mathrm{UBe}}_{13}$. These results suggest a close relationship between the field-induced multipolar correlations of $5f$-electron degrees of freedom and the Fermi-surface reconstruction accompanying the crossover from the NFL state to the Fermi-liquid state in ${\mathrm{UBe}}_{13}$.

We develop a comprehensive Ginzburg-Landau theory describing triple-Q magnetic orders on hexagonal lattices, focusing on $O\left(N\right)$ models with $N=2$ and $N=3$. Through systematic analysis of symmetry-allowed terms in the free energy, we establish complete phase diagrams governed by competing interaction parameters. Our theory reveals distinct magnetic configurations including single-Q, double-Q, and triple-Q states, each characterized by unique symmetry-breaking patterns and collective excitations. The framework provides fundamental insights into complex magnetic orders recently observed in materials such as ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$, where the interplay between geometric frustration and multiple ordering vectors leads to exotic magnetic states. Our results establish clear connections between microscopic interactions, broken symmetries, and experimentally observable properties, offering a powerful tool for understanding and predicting novel magnetic phases in frustrated magnets.

Spin-crossover complexes exhibit two stable configurations with distinct spin states. The investigation of these molecules using low-temperature scanning tunneling microscopy has opened new perspectives for understanding the associated switching mechanisms at the single-molecule level. While the role of tunneling electrons in driving the spin-state switching has been clearly evidenced, the underlying microscopic mechanism is not completely understood. In this study, we investigate the electron-induced switching of $\left[\text{Fe}{\left({\text{H}}_2\text{B}\left(\text{pz}\right)\left(\text{pypz}\right)\right)}_2\right]$ (pz = pyrazole, pypz = pyridylpyrazole) adsorbed on Ag(111). The current time traces show transitions between two current levels corresponding to the two spin states. We extract switching rates from these traces by analyzing waiting-time distributions. Their sample-voltage dependence can be explained within a simple model in which the switching is triggered by a transient charging of the molecule. The comparison between experimental data and theoretical modeling provides estimates for the energies of the lowest unoccupied molecular orbitals, which were so far experimentally inaccessible. Overall, our approach offers new insights into the electron-induced switching mechanism and predicts enhanced switching rates upon electronic decoupling of the molecule from the metallic substrate, for example by introducing an ultrathin insulating layer.

We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are the particle-number covariance between spatially separated regions, $G_{AB}$, and the two-point density correlation function, $\mathcal{C}\left(r\right)$. Our results exhibit a remarkable analogy to Anderson localization, with $G_{AB}$ corresponding to two-terminal conductance and $\mathcal{C}\left(r\right)$ to two-point conductance, albeit with different replica limits and unconventional symmetry class, geometry, and boundary conditions. In the delocalized phase, $G_{AB}$ exhibits “universal,” nearly Gaussian, fluctuations with variance of order unity. In the localized phase, we find a broad distribution of $G_{AB}$ with $\overline{-ln{G}_{AB}}\sim L$ (where $L$ is the system size) and the variance $\mathrm{var}(ln{G}_{AB})\sim L^{\mu }$, and similarly for $\mathcal{C}\left(r\right)$, with $\mu \approx 0.5$. At the transition point, the distribution function of $G_{AB}$ becomes scale invariant and $\mathcal{C}\left(r\right)$ exhibits multifractal statistics, $\overline{{\mathcal{C}}^q\left(r\right)}\sim r^{-q(d+1)-{\mathrm{\Delta }}_q}$. We characterize the spectrum of multifractal dimensions ${\mathrm{\Delta }}_q$. Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.

Spin-boson models are simple examples of quantum dissipative systems, but also serve as effective models in quantum magnetism and exhibit nontrivial quantum criticality. Recently, they have been established as a platform to study the nontrivial renormalization-group (RG) scenario of fixed-point annihilation, in which two intermediate-coupling RG fixed points collide and generate an extremely slow RG flow near the collision. For the Bose Kondo model, a single $S=\frac{1}{2}$ spin where each spin component couples to an independent bosonic bath with power-law spectrum $\propto {\omega }^s$ via dissipation strengths ${\alpha }_i, i\in \{x,y,z\}$, such phenomena occur sequentially for the U(1)-symmetric model at ${\alpha }_z=0$ and the SU(2)-symmetric case at ${\alpha }_z={\alpha }_{xy}$, as the bath exponent $s<1$ is tuned. Here we use an exact wormhole quantum Monte Carlo method for retarded interactions to explore how this nontrivial fixed-point structure affects the phase diagram and phase transitions of the anisotropic spin-boson model. In particular, we show how fixed-point annihilation within a symmetry-enhanced critical manifold leads to a variety of anisotropy-driven critical phenomena: (i) a continuous order-to-order transition beyond the Landau paradigm, (ii) a symmetry-enhanced first-order transition, and (iii) pseudocriticality. Depending on whether the attractive fixed point within the critical manifold corresponds to a critical or a localized phase, the transition between the two long-range ordered localized phases can be tuned from continuous to strongly first order and even becomes weakly first order in an extended regime close to the fixed-point collision. We extract critical exponents at the continuous transition, but also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent $s$. Moreover, we provide direct numerical evidence for pseudocritical scaling on both sides of the fixed-point collision, which manifests in an extremely slow drift of the correlation-length exponent, even at the continuous transition. In addition, we also study the crossover behavior away from the SU(2)-symmetric case and determine the phase boundary of an extended U(1)-symmetric critical phase for ${\alpha }_z<{\alpha }_{xy}$. Our work establishes the spin-boson model as a paradigmatic example to access tunable criticality and pseudocriticality across the fixed-point collision in large-scale simulations, which is reminiscent of a scenario discussed in the context of deconfined criticality.

