Bilayer phosphorene attracted considerable interest, giving a potential application in nanoelectronics owing to its natural bandgap and high carrier mobility. However, very little is known regarding the possible usefulness in spintronics as a quantum spin Hall (QSH) state of material characterized by a bulk energy gap and gapless spin-filtered edge states. Here, we report a strain-induced topological phase transition from normal to QSH state in bilayer phosphorene, accompanied by band-inversion that changes "Equation missing"<!-- image only, no MathML or LaTex --> number from 0 to 1, which is highly dependent on interlayer stacking. When the bottom layer is shifted by 1/2 unit-cell along zigzag/armchair direction with respect to the top layer, the maximum topological bandgap 92.5 meV is sufficiently large to realize QSH effect even at room-temperature. An optical measurement of QSH effect is therefore suggested in view of the wide optical absorption spectrum extending to far infra-red, making bilayer phosphorene a promising candidate for opto-spintronic devices.

We investigate the rotating spin-1 Bose-Einstein condensates with anisotropic spin-orbit coupling by using the damped projected Gross-Pitaevskii equation. The anisotropic spin-orbit coupling can cause some vortices to form the vortex chain, where the vortices link up with each other in a line. The formation of the vortex chain starts from very small rotation frequency and coexists with more remanent vortices with the increasing rotation frequency. By increasing the anisotropy of the spin-orbit coupling, the creation of the vortex chain is enhanced, accompanied by the emergence of several types of vortex chain and other vortex configurations. When the vortices of the ${m}_{F}=$-${}1$ and ${m}_{F}=+1$ components are of synchronous phases, such vortex configurations do not cause any topological excitation in the spin texture.

The ${\mathrm{Ni}}^{12+}, {\mathrm{Cu}}^{13+}, {\mathrm{Pd}}^{12+}$, and ${\mathrm{Ag}}^{13+}$ highly charged ions (HCIs) are proposed for making very accurate optical clocks with the fractional uncertainties below ${10}^{-19}$ level. These HCIs have simple atomic energy levels, clock transitions with quality factors larger than ${10}^{15}$, and optical magnetic-dipole $\left(M1\right)$ transitions that can be used for laser cooling and detecting quantum jumps on the clock transitions by the shelving method. To demonstrate the projected fractional uncertainties, we estimate orders of magnitude of the Zeeman, Stark, blackbody radiation, and electric quadrupole shifts of the clock transitions by performing calculations of the relevant atomic properties in the above HCIs.

By using the phase field crystal model, we simulate the morphological transition of the crystal growth of equilibrium crystal shape, dendrite, and spherical crystal shape. The relationship among growth morphology, velocity, and density distribution is investigated. The competition between interface energy anisotropy and interface kinetic anisotropy gives rise to the pattern selection of dendritic growth in the diffusion controlled regime under low-crystal-growth velocities. The trapping effect in density diffusion suppresses morphological instabilities under high-crystal-growth velocities, resulting in isotropic growth of spherical crystal. Finally, a morphological phase diagram of crystal growth is constructed as function of the phase field crystal model parameters.

We study various properties of the $2p{}^{2}P_{1/2}-2p{}^{2}P_{3/2}$ fine-structure splittings in the boronlike ${\mathrm{S}}^{11+}, {\mathrm{Cl}}^{12+}, {\mathrm{Ar}}^{13+}$, and ${\mathrm{K}}^{14+}$ ions and the $4p{}^{2}P_{1/2}-4p{}^{2}P_{3/2}$ fine-structure splittings in the galliumlike ${\mathrm{Nb}}^{10+}, {\mathrm{Mo}}^{11+}, {\mathrm{Tc}}^{12+}$, and ${\mathrm{Ru}}^{13+}$ ions to find out the feasibility of using these highly charged ions as suitable optical atomic clocks. The roles of the electron correlations due to the Dirac-Coulomb-Breit Hamiltonian and accounting for lower-order quantum electrodynamics effects are shown explicitly in the calculations of electron affinities, excitation energies, transition-matrix elements, lifetimes, hyperfine-structure constants, and electric quadrupole moments of the states involved with clock transitions using a relativistic couple-cluster method. We also estimate the most commonly appearing systematic effects in the atomic clock experiments due to the electric quadrupole, the second-order Zeeman, both the dc and ac Stark, and the black-body radiation shifts in the aforementioned fine-structure splittings to demonstrate typical orders of magnitude of fractional frequency shifts.

We investigate the transition between the fine structure levels of the ground state, $3p{}^2{P}_{1/2}\to 3p{}^2{P}_{3/2}$, of the highly charged Al-like ${}^{51}\mathrm{V}^{10+},{}^{53}\mathrm{Cr}^{11+},{}^{55}\mathrm{Mn}^{12+},{}^{57}\mathrm{Fe}^{13+},{}^{59}\mathrm{Co}^{14+},{}^{61}\mathrm{Ni}^{15+}$, and ${}^{63}\mathrm{Cu}^{16+}$ ions for frequency standards. To comprehend them as prospective atomic clocks, we determine their transition wavelengths, quality factors, and various plausible systematics during the measurements. Since most of these ions have nuclear spin $I=3/2$, uncertainties due to dominant quadrupole shifts can be evaded in the $F=0$ hyperfine level of the $3p{}^2{P}_{3/2}$ state. Other dominant systematics such as quadratic Stark and black-body radiation shifts have been evaluated precisely demonstrating the feasibility of achieving high accuracy, below ${10}^{-19}$ fractional uncertainty, atomic clocks using the above transitions. Moreover, relativistic sensitivity coefficients are determined to find out the aptness of these proposed clocks to investigate possible temporal variation of the fine structure constant. To carry out these analysis, a relativistic coupled-cluster method considering Dirac-Coulomb-Breit Hamiltonian along with lower-order quantum electrodynamics interactions is employed and many spectroscopic properties are evaluated. These properties are also of immense interest for astrophysical studies.