The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by local, few-body terms. Unfortunately, in nonequilibrium situations, analytic results are rare and largely confined to continuous field theories, which fail to accurately describe microscopic models. To address this gap, we present an analytic result for the EH following a quantum quench in noninteracting fermionic models, valid in the ballistic scaling regime. The derivation adapts the celebrated quasiparticle picture to operators, providing detailed insights into its physical properties. The resulting analytic formula serves as a foundation for engineering EHs in quantum optics experiments.

Non-Hermitian systems and their topological singularities, such as exceptional points (EPs), lines, and surfaces, have recently attracted intense interest. The investigation of these exceptional constituents has led to fruitful applications. The responsivity of the eigenvalue diverges at EPs, and chiral state transfer occurs when encircling an EP. Traditionally, it was believed that these exceptional features were unique to non-Hermitian systems requiring gain, loss, or nonreciprocal hopping. Here we show that these exceptional features are also present in nonlinear Hermitian systems. We consider two coupled resonators with Kerr nonlinearity in one resonator, and no non-Hermitian terms. We identify EP-like points (ELPs) on the eigenspectra where the critical behaviors are the same as those of typical EPs. Additionally, this nonlinear Hermitian system can be mapped to linear non-Hermitian systems, with ELPs corresponding to EPs. We also demonstrate that encirclement around an ELP in the parameter space leads to unique chiral state transfer behavior.

Recent experimental work indicates that the Kitaev spin liquid may be realizable close to zero magnetic field in exfoliated $\alpha \text{−}{\mathrm{RuCl}}_3$ flakes, thus providing a more versatile setting for studying non-Abelian anyons. Here, we propose a robust nanoscale signature of the Kitaev spin liquid that results from its edge states and manifests in the low-energy spin dynamics. In particular, we highlight a singular peak in the dynamical spin structure factor of a zigzag edge whose energy scales linearly with only one component of the magnetic field. This sharp feature in the local spin dynamics directly reflects the bond-directional Kitaev spin interactions and, more generally, the projective symmetries of the Kitaev spin liquid. We demonstrate that our proposed signature survives in the presence of edge disorder as well as non-Kitaev interactions, and provide detailed guidelines for experimentally observing it using inelastic electron tunneling spectroscopy and color-center relaxometry.

Bound states in the continuum (BICs) are radiation-free states whose energy is embedded in the continuum spectrum of the radiating modes. In general, BICs in periodic structures appear at isolated points in momentum space, whereas BICs forming a line require radiative continuum designs. Here, we demonstrate theoretically and experimentally that BICs can form continuous lines in a simple phononic crystal slab without special radiative continuums. Contrary to common sense, these BICs are symmetry-protected BICs not only at the center of the Brillouin zone ($\mathrm{\Gamma }$ point) but also along high-symmetry directions of momentum space. We utilize numerical simulations, a group theory method, and a mode expansion method to comprehensively understand the formation of the BICs. The BICs lines are observed experimentally by measuring the transmittance of the phononic crystal slab. Moreover, it is revealed that the BICs lines correspond to phase singularity lines of far-field radiation, and the phase winding number can be defined as a topological index. Our findings have the potential to improve multifrequency and multiwave-vector performance for applications such as high-intensity sound sources, filters, and sensors.

Metastable phases can lead to multistep nucleation processes, influencing the liquid-to-solid transition in various systems. In this study, we investigate the homogeneous nucleation of iron's crystalline phases under Earth's inner core conditions, employing two previously developed interatomic potentials. We compare the thermodynamic and kinetic properties of iron relevant to the nucleation as predicted by these potentials. While the potentials differ in their predictions of melting temperature by a few hundred Kelvin, they show a consistent description of the relative Gibbs free energy between solid and liquid phases with respect to the undercooling. Both potentials also predict that the metastable bcc phase exhibits a significantly higher nucleation rate than the hcp phase over a wide range of undercooling temperatures below the melting point. This substantially lowers the undercooling thresholds required for the initial nucleation of Earth's inner core. The results validate the commonality of the two-step nucleation mechanism of iron under Earth's inner core conditions for two different potentials, providing a foundation for future studies about the influence of other elements on the nucleation of Earth's core.

