Spin-Magnetic Moment of Dirac Electron, and Role of Zitterbewegung

The spin-magnetic moment of the electron is revisited. In the form of the relativistic quantum mechanics, we calculate the magnetic moment of Dirac electron with no orbital angular-momentum. It is inferred that obtained magnetic moment may be the spin-magnetic moment, because it is never due to orbital motion. A transition current flowing from a positive energy state to a negative energy state in Dirac Sea is found. Application to the band structure of semiconductor is suggested.

Electron transport in Dirac and Weyl semimetals

Recently, the Dirac and Weyl semimetals have attracted extensive attention in condensed matter physics due to both the fundamental interest and the potential application of a new generation of electronic devices. Here we review the exotic electrical transport phenomena in Dirac andWeyl semimetals. Section 1 is a brief introduction to the topological semimetals（TSMs）. In Section 2 and Section 3, the intriguing transport phenomena in Dirac semimetals（DSMs） andWeyl semimetals（WSMs） are reviewed, respectively. The most widely studied Cd_3A_（s2） and the TaAs family are selected as representatives to show the typical properties of DSMs and WSMs, respectively. Beyond these systems, the advances in other TSM materials,such as ZrTe_5 and the MoTe_2 family, are also introduced. In Section 4, we provide perspectives on the study of TSMs especially on the magnetotransport investigations.

A Physical Insight into the Origin of the Corrections to the Magnetic Moment of Free and Bound Electron

The main goal of the present work is a unitary approach of the physical origin of the corrections to the magnetic moment of free and bound electron. Based on this approach, estimations of lowest order corrections were easily obtained. In the non-relativistic limit, the Dirac electron appears as a distribution of charge and current extended over a region of linear dimension of the order of Compton wavelength, which generates its magnetic moment. The e.m. mass (self-energy) of electron outside this region does not participate to this internal dynamics, and consequently does not contribute to the mass term in the formula of the magnetic moment. This is the physical origin of the small increase of the magnetic moment of free electron compared to the value given by Dirac equation. We give arguments that this physical interpretation is self-consistent with the QED approach. The bound electron being localized, it has kinetic energy which means a mass increase from a relativistic point of view, which determines a magnetic moment decrease (relativistic Breit correction). On the other hand, the e.m. mass of electron decreases at the formation of the bound state due to coulomb interaction with the nucleus. We estimated this e.m. mass decrease of bound electron only in its internal dynamics region, and from it the corresponding increase of the magnetic moment (QED correction). The corrections to the mass value are at the origin of the lowest order corrections to the magnetic moment of free and bound electron.

On Zitterbewegung of Electron

Traditionally, all the discussions relativistic quantum mechanics. In this article, on zitterbewegung （zbw） of electron are based on from the viewpoint of quantum field theory and in terms of the creation and annihilation operators as well as the polarization vectors of spin-1 field, a more detailed description and some new perspectives for zbw are obtained. Especially, it is shown that zbw arises from a to-and-fro vacuum polarization that occurring in the neighborhood of electron; the zbw vectors form a vector triplet with total spin projections 0 and ±1 in the direction of the momentum of electron, respectively; the macroscopic velocity of the vacuum medium vanishes in all inertial systems.

二维六角角晶体材料中的Dirac电子

本文综述由碳、硅、硼氮和二硫化钼等单元素或双元素构成的二维六角晶体材料中Dirac电子的研究成果与最新进展。文章从引言开始,接着介绍这些二维六角晶体材料的空间结构和基本电子性质;然后探讨外场调控下这些材料在能谱和光吸收、量子输运、激子凝聚和热Josephson效应,以及拓扑量子相变等方面所表现出来的新奇的物理现象、简要的理论处理和可能的应用前景;最后给出二维六角晶体材料相关研究的总结和展望。谨以本文献给南京大学建立物理学科100周年。

无序对准一维矢势束缚中无质量Dirac电子的影响

通过有限差分的方法,数值计算了一个相对论性质的Dirac电子在磁场和无序同时存在时的能谱结构,并讨论了不同磁场强度和无序强度时电子密度分布的变化情况.结果发现:随着无序强度的增大,无序势削弱了磁场对电子的捕获,使局域化现象减弱,使得无质量Dirac电子出现了有别于Anderson局域化的现象.

