arXiv subjects
Publications and source records attributed to Li Lei.
We investigate Chern's conjecture for minimal submanifolds of higher codimension in the unit sphere. We establish two integral inequalities for closed minimal submanifolds. Then we obtain a new rigidity theorem under a pinching condition on the squared norm of the second fundamental form.
Magnetism, a fundamental property of solids arising from the collective alignment of electronic spins of magnetic atoms, has recently been expanded by the discovery of altermagnetism, a symmetry-driven phase distinct from both ferromagnetism and antiferromagnetism. Initial efforts to emulate altermagnetism in photonic systems are also being pursued, primarily through the magneto-optic response of materials; however, their intrinsic frequency limitations pose challenges for extending photonic altermagnetism into the optical regime, thereby restricting their material choices and optical applications. Here, we establish a microscopic framework of photonic magnetism through group theory symmetry analysis, defining photonic counterparts of electron spin and magnetic atoms. This approach enables the realization of photonic ferromagnetic, antiferromagnetic, and altermagnetic phases within structured optical lattices constructed by purely dielectric, nonmagnetic materials, which not only broadens the photonic magnetism concept, but also lifts the material and frequency limitations. Analytical models, numerical simulations, and experimental measurements reveal spin-momentum locking directly corresponding to their electronic analogs, showing d-, g-, and i-wave circular dichroism (CD) splitting bands at telecom wavelengths (around 1550 nm). These results demonstrate that altermagnetic order, and magnetism more broadly, can be reconstructed in photonic systems through symmetry and mode coupling alone, opening a new route towards spin-dependent light control and bosonic analogs of quantum magnetic phenomena in dielectric photonic crystals.
LLMs increasingly require surgical model editing to enhance domain-specific capabilities without incurring the computational cost or catastrophic forgetting associated with full fine-tuning. Sparse Autoencoders (SAEs) have emerged as a promising tool in this setting, in principle allowing for feature-level identification of where to intervene. In this work, we rigorously evaluate an SAE-guided editing pipeline for mathematical reasoning on Gemma-3-4B-IT and uncover a fundamental failure mode: the intuitively appealing approach of projecting task vectors onto SAE feature subspaces acts as an information bottleneck that discards approximately 97% of the modification energy, yielding no statistically significant improvements across seven math subjects. We show that this failure stems from a geometric misalignment between activation-space SAE directions and weight-space task vectors. We then propose a shift in perspective: SAE as a Stethoscope, Not a Scalpel, where SAEs are used for layer-level diagnosis rather than intervention-level filtering. By injecting unfiltered raw task vectors only into layers identified by an SAE-derived specificity score, we improve Number Theory accuracy from 29.6% to 39.4% (z=+3.41, p=0.0007) on the Minerva Math benchmark; 5 of 7 math subjects significantly improved and none significantly degraded. Our method is fully deterministic, requires no additional inference cost, and provides a principled framework for interpretability-guided model editing.
Recently, a class of dormant black hole binaries with luminous companions (dBH-LC) has been observed, such as $Gaia$ BH1, BH2, and BH3. Unlike previously discovered X-ray BH binaries, this type of dBH-LC has relatively long orbital periods (typically more than several tens to a few hundred days) and shows very weak X-ray emission. Therefore, studying the formation and evolution of the whole dBH-LC population is also a very interesting problem. Our aim is to study the contribution of massive stars to the dBH-LC population under different evolutionary models (isolated binary evolution (IBE) and hierarchical triple evolution), and different formation channels (such as mass transfer, common envelope evolution). Using the Massive Objects in Binary Stellar Evolution (MOBSE) code, the Triple Stellar Evolution (TSE) code, and the latest initial multiple-star distributions, we model the populations of massive stars. Finally, we calculate the orbital properties, mass distributions, and birthrates of the BH-LC populations formed under these different conditions. In the Milky Way, we calculate that the birthrate of dBH-LC formed through IBE is about 4.35$\times$$10^{-5}$ ${\rm yr}^{-1}$, while the birthrate through triple evolution is about 1.47$\times$$10^{-3}$ ${\rm yr}^{-1}$. This means that the birthrate from triple evolution is one to two orders of magnitude higher than that from IBE. We find that in triple evolution, the main formation channel of dBH-LC is post-merger binaries formed from inner binary mergers triggered by von Zeipel$-$Lidov$-$Kozai oscillations.
