Quantum spin Hall effect in tilted penta silicene and its isoelectronic substitutions.

Silicene, a competitive two-dimensional (2D) material for future electronic devices, has attracted intensive attention in condensed matter physics. Utilizing an adaptive genetic algorithm (AGA), we identify a topological allotrope of silicene, named tilted penta (tPenta) silicene. Based on first-principles calculations, the geometric and electronic properties of tPenta silicene and its isoelectronic substitutions (Ge, Sn) are investigated. Our results indicate that tPenta silicene exhibits a semimetallic state with distorted Dirac cones in the absence of spin-orbit coupling (SOC). When SOC is considered, it shows semiconducting behavior with a gap opening of 2.4 meV at the Dirac point. Based on the results of invariant ( = 1) and the helical edge states, we demonstrate that tPenta silicene is a topological insulator. Furthermore, the effect of isoelectronic substitutions on tPenta silicene is studied. Two stoichiometric phases, i.e., tPenta Si0.333Ge0.667 and tPenta Si0.333Sn0.667 are found to retain the geometric framework of tPenta silicene and exhibit high stabilities. Our calculations show that both tPenta Si0.333Ge0.667 and tPenta Si0.333Sn0.667 are QSH insulators with enlarged band gaps of 32.5 meV and 94.3 meV, respectively, at the HSE06 level, offering great potential for practical applications at room temperature.

Statistical properties of an electromagnetic Gaussian Schell-model beam propagating in uniaxial crystals along the optical axis.

Within the angular-spectrum representation, we study the partially coherent beam propagating in uniaxial crystals along the optical axis. By a method of vortex expansion, we derive the analytical solution for the cross-spectral density (CSD) function of an electromagnetic Gaussian Schell-model (EGSM) beam. We demonstrate that the analytical expression of CSD function can be written into a quasi-coherent-mode representation, whose basis vectors are constructed by the elegant Laguerre-Gaussian (eLG) functions. Several limits of the analytical solution are examined and good agreements with previous theories are obtained. Moreover, we calculate the energy density and degree of polarization (DOP) of the EGSM beam, from which the effects of coherent degree on the propagating properties are revealed. It is found that the energy conversion between circularly polarized components becomes rapid when the degree of coherence is decreasing. For all degree of coherence, the energy density and DOP exhibit a similar saturated behavior in the far field.

The transmission of structured light fields in uniaxial crystals employing the Laguerre-Gaussian mode spectrum.

In the plane-wave angular-spectrum representation, we derive the analytical expressions for any order Laguerre-Gaussian beams propagating along the optical axis of uniaxial crystals. We further prove the orthogonality of propagating modes inside the uniaxial crystals, and investigate the energy efficiency as well as the behavior of spin-orbital coupling. Based on the analytical solutions, we propose a scheme for the transmission of structured light fields through the uniaxial crystals, which firstly decomposes the input fields into LG spectrum and then superposes all OAM components inside crystals to obtain the propagating optical fields. We use the trefoil image as an example to demonstrate the effectiveness of our scheme. The evolution of optical fields and spectra of trefoil image are also studied.

Effect of truncation on photonic corner states in a Kagome lattice.

We theoretically present a simple nanophotonics platform, where the photonic corner states can be obtained in high frequencies. For the breathing Kagome lattice with three bearded truncations, we show that a pair of bonding and anti-bonding corner states can be observed in the gapped bulk bands, even for a topologically trivial lattice. In particular, this anti-bonding corner state is totally embedded in the bulk modes for topologically non-trivial structures, forming a bound state in continuum. We further verify that these corner states are protected by the symmetry and can be excited by merely one point source, even in a loss system. The newly found corner modes may expand our understanding of the high-order corner modes in a more general framework, involving both topology and symmetry.

Vortex generation and inhomogeneous Faraday rotation of a nonparaxial Gaussian beam in isotropic magneto-optic crystals.

