The rigid-rotor with a q-deformed moment of inertia is introduced to describe the nuclear rotational spectra. With the representations of quantum algebra, the normal deformed and superdeformed bands are naturally differentiated by softness. The yrast normal deformed bands in rare earth and actinium regions, as well as the yrast superdeformed bands in A-190 and 150 regions are investigated. The calculated results agree with experimental data qualitatively well, and the values of the parameters are physically reasonable. This indicates that the fixed deformation, the stretching effect and the many body statistics effect are three possible dominant factors to govern nuclear rotational bands.

Research of infinite-layer nickelates has unveiled a broken translation symmetry, which has sparked significant interest in its root, its relationship to superconductivity, and its comparison to charge order in cuprates. In this study, resonant x-ray scattering measurements were performed on thin films of infinite-layer PrNiO$_{2+\delta}$. The results show significant differences in the superlattice reflection at the Ni $L_{3}$ absorption edge compared to that at the Pr $M_{5}$ resonance in their dependence on energy, temperature, and local symmetry. These differences point to two distinct charge orders, although they share the same in-plane wavevectors. It is suggested that these dissimilarities could be linked to the excess oxygen dopants, given that the resonant reflections were observed in an incompletely reduced PrNiO$_{2+\delta}$ film. Furthermore, azimuthal analysis indicates that the oxygen ligands likely play a crucial role in the charge modulation revealed at the Ni $L_{3}$ resonance.

Large longitudinal magnetoresistance (LMR) was observed in nonmagnetic silver telluride films. The magnitude of the LMR is not simply dependent on T and H, for example, multi-peaks of ρ at low field and low temperature appear in the Ag-Te film. Because both of -Δρ/ρ and a transition from -Δρ/ρ to +Δρ/ρ exist in Ag-Te films, the magnetoresistance (MR) behavior of the Ag-Te film does not like the bulk Ag-Te, but likes the doped semiconductors. About -27% of LMR was observed at low field in the Ag-Te films, while it could be negligible in the doped semiconductors. The MR behavior in Ag-Te films is discussed by means of a formation of impurity bands in the films.

Through empirical analysis of the global structure of the Worldwide Marine Transportation Network (WMTN), we find that the WMTN, a small-world network, exhibits an exponential-like degree distribution. We hereby investigate the efficiency of the WMTN by employing a simple definition. Compared with many other transportation networks, the WMTN possesses relatively low efficiency. Furthermore, by exploring the relationship between the topological structure and the container throughput, we find that strong correlations exist among the container throughout the degree and the clustering coefficient. Also, considering the navigational process that a ship travels in a real shipping line, we obtain that the weight of a seaport is proportional to the total probability contributed by all the passing shipping lines.

Discovery of the X(3872) meson in 2003 ignited intense interest in exotic (neither $q\bar{q}$ nor $qqq$) hadrons, but a $c\bar{c}$ interpretation of this state was difficult to exclude. An unequivocal exotic was discovered in the $Z_c(3900)^+$ meson—a charged charmonium-like state. A variety of models of exotic structure have been advanced but consensus is elusive. The grand lesson from heavy quarkonia was that heavy quarks bring clarity. Thus, the recently reported triplet of all-charm tetraquark candidates—$X(6600)$, $X(6900)$, and $X(7100)$—decaying to $J/\psi\,J/\psi$ is a great boon, promising important insights. We review some history of exotics, chronicle the road to prospective all-charm tetraquarks, discuss in some detail the divergent modeling of $J/\psi\,J/\psi$ structures, and offer some inferences about them. These states form a Regge trajectory and appear to be a family of radial excitations. A reported, but unexplained, threshold excess could hint at a fourth family member. We close with a brief look at a step beyond: all-bottom tetraquarks.