We investigate the pressure-temperature $\left(p\text{−}T\right)$ phase diagram of elemental lithium (Li) up to multiterapascal (TPa) pressures using ab initio random structure search (AIRSS) and density functional theory (DFT). At zero temperature, beyond the high-pressure $Fd\overline{3}m$ diamond structure already predicted in previous studies, we find 11 solid-state phase transitions to structures of greatly varying complexity. The full $p\text{−}T$ dependence of the phase boundaries are computed within the vibrational quasi-harmonic approximation (QHA), and the solid-liquid melting line is calculated using two different ab initio molecular dynamics simulation methods (heat-until-melt and the Z method). Notably, between 39.1 and 55.7 TPa, Li adopts an elaborate monoclinic structure with 46 atoms in the primitive unit cell, and between 71.9 and 103 TPa, an incommensurate host-guest phase of the Ba-IV type. We find that Li, hitherto predicted to be an electride at TPa pressures, abruptly loses its electride character above 16 TPa, reverting back to normal metallic behavior with a corresponding rise in the Fermi-level electronic density of states (eDOS) and broadening of the electronic bands.

We report a study of a disorder-dependent real-space representation of the quantum geometry in topological systems. Thanks to the development of an efficient linear-scaling numerical methodology based on the kernel polynomial method, we can explore nontrivial behavior of the integrated quantum metric and Chern number in disordered systems with sizes reaching the experimental scale. We illustrate this approach in the disordered Haldane model, examining the impact of Anderson disorder and vacancies on the trivial and topological phases captured by this model.

Modeling the heat capacity of liquids presents fundamental difficulties due to the strong intermolecular particle interactions and large diffusivelike displacements. Based on the experimental evidence that the microscopic dynamics of liquids closely resemble those of solids, a phonon theory of liquid thermodynamics has been developed. Despite its success, the phonon theory of liquids relies on the questionable assumption that low-frequency shear excitations are propagating in nature and follow a Debye density of states. Furthermore, the same framework does not capture the contribution of intramolecular vibrations, which play a significant role in molecular liquids. In this work, we revisit the phonon theory of liquid heat capacity, introducing alternative approaches to model low-frequency shear modes. In particular, we consider the recently proposed idea of treating such modes as purely kinetic, and we propose an approach based on identifying those low-frequency excitations as overdamped liquidlike modes with a linear in frequency density of states. Moreover, we complete the theory by incorporating the effects of intramolecular vibrations. By comparing the theoretical predictions from these different approaches with the available data for the heat capacity of several liquids, we present a comprehensive evaluation of the original model and our proposed extensions. Although all approaches perform well at low temperatures, our results indicate that modeling low-frequency modes as overdamped liquidlike excitations yields the most accurate agreement with the data in the whole temperature range. Conversely, we demonstrate that treating these excitations as purely gaslike leads to significant inaccuracies, particularly at high temperatures.

Exchange bias, as one of the core working principles of spintronics, is widely used in the development of high-sensitivity, high-stability, and high-density spintronic devices. As an essential phenomenon in exchange-biased systems, asymmetric magnetization reversal has been extensively studied in antiferromagnetic/ferromagnetic systems. However, this phenomenon has not yet received an adequate theoretical explanation in hard magnetic (HM)/soft magnetic (SM) systems. This work uses micromagnetic simulations to investigate the exchange bias and asymmetric magnetization reversal in the FeCo layer of $L{1}_0$ FePt (HM)/FeCo (SM) bilayer thin film with in-plane anisotropy. It is found that different thicknesses of the FeCo layer and varying angles between the applied magnetic field (${\mathit{H}}_{\mathrm{appl}}$) and the magnetic easy-axis direction can change the magnetization reversal mechanism of the FeCo layer, thereby influencing the exchange bias and the asymmetry of magnetization reversal. An asymmetry in the hysteresis loop is observed when ${\mathit{H}}_{\mathrm{appl}}$ is in the angular range near the direction of the easy axis, and the increase of the FeCo layer thickness expands the angular range in which asymmetry occurs. The interaction between uniaxial anisotropy and unidirectional anisotropy influences the magnetization reversal, causing one branch of the hysteresis loop to be dominated by coherent rotation of the magnetic moments. In contrast, the main magnetization reversal mechanism of the other branch is the nucleation of magnetic domains and further propagation of magnetic domain walls, thus forming an asymmetric hysteresis loop. The exchange bias and asymmetry of magnetization reversal can be controlled by changing the FeCo layer thickness and the angle between ${\mathit{H}}_{\mathrm{appl}}$ and the easy axis. These understandings will provide additional ideas for research on magnetic devices.

