Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

Quantum oscillations and nontrivial transport in(Bi_(0.92)In_(0.08))_2Se_3

Quantum phase transition in topological insulators has drawn heightened attention in condensed matter physics and future device applications.Here we report the magnetotransport properties of single crystalline(Bi_(0.92)In_(0.08))_2Se_3.The average mobility of～1000 cm~2·V~(-1)·s~(-1)is obtained from the Lorentz law at the low field(3 T)up to 50 K.The quantum oscillations rise at a field of～5 T,revealing a high mobility of～1.4×10~4cm~2·V~(-1)·s~(-1)at 2 K.The Dirac surface state is evident by the nontrivial Berry phase in the Landau–Fan diagram.The properties make the(Bi_(0.92)In_(0.08))_2Se_3a promising platform for the investigation of quantum phase transition in topological insulators.     

Simulation and detection of massive Dirac fermions with cold atoms in one-dimensional optical lattice

We propose a simple but feasible experimental scheme to simulate and detect Dirac fermions with cold atoms trapped in one-dimensional optical lattice. In our scheme, through tuning the laser intensity, the one-dimensional optical lattice can have two sites in each unit cell and the atoms around the low energy behave as massive Dirac fermions. Furthermore, we show that these relativistic quasiparticles can be detected experimentally by using atomic density profile measurements and Bragg scattering.     

Gauge potential formulations of the spin Hall effect in graphene

Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit interaction is expressed in terms of kinematic momenta by introducing a gauge potential. A formulation of the spin Hall conductivity is established by requiring that the time evolution of this kinematic momentum vector vanishes. We then calculated the conductivity employing the Berry gauge fields. We show that both of the gauge fields can be deduced from the pure gauge field arising from the Foldy-Wouthuysen transformations.     

Manipulation of Dirac points in graphene-like crystals

We review different scenarios for the motion and merging of Dirac points in 2D crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point. For each scenario, we calculate the Landau level spectrum and show that it can be quantitatively described by a semiclassical quantization rule for the constant energy areas. This quantization depends on how many Dirac points are enclosed by these areas. We also emphasize that different scenarios are characterized by different numbers of topologically protected zero energy Landau levels.     

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.     

Crossover from weak localization to Shubnikov-de Haas oscillations in a high-mobility 2D electron gas

We study the magnetoresistance deltarho(xx)(B)/rho(0) of a high-mobility 2D electron gas in the domain of magnetic fields B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where deltarho(xx)(B)/rho(0) is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the second order in the interaction parameter lambda a linear B dependence, deltarho(xx)(B)/rho(0) approximately lambda(2)omega(c)/E(F) with a temperature-independent slope, emerges in this domain of B (here omega(c) and E(F) are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is unrelated to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B dependence of the phase of the impurity-induced Friedel oscillations.     

Observation of π Berry phase in quantum oscillations of three‐dimensional Fermi surface in topological insulator Bi2Se3

We report the quantum transport studies on Bi₂Se₃ single crystal with bulk carrier concentration of ～10¹⁹ cm^–3. The Bi₂Se₃ crystal exhibits metallic character, and at low temperatures, the field dependence of resistivity shows clear Shubnikov–de Haas (SdH) oscillations above 6 T. The analysis of these oscillations through Lifshitz–Kosevich theory reveals a non‐trivial π Berry phase coming from three‐dimensional (3D) Fermi surface, which is a strong signature of Dirac fermions with three‐dimensional dispersion. The large Dingle temperature and non zero slope of Williamson–Hall plot suggest the presence of enhanced local strain field in our system which possibly transforms the regions of topological insulator to 3D Dirac fermion metal state. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

The effect of inertia on the Dirac electron,the spin Hall current and the momentum space Berry curvature

We have studied the spin dependent force and the associated momentum space Berry curvature in an accelerating system. The results are derived by taking into consideration the non-relativistic limit of a generally covariant Dirac equation with an electromagnetic field present, where the methodology of the Foldy–Wouthuysen transformation is applied to achieve the non-relativistic limit. Spin currents appear due to the combined action of the external electric field, the crystal field and the induced inertial electric field via the total effective spin–orbit interaction. In an accelerating frame, the crucial role of momentum space Berry curvature in the spin dynamics has also been addressed from the perspective of spin Hall conductivity. For time dependent acceleration, the expression for the spin polarization has been derived.     