The orbital angular momentum (OAM) of light is a versatile degree of freedom with transformative impact across optical communication, imaging, and micromanipulation. These applications have motivated a growing demand for compact, reconfigurable vortex arrays with tunable topological charge, yet integrating these functionalities into nanophotonic platforms remains elusive. Among possible strategies to meet this challenge is exploiting the twist degree of freedom in layered structures, which enables both emerging moire physics and unprecedented reconfigurability of photonic and electronic properties. Here, we harness these capabilities in twisted bilayer moire photonic crystals (TBMPCs) to realize vortex array generation with tunable OAM, demonstrated both analytically and experimentally. Central to this advancement is a new class of quasi-bound state in the continuum: Bessel-type modes emerging from moire-induced interlayer coupling, which generate vortex beams with tailored spiral phase distributions. We experimentally demonstrate vortex beams spanning eight OAM orders, from -3 to 4, and achieve selective excitation of distinct topological charges at a fixed telecommunication wavelength by tuning the interlayer separation and twist angle. Furthermore, localized Bessel-type modes at AA stacking regions can be excited nonlocally across the moire superlattice, enabling vortex array generation. Our work offers new insights into moire physics and introduces an innovative approach for future multiplexing technology integrating OAM, wavelength, and spatial division.
Under cold compression, hydrogen bonding was considered to dominate intermolecular interaction during the ionization of ammonia. Here, we provide experimental and theoretical evidence of intermolecular HH coupling in dense ammonia. Ab initio molecular dynamics simulations (AIMD) reveal an increasing degree of proton disorder in ammonia with increasing pressure, which promotes intermolecular H-H coupling. At pressure below the ionization phase transition pressure (135 GPa), intermolecular HH coupling gives rise to a unique dissociation pathway in ammonia. Sporadic molecular hydrogen was observed without laser heating, accompanied by the absence of molecular nitrogen. At pressure above 135 GPa, intermolecular HH coupling serves as an intermediate state in the ionization of ammonia. Two fingerprint Raman modes previously assigned to the ionic phase disappear upon further compression or heating. Together with proton transfer based on hydrogen bond, a dual path mechanism exists in the ionization of ammonia. Our results demonstrate a case of hydrides phase transition pathway that occurs independently of hydrogen bonding under high pressure.
High pressure chemistry provides a powerful route to materials that are inaccessible or difficult to synthesize under ambient conditions. However, high pressure chemical reaction processes and mechanisms remain largely unexplored because of the challenges associated with in situ characterization under high pressure and high temperature, particularly within the deeply enclosed sample environment of a large volume press. Here, we employ the state of the art real time synchrotron X ray radiography to image a high pressure chemical reaction at 5.4 GPa and 1700 K within a large volume press. Using Fe2O3 and BN as precursors, we capture the complete dynamic metal oxide to nitride conversion and show that it differs fundamentally from conventional solid state diffusion controlled nitridation. Synchrotron X ray radiography clearly revealed that this conversion involves a two stage liquid liquid separation process (LLPS), including fluid nitrogen and fluid Fe N alloy. On the basis of these observations, we propose a nitrogen driven mechanism for LLPS in borate melts. Specifically, nitrogen reduces metal cations in the borate network, altering their coordination environments and triggering a substantial reorganization of the melt structure. This coordination induced restructuring destabilizes the borate melt and promotes the LLPS of fluid Fe N alloy. Our in-situ observations suggest a general pathway for high pressure metal oxide to nitride conversion. This study provides a direct visualization of a pres-sure-enabled chemical reaction that is inaccessible under ambient conditions, offering fundamental in-sight into how high pressure reshapes chemical reaction pathways and enables the synthesis of metal nitrides.
Despite the tremendous progress in spintronic studies of van der Waals (vdW) room-temperature ferromagnet Fe3GaTe2, much less effort has been spent on its lattice dynamics and possible interaction with spintronic degrees of freedom. In this work, by combining Raman spectroscopy in a wide range of pressure (atmospheric pressure~19.5 GPa) and temperature (80~690 K) with first-principles calculation, we systematically studied the lattice dynamics and phonon dispersion of Fe3GaTe2. Our results show that the phonon energies of Fe3GaTe2 located at 126.0 cm-1 and 143.5 cm-1 originate from the anharmonic and harmonic vibration modes, respectively. Furthermore, the first room-temperature spin-phonon coupling in vdW ferromagnet is observed with strength of ~0.81 cm-1 at 300 K, by identifying Raman anomalies in both phonon energy and full width at half maximum (FWHM) of below Curie temperature of Fe3GaTe2. Our findings are valuable for fundamental and applied studies of vdW materials under variable conditions.