High-pressure studies have revealed superconductivity in ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$, sparking interest in its ambient-pressure properties and the underlying electronic correlations. Motivated by experimental observations of an incommensurate spin-density wave (SDW) at ambient pressure, we investigate the SDW characteristics and possible superconductivity in ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ using a multiorbital random-phase approximation (RPA). Starting with a 12-orbital tight-binding model derived from density functional theory (DFT) calculations, we include Hubbard interactions to explore the interplay between electronic correlations and magnetic instabilities. Our analysis reveals a stripe-like SDW with a wave vector $\mathbf{Q}\approx (\pm 0.7\pi ,0)$, suggesting a possible density wave instability in agreement with experiments. This configuration is driven by nesting between the ${\alpha }_1$ pocket, primarily contributed by the outer-layer Ni $d_{z^2}$ orbitals, and the ${\beta }_1$ pocket, contributed by both the $d_{z^2}$ and $d_{x^2-y^2}$ orbitals of the outer layer. It exhibits interlayer antiferromagnetic ordering between the top and bottom NiO layers, with the magnetic moment of the middle layer being nearly zero. We demonstrate that the Hund coupling $J_H$ is the primary driver of the observed SDW and determine the specific criterion: $J_H>0.16U$. Building upon our findings on the SDW mechanism, we further demonstrate that hole doping ($\delta =-0.4$) enhances Fermi surface nesting, leading to the emergence of a superconducting state with a gap structure similar to that of the high-pressure phase.

By measuring magnetization hysteresis loops of the superconducting ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$ single crystals ($T_{\mathrm{c}}=133$ K), we observed three magnetization peaks in a wide temperature region. This is in contrast to the previous observation that there are only two magnetization peaks in many superconductors. A detailed analysis finds that the second peak here evolves from a kinky structure at low temperatures and gets enhanced at high temperatures; the third peak evolves from a general broad peak at low temperatures and evolves into a sharp peak and even a steplike one at high temperatures. We propose a general phase diagram to interpret these peaks, where the second peak is corresponding to the order-disorder transition, while the third peak is associated with the elastic-plastic crossover. Our work unifies the understanding of different “second peak” structures in different systems and thus sheds light in understanding the vortex dynamics in type-II superconductors.

We explore the ground-state properties of a one-dimensional model with two orbitals per site, where, in addition to atomic energies $\pm M$ and intra- and interorbital hoppings, the intraorbital Hubbard $\left(U\right)$ and nearest-neighbor density-density $\left(V\right)$ repulsions are included. Our results are primarily based on a Jastrow-Slater wave function and variational Monte Carlo methods but also corroborated by density-matrix renormalization group calculations. In the noninteracting limit, when varying $M>0$, a gapless point separates a trivial phase from a topological one. The inclusion of a finite Hubbard-$U$ repulsion does not give rise to any phase transition within the topological region, inducing a smooth crossover into a Haldane (spin gapped) insulator; notably, the string-order parameter, which characterizes the latter phase, is already finite in the noninteracting limit. Most importantly, at finite values of $U$, the transition between the trivial and topological states is not direct, since an emergent insulator, which shows evidence of sustaining gapless spin excitations, intrudes between them. A small-$V$ interaction further stabilizes the intermediate insulator, while a sufficiently large value of this nearest-neighbor repulsion gives rise to two different charge-density wave insulators, one fully gapped and another still supporting gapless spin excitations. Our results demonstrate the richness of multiorbital Hubbard models, in the presence of a topologically nontrivial band structure, and serve as a basis for future investigations on similar two-dimensional models.

We study a certain type of anomalous Hall current in magnetically and electrically biased bulk GaAs samples under the formation of Landau levels. The currents are generated by ultrafast optical excitation of spin-polarized carriers and detected by time-resolved measurements of the simultaneously emitted terahertz (THz) radiation. Due to the requirements of simultaneous magnetic and electric driving fields we refer to these currents as magnetic- and electric-field-induced anomalous Hall currents (BE-AHC). We find that the BE-AHC peaks for optical transitions between the band extrema of Landau levels of valence and conduction bands. These discrete features are attributed to the energy dependence of the geometric phases being responsible for anomalous transport effects in a semiconductor band structure. Surprisingly, we even detect the discrete Landau band transitions at room temperature, most likely due to the ultrafast local probing realized in our experiment. An analysis of the THz spectra using a model, based on the Boltzmann transport equation of optically excited carriers, shows that electron and hole contributions lead to complex current dynamics. While the cyclotronic motion of electrons results in a dip in the THz spectral response of BE-AHC, it causes a peak in the spectral response of normal Hall currents. Additionally, our experimental results strongly suggest that the Landau levels of the valence band play a significant role in the generation of BE-AHC. We expect that our results will initiate further studies on Berry-phase effects in Landau bands.