We study the propagation of a nonparaxial Gaussian beam in the isotropic Bi4Ge3O12 crystal under an external magnetic field. The analytical solutions in the paraxial limit are derived, which show that a vortex with topological charge m=2 (m=1) generates in the E_ (E(z)) component. Numerical calculations in the nonparaxial regime confirm that, with the assistance of an external magnetic field, the spin-to-orbital angular momentum coupling effect can occur even in the isotropic crystal. We also study the Faraday rotation of the nonparaxial Gaussian beam. At the center of the transverse plane, the rotation of the plane of polarization is linearly proportional to the magnetic field. However, the rotation is not uniform on the whole transverse plane, manifesting the nonparaxial effect.

Tunable hybrid-order Weyl semimetal via staggered magnetic flux.

We investigate a hybrid-order Weyl semimetal (HOWS) constructed by stacking the two-dimensional kagome lattice with staggered magnetic flux. By adjusting the magnitude of flux, higher-order topological phases are tunably intertwined with the first-order topological Chern insulators, which is governed by the evolution of Weyl points. Meanwhile the surface Fermi arcs undergo topological Lifshitz transition. Notably, due to the breaking of time-reversal symmetry (TRS), a novel split of a quadratic double Weyl point occurs, giving rise to additional three type-II Weyl points hybridizing with one type-I node. This phenomenon plays a crucial role in realizing high-Chern-number phases withC=±2and reveals a new mechanism for the emergence of type-II Weyl fermions in topological kagome semimetals. We anticipate that this study will stimulate further investigation into the unique physics of kagome materials and Weyl semimetals.

Anisotropic dynamics of optical vortex-beam propagating in biaxial crystals: a numerical method based on asymptotic expansion.

One difficulty of angular spectrum representation method in studying optical propagation inside anisotropic crystals is to calculate the double integrals containing highly oscillating functions. In this paper, we introduce an accuracy and numerically cheap method based on asymptotic expansion theory to overcome this difficulty, which therefore allows to compute optical fields with arbitrary incident beam and is not restricted to the paraxial limit. This numerical method is benchmarked against the analytical solutions in uniaxial crystals and excellent agreements between them are obtained. As an application, we adopt it to investigate the propagation of a Gaussian vortex-beam in a biaxial crystal. The general features of anisotropic dynamics and power conversion between field components are revealed. The numerical results is interpreted by making appropriate analytical approximation to the wave equations.

Spin-orbit interactions of a Gaussian light propagating in biaxial crystals.

Based on the plane-wave angular spectrum representation, we derive a formal expression for any light fields propagating in biaxial crystals, and particularly, present an effective numerical method to investigate the propagation behavior for a Gaussian light beam. Unlike uniaxial crystals, we observe the intriguing formation, repulsion and disappearance of vortex pairs, as the refractive indices deviate slightly and gradually from the uniaxial limit. In the Minkowski angular momentum picture, we also investigate the orbital angular momentum dynamics for both left- and right-handed circularly polarized components. Of further interest is the revelation of nonconservation of the angular momentum within the light field during the spin-orbit interactions, and the optical torque per photon that the light exerts on the biaxial crystal is quantified. We interpret these interesting phenomena by the weakly broken rotational invariance of biaxial crystals. The self-consistency of our theory is confirmed by the balance equation describing the conservation law of total angular momentum of filed and crystal in the Minkowski picture.

The topological properties of D + p-wave superconductors in the mixed Rashba/Dresselhaus systems.

We investigate the effect of mixing Rashba/Dresselhaus spin-orbit couplings (SOCs) on the topological properties of D + p-wave superconductors. It is known that the nodal D + p-wave Rashba superconductors become gapful under a Zeeman magnetic field. We extend this gap-generation mechanism to mixed Rashba/Dresselhaus systems and find that the induced energy gaps are strongly modified by the Dresselhaus component in the second quadrant of the Brillion zone (BZ). We further calculate the Chern number numerically and obtain the topological phase diagram. It is shown that the Dresselhaus SOCs have a negative effect on the topological properties; the topological nontrivial region with C = -4 in the phase diagram shrinks as the amplitude of the Dresselhaus component increases. In the Dresselhaus-dominated regime, the contributions of gapped nodes from different quadrants of the BZ cancel each other, resulting in zero Chern number in most of the phase diagram. The numerical results are well explained by an approximate analytical formula for Chern number.

Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect.

The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved.