Silicene is an intriguing 2D topological material which is closely analogous to graphene but with stronger spin orbit coupling effect and natural compatibility with current silicon-based electronics industry. Here we demonstrate that silicene decorated with certain 3d transition metals (Vanadium) can sustain a stable quantum anomalous Hall effect using both analytical model and first-principles Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our findings provide new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states which are highly desirable for future nanoelectronics and spintronics application.

We investigate the localized nonlinear matter waves of the quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity in the harmonic potential. It is shown that all of the Bose-Einstein condensates, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies, which are mathematically exact orthogonal solutions of the Gross-Pitaevskii equation. Their properties are determined by the principal quantum number n and secondary quantum number l: the parity of the matter wave functions and the corresponding energy levels depend only on n, and the numbers of density packets for each quantum state depend on both n and l, which describe the topological properties of the atom packets. We also give an experimental protocol to observe these phenomena in future experiments.

We obtain the rich phase diagrams in the Hubbard model on the triangular kagome lattice as a function of interaction, temperature, and asymmetry by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. The phase diagrams show the asymmetry separates the critical points in the Mott transition of two sublattices on the triangular kagome lattice and produces two novel phases called plaquette insulator with a clearly visible gap and a gapless Kondo metal. When the Coulomb interaction is stronger than the critical value Uc, a short range paramagnetic insulating state, which is a candidate for the short rang resonating valence-bond spin liquid, emerges before the ferrimagnetic order is formed independent of asymmetry. Furthermore, we discuss how to measure these phases in future experiments.

We consider the derivative nonlinear Schrödinger equation with constant potential as a model for wave propagation on a discrete nonlinear transmission line. This equation can be derived in the small amplitude and long wavelength limit using the standard reductive perturbation method and complex expansion. We construct some exact soliton and elliptic solutions of the mentioned equation by perturbation of its Stokes wave solutions. We find that for some values of the coefficients of the equation and for some parameters of solutions, the graphical representations show some kinds of symmetries such as mirror symmetry and rotational symmetry.

Two-dimensional (2D) magnetic materials are essential for the development of the next-generation spintronic technologies. Recently, layered van der Waals (vdW) compound MnBi₂Te₄ (MBT) has attracted great interest, and its 2D structure has been reported to host coexisting magnetism and topology. Here, we design several conceptual nanodevices based on MBT monolayer (MBT-ML) and reveal their spin-dependent transport properties by means of the first-principles calculations. The pn-junction diodes and sub-3-nm pin-junction field-effect transistors (FETs) show a strong rectifying effect and a spin filtering effect, with an ideality factor n close to 1 even at a reasonably high temperature. In addition, the pip- and nin-junction FETs give an interesting negative differential resistive (NDR) effect. The gate voltages can tune currents through these FETs in a large range. Furthermore, the MBT-ML has a strong response to light. Our results uncover the multifunctional nature of MBT-ML, pave the road for its applications in diverse next-generation semiconductor spin electric devices.

Supersolid is a long-sought exotic phase of matter, which is characterized by the coexistence of a diagonal long-range order of solid and an off-diagonal long-range order of superfluid. Possible candidates to realize such a phase have been previously considered, including hard-core bosons with long-range interaction and soft-core bosons. Here we demonstrate that an ultracold atomic condensate of hard-core bosons with contact interaction can establish a supersolid phase when simultaneously subjected to spin-orbit coupling and a spin-dependent periodic potential. This supersolid phase is accompanied by topologically nontrivial spin textures, and is signaled by the separation of momentum distribution peaks, which can be detected via time-of-flight measurements. We also discuss possibilities to produce and observe the supersolid phase for realistic experimental situations.