Room-temperature (RT) two-dimensional (2D) van der Waals (vdW) ferromagnets hold immense promise for next-generation spintronic devices for information storage and processing. To achieve high-density energy-efficient spintronic devices, it is essential to understand local magnetic properties of RT 2D vdW magnets. In this work, we realize noninvasive in situ magnetic detection in vdW-layered ferromagnet Fe3GaTe2 using divacancy spins quantum sensor in silicon carbide (SiC) at RT. The structural features and magnetic properties of the Fe3GaTe2 are characterized utilizing Raman spectrum, magnetization and magneto-transport measurements. Further detailed analysis of temperature- and magnetic field-dependent optically detected magnetic resonances of the PL6 divacancy near the Fe3GaTe2 reveal that, the Curie temperature (Tc) of Fe3GaTe2 is ~360K, and the magnetization increases with external magnetic fields. Additionally, spin relaxometry technology is employed to probe the magnetic fluctuations of Fe3GaTe2, revealing a peak in the spin relaxation rate around Tc. These experiments give insights into the intriguing local magnetic properties of 2D vdW RT ferromagnet Fe3GaTe2 and pave the way for the application of SiC quantum sensors in noninvasive in situ magnetic detection of related 2D vdW magnets.
In this paper, we investigate Liu-Xu-Ye-Zhao's conjecture [30] and prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in spheres which improves the convergence theorem of Baker [2] as well as the differentiable sphere theorems of Gu-Xu-Zhao [16, 50, 52].
In this survey, we will focus on the mean curvature flow theory with sphere theorems, and discuss the recent developments on the convergence theorems for the mean curvature flow of arbitrary codimension inspired by the Yau rigidity theory of submanifolds. Several new differentiable sphere theorems for submanifolds are obtained as consequences of the convergence theorems for the mean curvature flow. It should be emphasized that Theorem 4.1 is an optimal convergence theorem for the mean curvature flow of arbitrary codimension, which implies the first optimal differentiable sphere theorem for submanifolds with positive Ricci curvature. Finally, we present a list of unsolved problems in this area.
A new extended solid nitrogen, referred to post-layered-polymeric nitrogen (PLP-N), was observed by further heating the layered-polymeric nitrogen (LP-N) to above 2300 K at 161 GPa. The new phase is found to be very transparent and exhibits ultra-large d-spacings ranging from 2.8 to 4.9 Å at 172 GPa, suggesting a possible large-unit-cell 2D chain-like or 0D cluster-type structure with wide bandgap. However, the observed X-ray diffraction pattern and Raman scattering data cannot match any predicted structures in the published literature. This finding further complicates the phase diagram of nitrogen and also highlights the path dependence of the high-pressure dissociative transition in nitrogen. In addition, the forming boundary between cg-N and LP-N has been determined.
We have grown germanium selenide (GeSe) triangular nanoplate arrays (TNAs) with a high density (3.82E+6 / mm2) on the Si (111) substrate using a simple thermal evaporation method. The thickness and trilateral lengths of a single triangular nanoplate were statistically estimated by atomic force microscopy (AFM) as 44 nm, 365 nm, 458 nm and 605 nm, respectively. Transmission electron microscopy (TEM) images and X-ray diffraction (XRD) patterns show that the TNAs were composed of single crystalline GeSe phase. The Se-related defects in the lattice were also revealed by TEM images and Raman vibration modes. Unlike previously reported GeSe compounds, the GeSe TNAs exhibited temperature-dependent photoluminescence (PL). In addition, not previously reported PL peak (1.25 eV) of the 44 nm thick TNAs at 5 K was in the gaps between those of GeSe monolayers (1.5 nm) and thin films (400 nm), revealing a close relationship between the PL peak and the thickness of GeSe. The high-density structure and temperature-dependent PL of the TNAs on the Si substrate may be useful for temperature controllable semiconductor nanodevices.