Tunneling of Dirac fermions through magnetic barriers in graphene

We have studied the tunneling of Dirac fermions through magnetic barriers in graphene. Magnetic barriers are produced via delta function-like inhomogeneous magnetic fields in which Dirac fermions in graphene experience the tunneling barrier in the real sense in contrast to Klein paradox caused by electrostatic barriers. The transmission through the magnetic barriers as functions of incident energy and angle of incoming fermions shows characteristic oscillations associated with tunneling resonances. We have also found the confined states in the magnetic barrier region which turn out to correspond to the total internal reflection in the usual optics.     

Characterization of the Fermi surface of the organic superconductor - by measurements of Shubnikov-de Haas and angle-dependent magnetoresistance oscillations and by electronic band-structure calculations

The electronic structure of the quasi two-dimensional (2D) organic superconductor -(ET)₂SF₅CH₂CF₂SO₃ was examined by measuring Shubnikov-de Haas (SdH) and angle-dependent magnetoresistance (AMRO) oscillations and by comparing with electronic band-structure calculations. The SdH oscillation frequencies follow the angular dependence expected for a 2D Fermi surface (FS), and the observed fundamental frequency shows that the 2D FS is 5% of the first Brillouin zone in size. The AMRO data indicate that the shape of the 2D FS is significantly non-circular. The calculated electronic structure has a 2D FS in general agreement with experiment. From the temperature and angular dependence of the SdH amplitude, the cyclotron and band effective masses were estimated to be and ,where g is the conduction electron g factor and the free electron mass. The band effective mass is estimated to be from the calculated electronic band structure. Received: 3 March 1997 / Revised: 5 May 1997 / Received in final form: 5 November 1997 / Accepted: 10 November 1997     

二维六角晶体材料中的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。     

Unconventional field and angle dependences of the Shubnikov-de Haas oscillations spectra in the quasi two-dimensional organic superconductor (BEDO-TTF) 2ReO 4H 2O

We report on the inter-layer oscillatory conductance of the two-dimensional organic superconductor (BEDO-TTF)₂ReO₄H₂O measured in static and pulsed magnetic fields of up to 15 and 52 T, respectively. In agreement with previous in-plane studies, two Shubnikov-de Haas oscillation series linked to the two electron and the hole orbits are observed. The influence of the magnitude and orientation of the magnetic field with respect to the conducting plane is studied in the framework of the conventional two- and three-dimensional Lifshits-Kosevich (LK) model. Deviations of the data from this model are observed in low fields strongly tilted with respect to the normal to the conducting plane. In this latter case, the observed behaviour is consistent with an unexplained lowering of the cyclotron effective mass. At high magnetic field, the oscillatory data could have been compatible with the occurrence of a magnetic breakdown orbit built from the hole and electron orbits. However, the increase of the cyclotron effective mass, linked to the electron orbits, as the magnetic field increases above ∼12 T is consistent with a field-induced phase transition. In the lower field range, where the conventional LK model holds, the analysis of the angle dependence of the oscillations amplitude suggests significant renormalisation of the effective Landé factor. Received 22 August 2000 and Received in final form 20 December 2000     

General solution of the Dirac equation for quasi-two-dimensional electrons

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.     

Beatings of Shubnikov-de Haas oscillations in a two-dimensional hole system in an InGaAs quantum well

The magnetoresistance of an InGaAs/GaAs heterostructure with a two-dimensional hole channel has been measured in quantizing magnetic fields. Beatings of Shubnikov-de Haas oscillations have been observed, which indicate that the spin degeneracy of the system is lifted owing to the spin-orbit interaction. The oscillation pattern is independent of the magnetic field component parallel to the two-dimensional system; this independence is characteristic of size-quantization heavy-hole subbands.     

Quantum transport properties of the three-dimensional Dirac semimetal Cd_3As_2 single crystals

The discovery of the three-dimensional Dirac semimetals have expanded the family of topological materials,and attracted massive attentions in recent few years.In this short review,we briefly overview the quantum transport properties of a well-studied three-dimensional Dirac semimetal,Cd_3As_2.These unusual transport phenomena include the unexpected ultra-high charge mobility,large linear magnetoresistivity,remarkable Shubnikov-de Hass oscillations,and the evolution of the nontrivial Berry's phase.These quantum transport properties not only reflect the novel electronic structure of Dirac semimetals,but also give the possibilities for their future device applications.     

Quantum field as a quantum cellular automaton: The Dirac free evolution in one dimension

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance.