Abstract When the mass term M (scalar-like potential) and the electrostatic potential V (vector-like potential) in the radial Dirac equation are linear (parabolic), the accurate and full spectra obtained by the sectioned series expansion method are reported. The evolution of the energy levels with M and V is observed, along with the competing effects of M and V on the bound states. The introduction of a magnetic field (similar to the tensor potential) enriches the variation of the energy levels. When M = V for the parabolic case, analytical results are demonstrated, in mutual agreement with the numerical ones. This work provides a comprehensive understanding of the relativistic quantum confinement of Dirac electrons, with implications for engineering electronic properties in Dirac materials through external fields.
Abstract We demonstrate four switchable pulse states at 1.3 μm in a dual-wavelength bismuth-doped fiber laser based on nonlinear polarization rotation. By adjusting the pump power and polarization, we achieve four switchable pulse states: mode-locking, breathing, Q-switching, and Q-switched mode-locking. All states are dual-wavelength, operating at 1362 nm and 1426–1431 nm with a separation of 63–69 nm. The laser delivers a fundamental repetition rate of 1.71 MHz. At the breathing-pulse state, the pulse envelope undergoes periodic modulation with a characteristic period of 50 μs, whereas the Q-switching state operates at a repetition rate of 21.0 kHz. The Q-switched mode-locked envelope amplitude is continuously tunable via polarization.
Abstract Characterizing structural chirality in two-dimensional (2D) periodic crystals remains nontrivial because existing measures often require additional treatments of periodicity, structural correspondence, or reference configurations. Here, we introduce a signed pseudoscalar descriptor constructed directly from atomic coordinates and local atomic environments. It combines global structural asymmetry with local axiality, retains sensitivity to elemental occupation, and requires neither a predefined achiral reference nor explicit matching to a mirror-image counterpart. Because a particular primitive-cell representation of a globally achiral crystal may yield a finite value, we formulate a practical assessment procedure that considers nonprimitive translations and symmetry-equivalent unit-cell choices, supplemented by layer-group or point-group analysis when a vanishing descriptor is inconclusive. Applications to representative monolayer and bilayer systems illustrate its use in assessing structural chirality, distinguishing opposite-handed configurations through its sign, and tracking field-induced chirality within a fixed structural family. Although its value depends on the selected unit-cell representation and its absolute magnitude should not be compared between structurally unrelated materials, the descriptor provides a practical computational tool for handedness assignment and tracking structural chirality under consistent conventions.
Abstract The external tilt control state is one of the important factors affecting the long-term stable observation of superconducting gravimeters. Influenced by factors such as mechanical assembly errors of the instrument and relative position deviations between internal and external structures, the horizontal zero position of the external tilt control system is not necessarily equivalent to the optimal response state of the internal superconducting magnetic levitation sensing system. To address this issue, this paper proposes an optimization method for the external tilt setpoint based on the internal displacement voltage response, establishing a local response model among external tilt, magnetic levitation force balance, and displacement voltage under small tilt angle and locally quasi-static conditions. A local quadratic relationship is established using the mean tilt angle and mean displacement voltage within the plateau segment, and verified through the original local scanning and supplementary experiments adopting a fixed tilt step size and a unified recording duration. The supplementary experiments yield average extreme positions of -4309.75 μrad and -3997.92 μrad for the X-axis and Y-axis, respectively, with inter-test sample standard deviations of 6.89 μrad and 7.16 μrad, respectively. The average extreme positions of the two axes differ from the original experimental results by 2.04 μrad and 2.05 μrad, respectively. Under the local geometric approximation, the equivalent gravity projection corresponding to the inter-test variation in the extreme position is approximately 0.048 μGal. This method can provide a reference for the optimization of the external tilt setpoint during the installation and commissioning of superconducting gravimeters.
Abstract Carrier effective masses under strain are vital for GeSn band engineering. Using well-established full-zone 30-band k · p and continuum elasticity theories, we calculate band-structure, density-of-states (DOS) and conductivity effective masses of Ge 1-x Sn x (0 ≤ x ≤ 0.2) under six strain modes from -1.5% compressive to 1.5% tensile. For conduction bands, L-valley transverse mass governs the modulation, while longitudinal mass is largely insensitive to Sn composition and strain; the Γ valley exhibits near-isotropic band curvature, and its effective mass generally decreases with increasing Sn composition and tensile strain. For valence bands, light hole (LH) and heavy hole (HH) masses present orientation-dependent anisotropy, and DOS/hole conductivity masses peak near zero strain. Distinct strain responses are observed for different crystallographic orientations. Benchmarks comparisons support the reliability of our calculation framework. This work reveals the orientation- and valley-dependent strain-composition coupling of carrier effective masses in strained Ge 1-x Sn x alloys, and yields a unified set of effective-mass parameters for high-performance GeSn optoelectronic device design.