Topologically nontrivial Fe-based superconductors attract extensive attentions due to their ability of hosting Majorana zero modes (MZMs) which could be used for topological quantum computation. Topological defects such as vortex lines are required to generate MZMs. Here, we observe the robust edge states along the surface steps of CaKFe$_{4}$As$_{4}$. Remarkably, the tunneling spectra show a sharp zero-bias peak (ZBP) with multiple integer-quantized states at the step edge under zero magnetic field. We propose that the increasing hole doping around step edges may drive the local superconductivity into a state with possible spontaneous time-reversal symmetry breaking. Consequently, the ZBP can be interpreted as an MZM in an effective vortex in the superconducting topological surface state by proximity to the center of a tri-junction with different superconducting order parameters. Our results provide new insights into the interplay between topology and unconventional superconductivity, and pave a new path to generate MZMs without magnetic field.

Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical implications. This mini review provides a concise overview of recent developments in complexification, primarily covering finite temperature and equilibrium quantum phase transitions, as well as their connection with dynamical quantum phase transitions and non-Hermitian physics, with a particular focus on the significance of Fisher zeros. Starting from the newly discovered self-similarity phenomenon associated with complex partition functions, we further discuss research on self-similar systems briefly. Finally, we offer a perspective on these aspects.

Open quantum system simulations are essential for exploring novel quantum phenomena and evaluating noisy quantum circuits. In this Letter, we investigate whether mixed states generated from noisy quantum circuits can be efficiently represented by locally purified density operators (LPDOs). We map an LPDO of $N$ qubits to a pure state of size $2\times N$ defined on a ladder and introduce a unified method for managing virtual and Kraus bonds. We numerically simulate noisy random quantum circuits with depths of up to $d=40$ using fidelity and entanglement entropy as accuracy measures. The LPDO representation is effective in describing mixed states in both the quantum and classical regions; however, it encounters significant challenges at the quantum-classical critical point, restricting its applicability to the quantum region. In contrast, matrix product operators (MPO) successfully characterize the entanglement trend throughout the simulation, while the truncation in MPOs breaks the positivity condition required for a physical density matrix. This work advances our understanding of efficient mixed-state representations in open quantum systems and provides insights into the entanglement structure of noisy quantum circuits.

Layer-structured oxides Y_1−xBi_xBaCo₄O₇(0.00 ≤ x ≤ 0.05) were successfully synthesized and their structural and oxygen absorption properties were investigated by x−ray diffraction and thermogravimetry. Though Bi solubility was limited to about 5%, corresponding to Y_0.95Bi_0.05BaCo₄O₇, it is found that the structure and oxygen absorption properties of Y_1−xBi_xBaCo₄O₇ are affected significantly as the Bi content x increases. Rietveld refinement results show that Y_1−xBi_xBaCo₄O₇(x ≤ 0.05) is single phase with a hexagonal crystal structure (space group P6₃mc). Unit cell parameters and volume are changed and CoO₄ tetrahedra are distorted along the c−axis in Bi doped YBaCo₄O₇. The TG results show that Y_1−xBi_xBaCo₄O₇ undergoes two oxygen absorption processes in oxygen from room temperature to 1000°C and the maximum mass increase of the doped samples is less than that of YBaCo₄O₇. Bi doping effects on the structure and oxygen absorption properties are discussed on the basis of average radius and disorder of the Y site, the valence of Bi and the oxygen activation energy.

While density functional theory (DFT) serves as a prevalent computational approach in electronic structure calculations, its computational demands and scalability limitations persist. Recently, leveraging neural networks to parameterize the Kohn–Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations. Despite advancements, challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist. Addressing these hurdles, this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project. We demonstrate its generality in predicting electronic structures across the whole periodic table, including complex multi-elemental systems, solid-state electrolytes, Moiré twisted bilayer heterostructure, and metal-organic frameworks. Moreover, we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets, identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands. By offering a reliable efficient framework for computing electronic properties, this universal Hamiltonian model lays the groundwork for advancements in diverse fields, such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.