Effects of electron correlation and the Breit interaction on one- and two-electron one-photon transitions in double K hole states of He-like ions(10 ≤ Z ≤ 47)

The x-ray energies and transition rates associated with single and double electron radiative transitions from the double K hole state 2s2p to the 1s2s and 1s^2 configurations of 11 selected He-like ions(10 ≤ Z ≤ 47) are calculated using the fully relativistic multi-configuration Dirac–Fock method(MCDF). An appropriate electron correlation model is constructed with the aid of the active space method, which allows the electron correlation effects to be studied efficiently. The contributions of the electron correlation and the Breit interaction to the transition properties are analyzed in detail. It is found that the two-electron one-photon(TEOP) transition is correlation sensitive. The Breit interaction and electron correlation both contribute significantly to the radiative transition properties of the double K hole state of the He-like ions. Good agreement between the present calculation and previous work is achieved. The calculated data will be helpful to future investigations on double K hole decay processes of He-like ions.

A Variational Approach for Numerically Solving the Two-Component Radial Dirac Equation for One-Particle Systems

In this paper we propose a numerical approach to solve the relativistic Dirac equation suitable for computational calculations of one-electron systems. A variational procedure is carried out similar to the well-known Hylleraas computational method. An application of the method to hydrogen isoelectronic atoms is presented, showing its consistency and high accuracy, relative to the exact analytical eigenvalues.

Two-electron and one-photon transitions in highly charged nickel-like ions

This paper calculates the transition wavelengths and probabilities of the two-electron and one-photon （TEOP） transition from the （3s1/2^-14dj）J=1,2 to （3P3/2^-14s1/2）J=1 and the （3P1/2^-14s1/2）J=1 to （3dj^-14dj＇）J=1,2 for highly charged Ni-like ions with atomic number Z in the range 47 〈 Z 〈 92. In the calculations, the multi-configuration Dirac-Fock method and corresponding program packages GRASP92 and REOS99 were used, and the relativistic effects, correlation effects and relaxation effects were considered systematically. It is found that the TEOP transitions are very sensitive to the correlation of electrons, and the probabilities will be enhanced sharply in some special Z regions along the isoelectronic sequence. The present TEOP transition wavelengths are compared with the available data from some previous publications, good agreement is obtained.

Electron Dynamics in Solids

Following Ashcroft and Mermin, the conduction electrons (“electrons” or “holes”) are assumed to move as wave packets. Dirac’s theorem states that the quantum wave packets representing massive particles always move, following the classical mechanical laws of motion. It is shown here that the conduction electron in an orthorhombic crystal moves classical mechanically if the primitive rectangular-box unit cell is chosen as the wave packet, the condition requiring that the particle density is constant within the cell. All crystal systems except the triclinic system have k-vectors and energy bands. Materials are conducting if the Fermi energy falls on the energy bands. Energy bands and gaps are calculated by using the Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2 is a transition between conductors having three-dimensional and one-dimensional k-vectors.

Fermi-Dirac and Bose-Einstein Integrals and Their Applications to Resistivity in Some Magnetic Alloys, Part III

The Fermi-Dirac (FD) and Bose-Einstein (BE) integrals were applied to a quantum system to estimate the density of particles and relaxation time in some magnetic alloys at low temperatures. An integral part in the energy equations of vibrations (phonons), spin waves (magnons), and electrons was mathematically treated. Comparison between theoretical and experimental results gave good semi-empirical relations and some physical constants.

