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.     

硅纳米结点电子输运性质的计算

运用第一性原理密度泛函理论结合非平衡格林函数方法,对3个Si原子构成的直线链耦合在Au(100)面形成的三明治结构的纳米结点的电子输运进行计算.结果得到结点电导随距离的变化,当d_z=1.584 nm时,结合能最小,结构最稳定,此时Si-Si键长为0.216 nm,Si-Au键长为0.227 nm,电导为0.729 G₀(G₀=2e²/h),其电子传输通道主要由Si原子的p_x、p_y轨道电子构成;随着外电压的增大,结点的电导减小,而其I-V曲线表现出线性特征.     

高阶Adams公式的系数

当k的值不大时(例如k≤4),诸系数γiγi^*,β_kρ,β_kρ^*易于手工计算。但对大的k值(例如k≥5),手工计算已非易事。利用著名的计算机代数软件:REDUCE^[a],我们可以很容易地计算出诸系数γi,γi^*,β_kρ,β_kρ^*。     

周期磁场调制下的二维电子结构

基于有限差分方法,研究周期梯度磁场调制下二维电子气的电子性质.结果表明:由于周期梯度磁场的存在,体系展现出丰富的电子能带结构.其子带的宽度随|k_y|增大而不断变窄,|k_y|越大势阱越深;由于在k_y > 0和k_y < 0两个区域的有效势能不一样,其能带结构在两个区域不一致且在k_y > 0的区域中形成更多束缚态.通过改变磁条周期、磁条到2DEG的距离及磁化强度研究其对电子能带结构的影响.     

蜂巢光子晶格中光波的无衍射和反常折射

空间频率模式的光子带隙反映了光波在周期性结构中的线性传输特性.以这种线性传输特性为基础,研究了蜂巢光子晶格中光波的无衍射和反常折射.通过详细分析带隙结构第一通带上的衍射与折射特性,得出了光波发生反常衍射和折射的入射条件.匹配不同的入射条件,数值模拟了光波的无衍射传输和反常折射现象.结果表明:将入射光束的波矢设置在蜂巢晶格布里渊区中正常、反常衍射区的交界处,可使高斯光束沿x轴、y轴方向的衍射得到有效抑制;以多光束干涉场作为入射光场,可对蜂巢晶格进行模式匹配,激发第二布里渊区的传输模式;进一步将模式匹配后入射光场的波矢设置在反常折射区,可实现光波的反常折射.     

准周期层状铁磁超晶格的实空间重整化群方法

本文用实空间重整化群方法讨论了准周期层状铁磁超晶格的磁自旋波,用Reduce语言推导了decimation变换公式,从而求得了局域格林函数、局域态密度和约化磁矩。发现局域态密度的带宽和约化磁矩与最近邻相互作用J₁、J₂及格点自旋s_a、s_b密切相关。     

稠苯芳杂环及其烷基质子化学位移的计算

本文提出了予测稠苯芳杂环及其烷基链上质子化学位移的计算方法。 将稠苯芳杂环化合物用凯库勒式表示,计算式为为需考虑的苯环内的乙烯基效应。σ_mi,ci为各苯环的环流效应。σ_1,Hc为各芳杂环的屏蔽效应,对杂环上质子它就是该单独芳杂环上相应质子的δ值,对苯环上质子要将它分解为各结构因素的效应,即:σ_1,He=(1/2)^d-1δ_x=y(或σ_z)+σ_c-c·σ_m,H. σ_x-y与σ_z为杂原子或其基团的屏蔽效应,σ_c=c为存在于芳杂环中的乙烯基的效应,σ_m,Hc为芳杂环的环流效应,d为对不同质子所考虑的键数。有取代基时需考虑取代基的效应。计算环上烷基质子的公式为:δ=σ_p,CH3+ασ_c,CH3+βσ_t,CH3+σ_l,G σ_l,G为稠苯芳杂环基的某级效应。     

太赫兹场和倾斜磁场对超晶格电子动力学特性调控规律研究

微带超晶格在磁场和太赫兹场调控下表现出丰富而复杂的动力学行为, 研究微带电子在外场作用下的输运性质对于太赫兹器件设计与研制具有重要意义. 本文采用准经典的运动方程描述了超晶格微带电子在沿超晶格生长方向(z方向)的THz场和相对于z轴倾斜的磁场共同作用下的非线性动力学特性. 研究表明, 在太赫兹场和倾斜磁场共同作用下, 超晶格微带电子随时间的演化表现出周期和混沌等新奇的运动状态. 采用庞加莱分支图详细研究了微带电子在磁场和太赫兹场调控下的运动规律, 给出了电子运行于周期和混沌运动状态的参数区间. 在电场和磁场作用下, 微带电子将产生布洛赫振荡和回旋振荡, 形成复杂的协同耦合振荡. 太赫兹场与这些协同振荡模式之间的相互作用是导致电子表现出周期态、混沌态以及倍周期分叉等现象的主要原因.     