Two-dimensional (2D) materials have demonstrated promising prospects owing to their distinctive electronic properties and exceptional mechanical properties. Among them, 2D superconductors with $T_{\rm c}$ above the boiling point of liquid nitrogen (77 K) will exhibit tremendous applicable value in the future. Here, we design two 2D superconductors Na(BC)$_{2}$ and K(BC)$_{2}$ with MgB$_{2}$-like structures, which are theoretically predicted to host $T_{\rm c}$ as high as 99 and 102 K, respectively. The origin of such high $T_{\rm c}$ is ascribed to the presence of both $\sigma$-bonding bands and van Hove singularity at the Fermi level. Furthermore, $T_{\rm c}$ of Na(BC)$_{2}$ is boosted up to 153 K with a biaxial strain of 5%, which sets a new record among 2D superconductors. The predictions of Na(BC)$_{2}$ and K(BC)$_{2}$ open the door to explore 2D high-temperature superconductors and provide a potential future for developing new applications in 2D materials.

Perovskite-structured nickelates, ReNiO$_{3}$ (Re = rare earth), have long garnered significant research interest due to their sharp and highly tunable metal-insulator transitions (MITs). Doping the parent compound ReNiO$_{3}$ with alkaline earth metal can substantially suppress this MIT. Recently, intriguing superconductivity has been discovered in doped infinite-layer nickelates (ReNiO$_{2})$, while the mechanism behind A-site doping-suppressed MIT in the parent compound ReNiO$_{3}$ remains unclear. To address this problem, we grew a series of Nd$_{1-x}$Sr$_{x}$NiO$_{3}$ (NSNO, $x =0$–0.2) thin films and conducted systematic electrical transport measurements. Our resistivity and Hall measurements suggest that Sr-induced excessive holes are not the primary reason for MIT suppression. Instead, first-principles calculations indicate that Sr cations, with larger ionic radius, suppress breathing mode distortions and promote charge transfer between oxygen and Ni cations. This process weakens Ni–O bond disproportionation and Ni$^{2+}$/Ni$^{4+}$ charge disproportionation. Such significant modulations in lattice and electronic structures convert the ground state from a charge-disproportionated antiferromagnetic insulator to a paramagnetic metal, thereby suppressing the MIT. This scenario is further supported by the weakened MIT observed in the tensile-strained NSNO/SrTiO$_3$(001) films. Our work reveals the A-side doping-modulated electrical transport of perovskite nickelate films, providing deeper insights into novel electric phases in these strongly correlated nickelate systems.

The rare-earth chalcogenide $ARECh_{2}$ family ($A$ = alkali metal or monovalent ions, $RE$ = rare earth, $Ch$ = chalcogen) has emerged as a paradigmatic platform for studying frustrated magnetism on a triangular lattice. The family members exhibit a variety of ground states, from quantum spin liquid to exotic ordered phases, providing fascinating insight into quantum magnetism. Their simple crystal structure and chemical tunability enable systematic exploration of competing interactions in quantum magnets. Recent neutron scattering and thermodynamic studies have revealed rich phase diagrams and unusual excitations, refining theoretical models of frustrated systems. This review provides a succinct introduction to $ARECh_{2}$ research. It summarizes key findings on crystal structures, single-ion physics, magnetic Hamiltonians, ground states, and low-energy excitations. By highlighting current developments and open questions, we aim to catalyze further exploration and deeper physical understanding on this frontier of quantum magnetism.

The rapid developments of quantum information science (QIS) have opened up new avenues for exploring fundamental physics. Quantum nonlocality, a key aspect for distinguishing quantum information from classical one, has undergone extensive examinations in particles' decays through the violation of Bell-type inequalities. Despite these advancements, a comprehensive framework based on quantum information theory for particle interaction is still lacking. Trying to close this gap, we introduce a generalized quantum measurement description for decay processes of spin-1/2 hyperons. We validate this approach by aligning it with established theoretical calculations and apply it to the joint decay of $\varLambda\bar{\varLambda}$ pairs. We employ quantum simulation to observe the violation of Clauser–Horne–Shimony–Holt inequalities in $\eta_{c}/\chi_{c0} \to \varLambda\bar{\varLambda}$ processes. Our generalized measurement description is adaptable and can be extended to a variety of high energy processes, including decays of vector mesons, $J/\psi,\,\psi(2S)\rightarrow\varLambda\bar{\varLambda}$, in the Beijing Spectrometer III (BESIII) experiment at the Beijing Electron Positron Collider (BEPC). The methodology developed in this study can be applied to quantum correlation and information processing in fundamental interactions.