Two-dimensional hole gases (2DHGs) have strong intrinsic spin-orbit coupling and could be used to build spin filters by utilizing transverse magnetic focusing (TMF). However, with an increase in the spin degree of freedom, holes demonstrate significantly different behavior to electrons in TMF experiments, making it difficult to interpret the results of these experiments. In this paper, we numerically model TMF in a 2DHG within a $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructure. Our band structure calculations show that the heavy $(\langle J_z\rangle =\pm 3/2)$ and light $(\langle J_z\rangle =\pm 1/2)$ hole states in the valence band mix at finite $k$, and the heavy-hole subbands which are spin-split due to the Rashba effect are not spin-polarized. This lack of spin polarization casts doubt on the viability of spin filtering using TMF in 2DHGs within conventional $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures. We then calculate the transport properties of the 2DHG with spin projection and offer a different perspective on interpreting and designing TMF experiments in 2DHGs.

Hole spin qubits in Ge, investigated for all-electrical spin manipulation because of their large spin-orbit coupling, are exposed to charge noise, leading to decoherence. Here, we employ a model of $1/f$ noise due to individual fluctuators and determine the dephasing time $T_2^{*}$ as a function of qubit properties. $T_2^{*}$ decreases with increasing magnetic field and is an order of magnitude longer for out-of-plane fields than for in-plane fields for the same Zeeman energy. $T_2^{*}$ shows little variation as a function of the top gate field and is a complex function of the dot radius. Our results should help experiments enhance coherence in hole qubit architectures.

The nonlinear Hall effect (NLHE) characterized by the currents occurring in high-order response to external electric field holds great promise for advancements in spintronics, quantum computing, and advanced electronic devices. In systems with time-reversal symmetry, the nonvanishing Berry curvature dipole (BCD) in momentum space, is crucial for the manifestation of NLHE. However, the practical application of NLHE has been hindered by the typically low BCD value $(\sim {10}^{-2}\text{−}{10}^0\AA )$ and the intricate regulation requirement. In this study, we present an innovative all-electric approach to significantly enhance the BCD in two-dimensional materials. Using monolayer ${\mathrm{MoS}}_2$ as a model system, we demonstrate that the application of a one-dimensional periodic electric potential can efficiently modulate the BCD, achieving a giant value of ∼800 Å, which is about 2–4 orders of magnitude greater than those predicted in conventional materials. Furthermore, we show that the BCD can be finely tuned by adjusting the amplitude and gradient of the electric potential, the orientation of periodicity, and the warping effects within the system. Our findings pave the way for the development of sensors and memory devices that leverage the nonlinear response for enhanced performance.

Recently, the synthesis of a ${\mathrm{NbOCl}}_2$ monolayer has been reported, revealing notable anisotropic properties and linear dichroism [Guo et al., Nature (London) 613, 53 (2023)]. Inspired by this progress, we have engineered a Janus NbOClI monolayer by breaking the out-of-plane spatial inversion symmetry in ${\mathrm{NbOCl}}_2$. Through rigorous first-principles calculations, we present a detailed and comprehensive investigation of its mechanical and optical characteristics. We find that it exhibits a substantial out-of-plane piezoelectric response ($d_{31}=0.87$ pm/V), driven by atomic electronegativity differences and Peierls distortion. The intrinsic electric field within NbOClI enables robust photocatalytic water-splitting capabilities across a broad pH spectrum, independent of external strain. Capitalizing on its pronounced linear dichroism, we construct a polarization-sensitive photodetector that leverages the photogalvanic effect to produce an anisotropic, self-powered photocurrent. Notably, this photocurrent is significantly amplified by a strain gradient, achieving self-rectification via the synergistic coupling of flexoelectric and piezoelectric fields. Building upon these achievements, a proof-of-concept three-channel optical communication scheme is shown to amplify the output efficiency of binary signals by an additional $50\%$. Our results present a fascinating functional coupling architecture that simultaneously enables excellent force-electric conversion, efficient photocatalytic water splitting, polarization-sensitive self-powered photodetection, and multichannel optical communication in Janus NbOClI-based optoelectronic devices. This brings us closer to realizing the next generation of chip-scale integrated optoelectronics.