Relativistic Gauge Invariant Wave Equation of the Electron-Neutrino

With the right and the left waves of an electron, plus the left wave of its neutrino, we write the tensorial densities coming from all associations of these three spinors. We recover the wave equation of the electro-weak theory. A new non linear mass term comes out. The wave equation is form invariant, then relativistic invariant, and it is gauge invariant under the U(1)×SU(2), Lie group of electro-weak interactions. The invariant form of the wave equation has the Lagrangian density as real scalar part. One of the real equations equivalent to the invariant form is the law of conservation of the total current.

Resonance enhanced electron impact excitation for P-like Cu XV

Employing both the Dirac R-matrix and the relativistic distorted wave with independent process and isolated reso- nance approaches, we report resonance enhanced electron impact excitation data （specifically, effective collision strengths） among the lowest 41 levels from the n = 3 configurations of Cu XV. The results show that the latter approach can obtain resonance contributions reasonably well for most excitations of Cu XV, though a comparison between the two approaches shows that the close-coupling effects are truly significant for rather weak excitations, especially for two-electron excitations from the 3s3p4 to 3s23p23d configuration. Resonance contributions are significant （more than two orders of magnitude） for many excitations and dramatically influence the line intensity ratios associated with density diagnostics.

Electronic Band Structure of Graphene Based on the Rectangular 4-Atom Unit Cell

The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.

论固体膜形成纳米管的机理(英文)

Oliver G.Schmidt和Karl Eberl在自然杂志上发表了1个重要的发现:几乎对于任何材料的固体薄膜,一旦薄膜从基体上剥离开,几乎在任意部位都可以形成纳米管,这个试验结果可以用TFDC(托马斯-费米尔-迪拉克-程氏)电子理论来解释。

锗烯在金属衬底上的结构及电子性质的第一性原理研究

基于密度泛函理论的第一性原理计算,我们系统的研究了锗烯在Pt(111)、Au(111)和Al(111)表面的几何和电子结构.在这三种金属衬底上寻找到了9种结构,其中Al(111)-a、Au(111)-b和Pt(111)-c结构就是目前实验上已经成功制备的结构.我们还发现了其余6种目前理论和实验均没有提出,此外,Al(111)-b、Au(111)-a和Pt(111)-b结构的Dirac态仍保留,这些结构的形成能均大于范德瓦尔斯作用,因此非常有希望在实验上制备出来,应用于量子自旋霍尔效应的研究.本文的研究为锗烯在半导体衬底上的制备及应用奠定了理论基础.

原子相对论波函数的平均自洽场计算

利用Dirac-Slater相对论自洽场理论研究了原子中电子的相对论波函数,说明了其主要特征:电子相对论波函数大小分量的变化趋势不完全"同步",即核外电子的分布没有严格的零几率点;通常电子相对论波函数的大小分量相差非常悬殊,但当束缚电子波函数的空间压缩较为严重、或自由电子的动能较大时,其相对论波函数的小分量的相对值就会增大,并在此基础上分析了束缚电子与自由电子波函数的主要异同点.

Zitterbewegung in quantum field theory

Traditionally, the zitterbewegung （ZB） of the Dirac electron has just been studied at the level of quantum mechanics. Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic, graphene, and superconducting systems, etc., this paper presents a quantum-field-theory investigation on ZB and obtains the conclusion that, the ZB of an electron arises from the influence of virtual electron-positron pairs （or vacuum fluctuations） on the electron.

二维无质量狄拉克电子朗道能级的解析处理

从量子力学的基本概念出发,在朗道规范和对称规范两种规范变换下,借助特殊函数方程理论,推导出单层石墨中二维无质量狄拉克电子朗道能级的解析表达式,并讨论它与通常二维电子气中薛定谔型电子的朗道能谱间存在的差异.

论共晶结构的机理

本文是Thomas-Fermi-Dirac-Cheng电子理论对共晶机理的阐述。提出了薄膜两组元之间的化学势差和电子密度差导致系统总能量改变的新思想,给出了研究稳定共晶态的最佳尺寸和能量的方法。