High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in the temporal domain enables the production of the single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in the spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography, and microscopy. However, the active control of second-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of second-order spatial quantum coherence, which exhibits the capability of switching between bunching and anti-bunching, by mapping the entanglement of spatially structured photons. We also show that signal processing based on quantum coherence exhibits robust resistance to intensity disturbance. Our findings not only enhance existing applications but also pave the way for broader utilization of higher-order spatial quantum coherence.

It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average `density' <ρ(r)> of complex networks follows a better power-law function as a function of distance r with the exponent d_f, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between d_f and the shortcuts N_add in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension d_f on the complex network structure.

Superconducting materials hold great potential in high field magnetic applications compared to traditional conductive materials. At present, practical superconducting materials include low-temperature superconductors such as NbTi and Nb$_{3}$Sn, high-temperature superconductors such as Bi-2212, Bi-2223, YBCO, iron-based superconductors and MgB$_{2}$. The development of low-temperature superconducting wires started earlier and has now entered the stage of industrialized production, showing obvious advantages in mechanical properties and cost under low temperature and middle-low magnetic field. However, due to the insufficient intrinsic superconducting performance, low-temperature superconductors are unable to exhibit excellent performance at high temperature or high fields. Further improvement of supercurrent carrying performance mainly depends on the enhancement of pinning ability. High-temperature superconductors have greater advantages in high temperature and high field, but many of them are still in the stage of further performance improvement. Many high-temperature superconductors are limited by the deficiency in their polycrystalline structure, and further optimization of intergranular connectivity is required. In addition, it is also necessary to further enhance their pinning ability. The numerous successful application instances of high-temperature superconducting wires and tapes also prove their tremendous potential in electric power applications.

Quantum technology establishes a foundation for secure communication via quantum key distribution (QKD). In the last two decades, the rapid development of QKD makes a global quantum communication network feasible. In order to construct this network, it is economical to consider small-sized and low-cost QKD payloads, which can be assembled on satellites with different sizes, such as space stations. Here we report an experimental demonstration of space-to-ground QKD using a small-sized payload, from Tiangong-2 space lab to Nanshan ground station. The 57.9-kg payload integrates a tracking system, a QKD transmitter along with modules for synchronization, and a laser communication transmitter. In the space lab, a 50 MHz vacuum + weak decoy-state optical source is sent through a reflective telescope with an aperture of 200 mm. On the ground station, a telescope with an aperture of 1200 mm collects the signal photons. A stable and high-transmittance communication channel is set up with a high-precision bidirectional tracking system, a polarization compensation module, and a synchronization system. When the quantum link is successfully established, we obtain a key rate over 100 bps with a communication distance up to 719 km. Together with our recent development of QKD in daylight, the present demonstration paves the way towards a practical satellite-constellation-based global quantum secure network with small-sized QKD payloads.

The chiral $2\times 2$ charge order has been reported and confirmed in the kagome superconductor RbV$_{3}$Sb$_{5}$, while its interplay with superconductivity remains elusive owing to its lowest superconducting transition temperature $T_{\scriptscriptstyle{\rm C}}$ of about 0.85 K in the AV$_{3}$Sb$_{5}$ family (A = K, Rb, Cs) that severely challenges electronic spectroscopic probes. Here, utilizing dilution-refrigerator-based scanning tunneling microscopy down to 30 mK, we observe chiral $2\times 2$ pair density waves with residual Fermi arcs in RbV$_{3}$Sb$_{5}$. We find a superconducting gap of 150 µeV with substantial residual in-gap states. The spatial distribution of this gap exhibits chiral $2\times 2$ modulations, signaling a chiral pair density wave (PDW). Our quasi-particle interference imaging of the zero-energy residual states further reveals arc-like patterns. We discuss the relation of the gap modulations with the residual Fermi arcs under the space-momentum correspondence between PDW and Bogoliubov Fermi states.