BaTi2Bi2O的电子结构与磁性

采用第一性原理方法,对BaTi₂Bi₂O的电子结构和磁性进行计算.非磁性态的计算结果显示:费米能级处的态密度主要来自d_z²,d_x²-y²和d_xy三个轨道,同时费米面也主要有三部分组成,并且将其沿着矢量q₁=(π/a,0,0)和q₂=(0,π/a,0)平移时,第三部分费米面(沿着X-R连线)与第一部分费米面(M-A连线)嵌套明显,计算得出磁化系数χ₀(q)在X点出现峰值,与峰值出现在M点的FeAs基超导体不同.上述磁化率峰值可以诱导产生自旋密度波,使得BaTi₂Bi₂O材料的磁性基态是bi-collinear antiferromagnetism(AF3)与blocked checkerboard antiferromagnetism(AF4)的二度简并态.随着空穴掺杂,χ₀(q)的峰值降低,而电子掺杂则导致峰值变大.当自旋涨落被完全压制时,超导出现,这可以解释为什么超导只出现在空穴掺杂型化合物而非电子掺杂型.     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

Incommensurate magnetic structure of CeSi as observed by neutron diffraction

The magnetic ordering of the orthorhombic compound CeSi (Pama space group, FeB type of structure, Z = 4) T_n = 5.6 K was investigated by means of powder neutron diffraction in the temperatures 1.5 and 10 K. Our results show that the magnetic ordering is associated with a three dimensionally amplitude-modulated phase which is incommensurate with the crystal lattice with wave vector q = (q_χ,q_y,q_z). The ordered Ce³⁺ moments are confined to the plane (a,b) at an angle of 16.7° with the b direction. It follows from the present data analysis that the dominant wave vector component is q_z, which approximately corresponds to a transversal modulation, however the incommensurateness involves also the q_x and q_y components. The amplitude of the sine wave is μ⁰_j = 1.667μ_B at 1.5 K which corresponds to quite a reduced ordered moment value compared to the Ce³⁺ free ion value gJ = 2.14μ_B.     

计算自旋-s算子幺正演化矩阵ds(t)的新方法及其应用

提出了一种严格求解任意自旋-s算子幺正演化矩阵的方法,该方法不同于群论的方法和直接计算的方法,是一种间接的算法.方法的核心是利用两个系统表示的等价性：即自旋-s算子Hamiltonian量H_s=S_x与Heisenberg XX开链带相互作用J_n=n(N-n)的Hamiltonian量的等价性,由于存在这种等价性,自旋-s算子幺正演化矩阵的计算可通过Heisenberg XX开链中态的演化来实现.采用该方法计算了s=3/2,s=2和s=5/2时对应的幺正演化矩阵.由于初始态|sm〉在算子e^-itS_x下的演化实质上相当于对态|sm〉进行一个绕x轴转角为β＝t的转动,演化矩阵元d^s_m'm(t)=〈sm′|e^-itS_x|sm〉就是转动后的态e^-itS_x|sm〉在|sm′〉态上的投影值,所以在t＝π时刻的演化矩阵刚好对应Heisenberg XX开链上量子态的理想传输. 关键词： s算子')" href="#">自旋-s算子 幺正演化矩阵 量子态传输     

NFX(X=-1,0,+1)分子离子基态的结构与势能函数

用密度泛函理论的B3LYP方法,分别以6-311++g(df,3pd),6-311g(3d,3p)和6-311++g(3df,3pd)为基函数对NF分子、NF⁺和NF^-离子基态进行几何优化和频率计算,并进行单点能扫描计算.用最小二乘法拟合得到NF^X(X=-1,0,+1)分子离子基态的Murrell-Sorbie势能函数.利用得到的解析势能函数计算出的NF分子和NF⁺离子基态光谱常数(B_e,α_e,ω_e,ω_eχ_e)与实验值符合很好.首次得到NF^-离子基态的光谱常数(B_e,α_e,ω_e,ω_eχ_e)和力常数(f₂,f₃,f₄),为NF-离子基态的后期研究提供理论参考.     

H掺杂α-Fe2O3的第一性原理研究

α-Fe₂O₃是一种重要的磁性半导体材料, 在电子器件中应用广泛, 具有重要的研究意义. 本文基于密度泛函理论, 采用GGA+U方法, 应用第一性原理对间隙H掺杂前后的六方相α-Fe₂O₃的晶格常数、态密度、Bader 电荷分布进行了计算分析. 研究了U值对结果的影响, 发现U=6 eV时, 体相α-Fe₂O₃的晶胞平衡体积、Fe原子磁矩、带隙值与实验值最符合. 在选取合适U值后, 第一性原理计算结果表明, H掺杂后, 间隙H部分被氧化, 其最近邻的Fe 和O部分被还原, H和O有一定程度的成键. 在费米面附近, 出现了新的杂化能级, 杂化能级扩展了价带顶的宽度, 同时导带底下移, 引起带隙减小, 表明H掺杂是一种有效的能带结构调控方法.     

