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The experimental evidence of the ultra-high electron mobility and strong spin-orbit coupling in the two-dimensional (2D) layered bismuth-based oxyselenide, Bi$_{2}$O$_{2}$Se, makes it a potential material for spintronic devices. However, its spin-related properties have not been extensively studied due to the centrosymmetric nature of its crystal structure. By using first-principles density-functional theory calculation, this study reports the emergence of Rashba-spin-valley states in Bi$_{2}$O$_{2}$Se monolayer (ML). Breaking the crystal inversion symmetry of Bi$_{2}$O$_{2}$Se ML using an external electric field enables the Rashba-spin-valley formation, causing the appearance of the Rashba-type splitting around the $\Gamma$ valley and spin-valley coupling at the $D$ valleys located near the middle of $\Gamma-M$ line. In addition to the typical Rashba-type spin textures around the $\Gamma$ valley, the study also observed in-plane unidirectional spin textures around the $D$ valleys, which is a rare phenomenon in 2D materials. The observed Rashba-spin-valley states are driven by the lowering point group symmetry of the crystal from $D_{4h}$ to $C_{4v}$ enforced by the electric field, as clarified through $\vec{k}\cdot\vec{p}$ model derived from symmetry analysis. More importantly, tuning the Rashba and spin-valley states by using biaxial strain offers a promising route to regulate the spin textures and spin splitting preventing the electron from back-scattering in spin transport. Finally, we proposed a more realistic system, namely, Bi$_{2}$O$_{2}$Se ML/SrTiO$_{3}$ (001) heterointerface that supports the strong Rashba-spin-valley states and highlighting the potential of the Bi$_{2}$O$_{2}$Se ML for future spintronics and valleytronics-based devices., Comment: 7 Figures

The muon spin relaxation method ({\mu}SR) is a powerful microscopic tool to probe electronic states of materials observing local magnetic field distributions on the muon. It often happens that a distribution of local magnetic fields shows intermediate state between Gaussian and Lorentzian shapes. In order to generally describe intermediate field distributions, we dealt the convolution of two isotropic distributions in the three dimension and derived exact muon-spin relaxation functions which can be applied to all crossover regimes between the Gaussian and Lorentzian., Comment: 23 pages, 10 figures, see https://doi.org/10.1093/ptep/ptab074

In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited area (in a quantum sized-volume) like random vibrating system where the particle will diffuse in a quantum-sized volume when it absorbs or emits the quantized amount of energy. The quantum sized-volume can move too and plays role similar to the carrier amplitude, while the vibrational motion of the fundamental particle with frequency and amplitude represents a modulating signal. The current of diffusion process taking place in the quantum sized-volume will represent the emergence of a spin phenomenon shown by the existence of Clifford algebra. Second, the particle is pure energy concentrated on the surface of 3 dimensional sphere-form (2-manifold without boundary). Afterward we show that by defining the particle mass as an invariant quantity based on the two fundamental ideas, we can derive both the diffusion constant of the particle in the quantum sized-volume as $\beta = \hslash/2m$ and the Schr\"{o}dinger equation. Furthermore, by posing that the vibrational motion of the particle limited on the quantum sized-volume plays fundamental role as time interval unit (proper time or particle clock), we show that the relativistic effects of the particle must represent atomic processes., Comment: 59 pages