Phase transitions and critical phenomena are among the most intriguing phenomena in nature and society. They are classified into first-order phase transitions (FOPTs) and continuous ones. While the latter shows marvelous phenomena of scaling and universality, whether the former behaves similarly is a long-standing controversial issue. Here we definitely demonstrate complete universal scaling in field driven FOPTs for Langevin equations in both zero and two spatial dimensions by rescaling all parameters and subtracting nonuniversal contributions with singular dimensions from an effective temperature and a special field according to an effective theory. This offers a perspective different from the usual nucleation and growth but conforming to continuous phase transitions to study FOPTs.

We propose a simple quantum voting machine using microwave photon qubit encoding, based on a setup comprising multiple microwave cavities and a coupled superconducting flux qutrit. This approach primarily relies on a multi-control single-target quantum phase gate. The scheme offers operational simplicity, requiring only a single step, while ensuring verifiability through the measurement of a single qubit phase information to obtain the voting results. It provides voter anonymity, as the voting outcome is solely tied to the total number of affirmative votes. Our quantum voting machine also has scalability in terms of the number of voters. Additionally, the physical realization of the quantum voting machine is general and not limited to circuit quantum electrodynamics. Quantum voting machine can be implemented as long as the multi-control single-phase quantum phase gate is realized in other physical systems. Numerical simulations indicate the feasibility of this quantum voting machine within the current quantum technology.

Twisted bilayer graphene (TBG), which has drawn much attention in recent years, arises from van der Waals materials gathering each component together via van der Waals force. It is composed of two sheets of graphene rotated relatively to each other. Moiré potential, resulting from misorientation between layers, plays an essential role in determining the band structure of TBG, which directly relies on the twist angle. Once the twist angle approaches a certain critical value, flat bands will show up, indicating the suppression of kinetic energy, which significantly enhances the importance of Coulomb interaction between electrons. As a result, correlated states like correlated insulators emerge from TBG. Surprisingly, superconductivity in TBG is also reported in many experiments, which drags researchers into thinking about the underlying mechanism. Recently, the interest in the atomic reconstruction of TBG at small twist angles comes up and reinforces further understandings of properties of TBG. In addition, twisted multilayer graphene receives more and more attention, as they could likely outperform TBG although they are more difficult to handle experimentally. In this review, we mainly introduce theoretical and experimental progress on TBG. Besides the basic knowledge of TBG, we emphasize the essential role of atomic reconstruction in both experimental and theoretical investigations. The consideration of atomic reconstruction in small-twist situations can provide us with another aspect to have an insight into physical mechanism in TBG. In addition, we cover the recent hot topic, twisted multilayer graphene. While the bilayer situation can be relatively easy to resolve, multilayer situations can be really complicated, which could foster more unique and novel properties. Therefore, in the end of the review, we look forward to future development of twisted multilayer graphene.

The performance of the oxide-confined surface-relief (SR) structure vertical-cavity surface-emitting laser (VCSEL) is simulated and analyzed by using the three-dimensional finite-difference time-domain (FDTD) method. The impacts of the device structure parameters on the far-field characteristics are researched. A single-fundamental-mode SR VCSEL with an oxide-aperture of 15 μm is designed and produced. The single-mode power of the VCSEL is 5 mW, the threshold current is 2.5 mA, far-field divergent angles range from 7.8° to 10.8° and the side-mode suppression ratio is over 30 dB. The optical and electrical properties of the device are in agreement with the results of FDTD simulation, which shows that the SR technology can effectively suppress the higher-order-mode lasing, and make the SR VCSEL work in a single mode under a larger oxide aperture.

If quantum bits (qubits) couple to the Same environment, it has been found the qubits decohere coherently. An interesting result from this phenomenon is that, for a kind of input states, i. e., the coherence-preserving states, coherence of the qubits can be preserved perfectly in quantum memory. In this paper, we propose a feasible scheme to transform an arbitrary unknown input state to the corresponding coherence-preserving state. The transformed state undergoes no decoherence in the noisy memory and, after that, it can be transformed back into the original state with decoherence much reduced. This scheme involves the use of an analogy of the ideas of quantum teleportation.

