On a new semi‐empirical electrotopological index for QSRR models

A new semi‐empirical electrotopological index, I_SET, for quantitative structure–retention relationships (QSRR) models was developed based on the refinement of the previously published semi‐empirical topological index, I_ET. We demonstrate that the values of C_i fragments that were firstly attributed from the experimental chromatographic retention and theoretical deductions have an excellent relationship with the net atomic charge of the carbon atoms. Thus, the values attributed to the vertices in the hydrogen‐suppressed graph of carbon atoms (C_i) are calculated from the correlation of the net atomic charge in each carbon atom, which is obtained from quantum chemical semi‐empirical calculations, and the C_i fragments for primary, secondary, tertiary and quaternary carbon atoms (1.0, 0.9, 0.8 and 0.7, respectively) obtained from the experimental values. This shows that I_ET encoded this quantum physical reality and that it is possible to calculate a new I_SET (the semi‐empirical electrotopological index) through the net atomic charge values obtained from a Mulliken population analysis using the semi‐empirical AM1 method and their correlation with the values attributed to the different types of carbon atoms. This demonstrates that the I_SET encodes information on the charge distribution of the solute on which dispersive and electrostatic interactions between the solute (alkanes and alkenes) and the stationary phase strongly depend. Thus, this new method can be considered as an initial step towards forthcoming QSRR/QSAR studies. Copyright © 2008 John Wiley & Sons, Ltd.     

Topological Vortices in a Spin-Triplet Superconductor

Based on the complex three-component order parameter model of a spin-triplet superconductor, by using the C-mapping theory, we derive a new equation describing the distribution of the magnetic field for vortices, which can be reduced to the modified London equation in the case of ｜ψ^2｜^2 ~- ｜ψ^3｜^2 = 0 and Wl^1= 1. A magnetic flux quantization condition for vortices in a spin-triplet superconductor is also derived, which is topological-invariant. Fhrthermore, the branch processes during the evolution of the vortices in a spin-triplet superconductor are discussed. We also point out that the sum of the magnetic flux quantization that those vortices carried is 2nФo （Фo is the unit magnetic flux）, that is to say, the sum of winding number is even, which needs to be proved by experiment.     

乌药化学成分结构参数与色谱保留时间的关系

乌药含有呋喃倍半萜、黄酮、生物碱、挥发油等多种化学成分,具有抗氧化、抗肿瘤及抑菌等活性.为研究乌药化学成分的性质,计算了乌药化学成分的分子连接性指数和电性拓扑状态指数,并筛选分子连接性指数中的⁰X,⁵X和⁵X_c,以及电性拓扑状态指数中的E₁,E₂和E₃,将这6种结构指数作为神经网络的输入层变量,色谱保留时间作为输出层变量,做回归分析,采用6∶5∶1的神经网络结构,构建了预测能力较强的预测模型.该模型总相关系数r_t为0.994 0,训练集相关系数为0.992 9,测试集相关系数为0.997 0,验证集相关系数为0.997 9,利用该模型计算得到的保留时间预测值与实验值吻合度较好,相对平均误差为2.66%.结果表明,乌药化学成分的色谱保留时间与6种结构参数之间具有良好的非线性关系.     

Alkali-metal-induced topological nodal line semimetalin layered XN2 (X= Cr,Mo, W)

Based on first principles calculations and the K·p effective model, we propose that alkali metal deposition on the surface of hexagonal XN₂ (X= Cr, Mo, W) nanosheets induces topologically nontrivial phases in these systems. When spin orbit coupling (SOC) is disregarded, the electron-like conduction band from N-p_z orbitals can be considered to cross the hole-like valence band from X-d²_z orbitals, thereby giving rise to a topological nodal line state in lithium-functionalized XN₂ sheets (Li₂MoN₂ and Li₂WN₂). Such band crossing is protected by the existence of mirror reflection and time reversal symmetry. More interestingly, the bands cross exactly at the Fermi level, and the linear dispersion regions of such band crossings extend to as high as 0.9 eV above the crossing. For Li₂CrN₂, the results reveal the emergence of a Dirac cone at the Fermi level. Our calculations show that lattice compression decreases the thickness of a Li₂CrN₂ nanosheet, leading to phase transition to a nodal line semimetal. The evolution of the band gap of Li₂XN₂ at the Γ point indicates that the nontrivial topological character of Li₂XN₂ nanolayers is stable over a large strain range. When SOC is included, the band crossing point is gapped out giving rise to quantum spin Hall states in Li₂CrN₂ nanosheets, while for Li₂MoN₂, the SOC-induced gap at the crossing points is negligible.     

Chiral universality class of normal-superconducting and exciton condensation transitions on surface of topological insulator

New two-dimensional systems such as the surfaces of topological insulators (TIs) and graphene offer the possibility of experimentally investigating situations considered exotic just a decade ago. These situations include the quantum phase transition of the chiral type in electronic systems with a relativistic spectrum. Phonon-mediated (conventional) pairing in the Dirac semimetal appearing on the surface of a TI causes a transition into a chiral superconducting state, and exciton condensation in these gapless systems has long been envisioned in the physics of narrow-band semiconductors. Starting from the microscopic Dirac Hamiltonian with local attraction or repulsion, the Bardeen–Cooper–Schrieffer type of Gaussian approximation is developed in the framework of functional integrals. It is shown that owing to an ultrarelativistic dispersion relation, there is a quantum critical point governing the zero-temperature transition to a superconducting state or the exciton condensed state. Quantum transitions having critical exponents differ greatly from conventional ones and belong to the chiral universality class. We discuss the application of these results to recent experiments in which surface superconductivity was found in TIs and estimate the feasibility of phonon pairing.     

Study on local topology model of low/high streak structures in wall-bounded turbulence by tomographic time-resolved particle image velocimetry

The relationship between the bursting event and the low/high-speed streak in the logarithmic law (log-law) region of a turbulent boundary layer is investigated. A tomographic time-resolved particle image velocimetry (TRPIV) system is used to measure the instantaneous three-dimensional-three-component (3D-3C) velocity field. The momentum thickness based Reynolds number is about 2 460. The topological information in the log-law region is obtained experimentally. It is found that the existence of the quadrupole topological structure implies a three-pair hairpin-like vortex packet, which is in connection with the low/high-speed streak. An idealized 3D topological model is then proposed to characterize the observed hairpin vortex packet and low/high-speed streak.     

A computational investigation of topological insulator Bi2Se3 film

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.     

Quantum spin Hall effect in inverted InAs/GaSb quantum wells

We review the recent experimental progress towards observing quantum spin Hall effect in inverted InAs/GaSb quantum wells (QWs). Low temperature transport measurements in the hybridization gap show bulk conductivity of a non-trivial origin, while the length and width dependence of conductance in this regime show strong evidence for the existence of helical edge modes proposed by Liu et al. [Phys. Rev. Lett., 2008, 100: 236601]. Surprisingly, edge modes persist in spite of comparable bulk conduction and show only weak dependence on magnetic field. We elucidate that seeming independence of edge on bulk transport comes due to the disparity in Fermi-wave vectors between the bulk and the edge, leading to a total internal reflection of the edge modes.