The Arnol''d cat: Failure of the correspondence principle

The classical Hamiltonian H = p²/2m + ε(q²/2)Σδ[s-(t/T)] has an integrable mapping of the plane, [q_n+1, p_n+1]= [q_n+1+p_n, q_n+2p_n], as its equations of motion. But then by introducing periodic boundary conditions via (mod 1) applied to both q and p variables, the equations of motion become the Arnol'd cat map, [q_n+1, p_n+1] = [q_n + p_n, q_n + 2p_n], (mod 1), revealing it to be one of the simplest fully chaotic systems which can be derived from a Hamiltonian and analyzed. Consequently, we here quantize the Arnol'd cat and examine its quantum motion for signs of chaos using algorithmic complexity as the litmus. Our analysis reveals that the quantum cat is not chaotic in the deep quantum domain nor does it become chaotic in the classical limit as required by the correspondence principle. We therefore conclude that the correspondence principle, as defined herein, fails for the quantum Arnol'd cat.     

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.     

单轴压力下Ge2X2Te5(X=Sb,Bi)薄膜拓扑相变的第一性原理研究

随着拓扑绝缘体的发现, 材料拓扑物性的研究成为凝聚态物理研究的热点领域. 本文基于第一性原理计算, 研究了化合物Ge₂X₂Te₅ (X=Sb, Bi) 的块体结构和二维单层和双层薄膜结构的拓扑物性, 以及单双层薄膜在垂直方向单轴压力下的拓扑量子相变. 研究发现, A型原子序列排列的这两种化合物都是拓扑绝缘体, 其单层薄膜都是普通金属, 而双层薄膜都是拓扑金属, 单层和双层薄膜在单轴加压过程中都没有发生拓扑量子相变; 这两种化合物的B型原子序列的晶体是普通绝缘体, 其所对应的薄膜, Ge₂Sb₂Te₅单层是普通金属, 双层薄膜和Ge₂Bi₂Te₅的单层和双层薄膜均为普通绝缘体, 但是在单轴加压过程中B 型原子序列所对应的单层和双层薄膜都转变为拓扑金属.     

Model two-dimensional diffraction profiles from disordered vicinal surfaces and random island configurations

Methods for calculating model diffraction profiles of vicinal surfaces and distributions of islands are described. Modeling of rough terrace edges, and of island structures on terraces, has been performed using phenomenological Hamiltonians. The methods are developed for calculating diffraction profiles in all components, s_x, s_z, and s_y, of the momentum transfer. It is s of step structure irregularities is related to profile shape. Qualitative comparison with experiment is made based on the observed characteristics of terraces obtained from STM and LEED data of vicinal Si(OO1).     

Abnormal breakdown of Stokes–Einstein relation in liquid aluminium

We present the results of systematic molecular dynamics simulations of pure aluminium melt with a well-accepted embedded atom potential. The structure and dynamics were calculated over a wide temperature range, and the calculated results(including the pair correlation function, self-diffusion coefficient, and viscosity) agree well with the available experimental observations. The calculated data were used to examine the Stokes–Einstein relation(SER). The results indicate that the SER begins to break down at a temperature T_x(~1090 K) which is well above the equilibrium melting point(912.5 K).This high-temperature breakdown is confirmed by the evolution of dynamics heterogeneity, which is characterised by the non-Gaussian parameter α_2(t). The maximum value of α 2(t), α_(2,max), increases at an accelerating rate as the temperature falls below Tx. The development of α_(2,max) was found to be related to the liquid structure change evidenced by local fivefold symmetry. Accordingly, we suggest that this high-temperature breakdown of SER has a structural origin. The results of this study are expected to make researchers reconsider the applicability of SER and promote greater understanding of the relationship between dynamics and structure.     

A complete measurement of spin-observables for intermediate-energy inclusive quasielastic polarized proton scattering from C

The complete set of Wolfenstein parameters, the polarization, the asymmetry of scattering and the unpolarized double-differential cross section are presented for inclusive quasielastic proton scattering from ¹²C at a central momentum transfer of q = 1.9 fm⁻¹ and incident energies of 290 and 420 MeV. The spin observables D₀, D_x, D_y and D_z as well as the longitudinal-to-transverse ratio of spin-flip probabilities are extracted from the data. Across the quasielastic continuum, the experimental data is compared to the variations expected from a single-scattering Fermi-gas approximation using the free NN amplitudes. Medium effects are evident in the pronounced quenching of the polarization parameter relative to the free value.