The interaction between lasers and nanoparticles holds significant theoretical and practical importance. Here, we investigate the near-field enhancement effects on silver nanotriangles and nanodiscs under ultrafast laser pulses, as well as the dynamics of protons and ions attached to the nanoparticle surfaces. By adjusting the size parameters of the nanoparticles, we explore the near-field enhancement effects and proton emission dynamics at different laser wavelengths. The results demonstrate that nanoparticles with varying morphologies substantially impact the proton momentum spectrum. The directional proton emission of nanotriangle structures is more pronounced compared to that of nanodiscs, and this effect can be further enhanced by adjusting the laser wavelength. Additionally, manipulating the thickness of particles also controls the Mie scattering phenomenon of light. Finally, we qualitatively discuss the emission processes of alpha particles and $^{9}$C$^{6+}$ heavy ions. This research has important implications for proton and heavy ion radiotherapy in cancer treatment and targeted drug delivery, while providing theoretical foundations for understanding, characterizing, and controlling experimental studies of nanosystems with significant potential for expanding research into microdynamic behavior in complex nanomaterial superstructures.

Near-ultraviolet (UV) InGaN/AlGaN light-emitting diodes (LEDs) are grown by low-pressure metal-organic chemical vapor deposition. The scanning electronic microscope image shows that the p-GaN micro-rods are formed above the interface of p-AlGaN/p-GaN due to the rapid growth rate of p-GaN in the vertical direction. The p-GaN micro-rods greatly increase the escape probability of photons inside the LED structure. Electroluminescence intensities of the 372 nm UV LED lamps with p-GaN micro rods are 88% higher than those of the flat surface LED samples.

For designing low-impedance magnetic tunnel junctions (MTJs), it has been found that tunneling magnetoresistance strongly correlates with the insulating barrier thickness, imposing a fundamental problem about the relationship between spin polarization of ferromagnet and the insulating barrier thickness in MTJs. Here, we investigate the influence of alumina barrier thickness on tunneling spin polarization (TSP) through a combination of theoretical calculations and experimental verification. Our simulating results reveal a significant impact of barrier thickness on TSP, exhibiting an oscillating decay of TSP with the barrier layer thinning. Experimental verification is realized on FeNi/AlO$_x$/Al superconducting tunnel junctions to directly probe the spin polarization of FeNi ferromagnet using Zeeman-split tunneling spectroscopy technique. These findings provide valuable insights for designs of high-performance spintronic devices, particularly in applications such as magnetic random access memories, where precise control over the insulating barrier layer is crucial.

The results of particle-in-cell (PIC) simulations are presented on the evolution of the electron whistler waves during the collisionless magnetic reconnection. The simulation results show that the electron whistler waves with frequency higher than the lower hybrid frequency are found to occur in the electrons outflow region. Moreover, the present results indicate that these electron whistler waves with high-frequency in the region greater than an ion inertial scale of the x-line are irrelevant to the fast reconnection, but are generated as a result of the reconnection processes.

Doped HfO$_{2}$-based ferroelectric (FE) films are emerging as leading contenders for next-generation FE non-volatile memories due to their excellent compatibility with complementary metal oxide semiconductor processes and robust ferroelectricity at nanoscale dimensions. Despite the considerable attention paid to the FE properties of HfO$_{2}$-based films in recent years, enhancing their polarization switching speed remains a critical research challenge. We demonstrate the strong ferroelectricity of sub-10 nm Hf$_{0.5}$Zr$_{0.5}$O$_{2}$ (HZO) thin films and show that the polarization switching speed of these thin films can be significantly affected by HZO thickness and anisotropically strained La$_{0.67}$Sr$_{0.33}$MO$_{3}$-buffered layer. Our observations indicate that the HZO thin film thickness and anisotropically strained La$_{0.67}$Sr$_{0.33}$MO$_{3}$ layer influence the nucleation of reverse domains by altering the phase composition of the HZO thin film, thereby reducing the polarization switching time. Although the increase in HZO thickness and anisotropic compressive strain hinder the formation of the FE phase, they can enable faster switching. Our findings suggest that FE HZO ultrathin films with polar orthorhombic structures have broad application prospects in microelectronic devices. These insights into novel methods for increasing polarization switching speed are poised to advance the development of high-performance FE devices.