Controlling multiple wave properties simultaneously poses a key challenge in coherent control of wave transport. We present a theory for joint coherent control of transmission, reflection, and absorption in linear systems. We prove that the numerical range provides the mathematical structure governing achievable responses, and reveal non-Abelian effects due to noncommutativity between transmission, reflection, and absorption matrices. We provide an algorithm to achieve arbitrary target responses. Our results establish a theoretical foundation for joint coherent control of waves.

A field-induced quantum spin liquid (QSL) state is an extraordinary phenomenon, hitherto unobserved in metallic frustrated compounds. Recent bulk measurements have revealed intriguing field-induced magnetic states in metallic frustrated CePdAl. However, the nature of these field-induced states, potentially including a QSL state, remains unclear due to the lack of detailed microscopic investigation. To elucidate these field-induced states, we employed the transverse-field muon spin relaxation/rotation (TF-$\mu \mathrm{SR}$) technique, applying various magnetic fields parallel to the $c$-axis in single-crystalline CePdAl over a broad temperature range (100 K–100 mK). Our $\mu \mathrm{SR}$ data indicate that field-induced low-temperature states for fields $\mathrm{B}\le B_{c2}(=3.4T)$ exhibit long-range magnetic order, whereas for B > $B_{c2}$ they yield contrasting behavior. Notably, at 3.75 T, the transverse relaxation rate (${\lambda }_T$) diverges following a power-law dependence below 800 mK along with an indication of finite frustration whereas the Knight shift is temperature independent. These observations corroborate the signature of a critical spin liquid (CSL) with antiferromagnetic spin fluctuations. Furthermore, at 4.3 T, a non-Fermi liquid state is observed where frustration is absent. This comprehensive microscopic study strongly suggest the existence of a CSL state in a metallic frustrated system.

Complex chalcogenides in the $M{\mathrm{PS}}_3$ family of materials ($M=\mathrm{Mn}$, Fe, Co, and Ni) display remarkably different phase progressions depending upon the metal center orbital filling, character of the P–P linkage, and size of the van der Waals gap. There is also a stacking pattern and spin-state difference between the “lighter” and “heavier” transition-metal-containing systems that places ${\mathrm{CoPS}}_3$ at the nexus of these activities. Despite these unique properties, this compound is underexplored. Here, we bring together Raman scattering spectroscopy and infrared absorption spectroscopy with x-ray techniques to identify a structural component to the 119 K magnetic ordering transition. With temperature-dependent Raman scattering, we discover a set of magnon-phonon pairs that engages in avoided crossings below $T_{\text{Néel}}$. These findings point to strong spin-phonon entanglement as well as opportunities to control these effects under external stimuli.

We study the effect of noise on two-dimensional periodically driven topological phases, focusing on two examples: the anomalous Floquet-Anderson phase and the disordered Floquet-Chern phase. Both phases show an unexpected robustness against timing noise. The noise-induced decay of initially populated topological edge modes occurs in two stages: At short times, thermalization among edge modes leads to exponential decay. This is followed by slow algebraic decay $\sim n^{-1/2}$ with the number of Floquet cycles $n$. The exponent of $1/2$ is characteristic for one-dimensional diffusion, here occurring along the direction perpendicular to the edge. In contrast, localized modes in the bulk exhibit faster decay, $\sim n^{-1}$, corresponding to two-dimensional diffusion. We demonstrate these behaviors through full-scale numerical simulations and support our conclusions using analytical results based upon a phenomenological model. Our findings indicate that two-dimensional Floquet topological phases are ideal candidates for potential applications of Floquet topology, given the unavoidable presence of both quenched disorder and decoherence in experiments.

Abelian fractional Chern insulators have been previously investigated in hyperbolic kagome lattices with constant negative curvature, in which the geometric degree of freedom has been revealed. In this work, we study the $\nu =1$ non-Abelian fractional Chern insulator (FCI) with three-body hard-core bosons loaded into a topological flat band (TFB) model constructed in the hyperbolic analog of kagome lattice. Convincing numerical evidence is found for this non-Abelian FCI state, which is the Moore-Read-like ground state with clear edge excitation spectra. We also construct the trial wave function for this non-Abelian FCI based on the generalized Pauli principle, the Jack polynomials for the Moore-Read state, and single-particle states of the hyperbolic TFB model. A high value of overlap between the trial wave function and the exact diagonalization results demonstrates the existence of a hyperbolic non-Abelian FCI state. The inherent geometry of the hyperbolic non-Abelian FCI state is revealed as well.

Magnetic van der Waals materials are an important building block to realize spintronic functionalities in heterostructures of two-dimensional (2D) materials. However, establishing their magnetic and electronic properties and the interrelationship between the magnetic ground state and electronic structure is often challenging because only a limited number of techniques can probe magnetism and electronic structure on length scales of tens to hundreds of nanometers. Chromium chalcogenides are a class of 2D magnetic materials for which a rich interplay between structure and magnetism has been predicted. Here, we combine angle-resolved photoemission and quasiparticle interference imaging to establish the electronic structure of a monolayer of ${\mathrm{CrTe}}_2$ on graphite. From a comparison of model calculations with spectroscopic mapping using angle-resolved photoemission spectroscopy and scanning tunneling microscopy we establish the magnetic ground state and the low-energy electronic structure. We demonstrate that the band structure of monolayer ${\mathrm{CrTe}}_2$ is captured well by density functional theory (DFT) in a $\mathrm{DFT}+U$ framework when a Coulomb repulsion of $U=2.5\mathrm{eV}$ is accounted for.