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In this paper, we introduce the Dual-minus partial order, get some characterizations of the partial order, and prove that both the dual star partial order and the dual sharp partial order are Dual-minus-type partial orders. Based on the Dual-minus partial order, we introduce the Dual-minus sharp partial order and the Dual-minus star partial order, which are also Dual-minus-type partial orders. In addition, we discuss relationships among the Dual-minus sharp partial order, the D-sharp partial order and the G-sharp partial order(the Dual-minus star partial order, the D-star partial order and the P-star partial order)., Comment: 23 pages

Our study reveals electron spin in a cavity as a stable circulating current density, characterized by a torus topology. This current density circulates concentrically beyond the cavity boundary, illustrating the concept of evanescent wave spin. While the interaction with a uniform magnetic field aligns with established spin-field observations, our analysis of regional contributions deviates from particle-based spin predictions. The integration of charge and spin properties into a single Lorentz covariant entity suggests that the electron wave constitutes the fundamental and deterministic reality of the electron., Comment: 12 pages, 2 figures

Our study shows that an evanescent electron wave exists outside both finite and infinite quantum wells, by solving exact solutions of the Dirac equation in a cylindrical quantum well and maintaining wavefunction continuity at the boundary. Furthermore, we demonstrate that the evanescent wave spins concurrently with the wave inside the quantum well, by deriving analytical expressions of the current density in the whole region. Our findings suggest that it is possible to probe or eavesdrop on quantum spin information through the evanescent wave spin without destroying the entire spin state. The wave spin picture interprets spin as a global and deterministic property of the electron wave that includes both the evanescent and confined wavefunctions. This suggests that a quantum process or device based on the manipulation and probing of the electron wave spin is deterministic in nature rather than probabilistic., Comment: 6 pages, 5 figures

The wave spin of an electron can be fully characterized by the current density calculated from the exact four-spinor solution of the Dirac equation. In the excited states of the electron in a magnetic field-free quantum well, the current density has a multiple vortex topology. The interaction of the current with a magnetic potential produces a finer structure of anomalous Zeeman splitting. When the magnetic potential is comparable to the size of the individual vortices, fractional or zero spin effects can be observed., Comment: 6 pages, 4 figures

Electronic phase separation (EPS) originates from an incomplete transformation between electronic phases, causing the inhomogeneous spatial distribution of electronic properties. In the system of two-dimensional electron gas (2DEG), the EPS is usually identified based on a percolative metal-to-superconductor transition. Here, we report a metal-insulator transition (MIT) in KTaO3-based 2DEG with the width of conductive channel decreasing into micrometer scale. Hysteretic resistance-temperature relations are observed due to the competition between metallic and insulating phases, which is tunable by magnetic field. Such a size-dependent MIT effect is attributed to the coexistence and separation of metallic and insulating phases. Combining density functional theory calculation, we propose a theoretical model to simulate the dynamic process of the EPS using the percolation theory, demonstrating the mechanism of size-dependent MIT. Our work suggests a clear and simple 2DEG platform to achieve the spatial coexistence of metallic and insulating phases.

Ferroelectrics are essential in low-dimensional memory devices for multi-bit storage and high-density integration. A polar structure is a necessary premise for ferroelectricity, mainly existing in compounds. However, it is usually rare in elemental materials, causing a lack of spontaneous electric polarization. Here, we report an unexpected room-temperature ferroelectricity in few-chain Te nanowires. Out-of-plane ferroelectric loops and domain reversal are observed by piezoresponse force microscopy. Through density functional theory, we attribute the ferroelectricity to the ion-displacement created by the interlayer interaction between lone pair electrons. Ferroelectric polarization can induce a strong field effect on the transport along the Te chain, supporting a self-gated field-effect transistor. It enables a nonvolatile memory with high in-plane mobility, zero supply voltage, multilevel resistive states, and a high on/off ratio. Our work provides new opportunities for elemental ferroelectrics with polar structures and paves a way towards applications such as low-power dissipation electronics and computing-in-memory devices.

In this paper, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse and matrix decomposition, we give several characterizations of the dual index when it is equal to one. And we get that if DCGI exists, then it is unique. We derive a compact formula for DCGI and a series of equivalent characterizations of the existence of the inverse. It is worth nothing that the dual index of $\hat{M}$ is equal to one if and only if its DCGI exists. When the dual index of $\hat{M}$ is equal to one, we study dual Moore-Penrose generalized inverse (DMPGI) and dual group generalized inverse (DGGI), and consider the relationships among DCGI, DMPGI, DGGI, Moore-Penrose dual generalized inverse (MPDGI) and other dual generalized inverses. In addition, we consider symmetric dual matrix and its dual generalized inverses. At last, two examples are given to illustrate the application of DCGI in linear dual equations.

The particle-wave duality of the electron poses a principle question of whether the spin is a property of the particle or the wave. In this paper, the wave nature of the spin is studied for an electron inside a two-dimensional quantum well. By solving the exact $4-$spinor eigen solution to the Dirac equation, we show that a stable circulating total current density exists inside the well with a donut shaped topography. A spin value is modified by the confining geometry of the well. Our analysis also shows that a free electron Gaussian wavepacket is unstable and experiences quick decoherence., Comment: 5 pages, 4 figures

Perturbation theory is a kind of estimation method based on theorem of Taylor expansion, and is useful to investigate electromagnetic solutions of small changes. By considering a sharp boundary as a limit of smoothed systems, previous study has solved the problem when applying standard perturbation theory to Maxwell's equations for small shifts in isotropic dielectric interfaces. However, when dealing with anisotropic materials, an approximation is conducted and leads to an unsatisfactory error. Here we develop a modified perturbation theory for small shifts in anisotropically dielectric interfaces. By using optimized smoothing function for each component of permittivity, we obtain a method to calculate the intrinsic frequency shifts of anisotropic permittivity field when boundaries shift, without approximation. Our method shows accurate results when calculating eigenfrequency's shifts in strong-anisotropy materials, and can be widely used for small shifts in anisotropically dielectric interfaces.

Van der Waals (vdW) heterojunctions, based on two-dimensional (2D) materials, show great potential for the development of eco-friendly and high-efficiency nano-devices. Considerable research has been performed and has reported valuable applications of photovoltaic cells, photodetectors, etc. However, simultaneous energy conversion and storage in a single device has not been achieved. Here, we demonstrate a simple strategy to construct a vdW p-n junction between a WSe2 layer and quasi-2D electron gas. After once optical illumination, the device stores the light-generated electrons and holes for up to seven days, and then releases a very large photocurrent of 2.9 mA with bias voltage applied in darkness; this is referred to as chargeable photoconductivity (CPC), which completely differs from any previously observed photoelectric phenomenon. In normal photoconductivity, the recombination of electron-hole pairs takes place at the end of their lifetime, causing a release of heat; in contrast, infinite-lifetime photocarriers can be generated in CPC devices without a thermal loss. The photoelectric conversion and storage are completely self-excited during the charging process. The ratio between currents in full- and empty-energy states below the critical temperature reaches as high as 109, with an external quantum efficiency of 4410000% during optical charging. A theoretical model developed to explain the mechanism of this effect is in good agreement with the experimental data. This work paves a path towards storage-type photoconductors and high-efficiency entropy-decreasing devices.