Microwave plasma chemical vapor deposition (MPCVD) has been traditionally used to synthesize carbon-based materials such as diamonds, carbon nanotubes and graphene. Here we report that a rapid and catalyst-free growth of SnSe thin films can be achieved by using single-mode MPCVD with appropriate source materials. The analysis combing microscope images, X-ray diffraction patterns and lattice vibration modes shows that the grown thin films were composed of orthorhombic structured SnSe polycrystals mainly along the (111) direction. Further thermoelectric (TE) characterizations reveal that the power factor of the SnSe films reached 3.98 μW cm-1K-2 at 600 K, comparable to the highest reported values of SnSe thin films. Our results may open an avenue for rapid synthesis of new types of materials such as IV-VI compounds and be useful for TE application of these materials.
In this paper we investigate the rigidity of ancient solutions of the mean curvature flow with arbitrary codimension in space forms. We first prove that under certain sharp asymptotic pointwise curvature pinching condition the ancient solution in a sphere is either a shrinking spherical cap or a totally geodesic sphere. Then we show that under certain pointwise curvature pinching condition the ancient solution in a hyperbolic space is a family of shrinking spheres. We also obtain a rigidity result for ancient solutions in a nonnegatively curved space form under an asymptotic integral curvature pinching condition.
Understanding high-pressure transitions in prototypical linear diatomic molecules, such as hydrogen, nitrogen, and oxygen, is an important objective in high-pressure physics. Recent ultrahigh-pressure study on hydrogen revealed that there exists a molecular-symmetry-breaking isostructural electronic transition in hydrogen. The pressure-induced symmetry breaking could also lead to a series of solid molecular phases in nitrogen associated with the splitting of vibron, walking a path from fluid nitrogen to molecular solids and then to polymetric nitrogen phases. However, isostructural transition in nitrogen has not been reported so far, which may provide crucial information on the crystallographic nature of the pressure-induced dissociation transitions in nitrogen. Here we present a high-pressure Raman scattering and high-pressure angle dispersive X-ray diffraction study of the previously reported lambda-N2 and reveal an isostructural transition from the lambda-N2 to a new derivative phase, lambda-N2. Under compression, lambda-N2 remains in the monoclinic crystal lattice, accompanied by a monotonic increase in anisotropy. The pressure-dependent decrease of the unit cell parameters exhibits a discontinuity at the pressure of 54 GPa, accompany with sudden broadening and turnover of vibron.
Intel(R) Software Guard Extensions (Intel(R) SGX) is a promising technology to securely process information in otherwise untrusted environments. An important aspect of Intel SGX is the ability to perform remote attestation to assess the endpoint's trustworthiness. Ultimately, remote attestation will result in an attested secure channel to provision secrets to the enclave. We seamlessly combine Intel SGX remote attestation with the establishment of a standard Transport Layer Security (TLS) connection. Remote attestation is performed during the connection setup. To achieve this, we neither change the TLS protocol, nor do we modify existing protocol implementations. We have prototype implementations for three widely used open-source TLS libraries: OpenSSL, wolfSSL and mbedTLS. We describe the requirements, design and implementation details to seamlessly bind attested TLS endpoints to Intel SGX enclaves.
Hardware/Software (HW/SW) interfaces, mostly implemented as devices and device drivers, are pervasive in various computer systems. Nowadays HW/SW interfaces typically undergo intensive testing and validation before release, but they are still unreliable and insecure when deployed together with computer systems to end users. Escaped logic bugs, hardware transient failures, and malicious exploits are prevalent in HW/SW interactions, making the entire system vulnerable and unstable. We present HW/SW co-monitoring, a runtime co-verification approach to detecting failures and malicious exploits in device/driver interactions. Our approach utilizes a formal device model (FDM), a transaction-level model derived from the device specification, to shadow the real device execution. Based on the co-execution of the device and FDM, HW/SW co-monitoring carries out two-tier runtime checking: (1) device checking checks if the device behaviors conform to the FDM behaviors; (2) property checking detects invalid driver commands issued to the device by verifying system properties against driver/device interactions. We have applied HW/SW co-monitoring to five widely-used devices and their Linux drivers, discovering 9 real bugs and vulnerabilities while introducing modest runtime overhead. The results demonstrate the major potential of HW/SW co-monitoring in improving system reliability and security.