Wave-vector filtering effect of electric–magnetic barrier in HgTe quantum wells

Because of helicity of electrons in HgTe quantum wells (QWs) with inverted band structure, the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in HgTe QWs. This behavior is similar to Dirac electrons in graphene. In this paper, we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier. We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers. The confining effect will have potential application in nanodevices based on HgTe QWs.     

Wave-vector filtering effect of the electric-magnetic barrier in HgTe quantum wells

Because of the helicity of electrons in HgTe quantum wells(QWs) with inverted band structures,the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in the HgTe QWs.This behavior is similar to Dirac electrons in graphene.In this paper,we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier.We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers.The confining effect will have a potential application in nanodevices based on HgTe QWs.     

Planar Dirac electrons in magnetic quantum dots

In this paper, we explore the size- and mass-dependent energy spectra and the electronic correlation of two- and three-electron graphene magnetic quantum dots. It is found that only the magnetic dots with large size can well confine the electrons. For large graphene magnetic dots with massless (ultra-relativity) electrons, the energy level structures of two Dirac electrons and even the ground state spin and angular momentum of three electrons are quite different from those of the usual semiconductor quantum dots. Also we reveal that such differences are not due to the magnetic confinement but originate from the character of the Coulomb interaction of two-component electronic wavefunctions in graphene. We reveal that the increase of the mass leads to both the crossover of the energy spectrum structures from the ultra-relativity to non-relativity ones and the increasing of the crystallization. The results are helpful for the understanding of the mass and size effects and may be useful in controlling the few-electron states in graphene-based nanodevices.     

Magnetic barriers and confinement of Dirac-Weyl quasiparticles in graphene

We discuss the properties of the two-dimensional massless Dirac-Weyl quasiparticles realized in graphene monolayers in the presence of inhomogeneous magnetic fields. We show that in contrast to electrostatic barriers, appropriate magnetic barriers are able to confine these quasiparticles. This allows for a novel way of designing mesoscopic structures (e.g., quantum dots, quantum point contacts) in graphene.     

Echoes of relativistic Landau levels in graphene and bilayer graphene

The problem of echo effects that can originate in graphene and bilayer graphene upon the generation of relativistic Landau levels in a quantizing magnetic field is considered. Graphene (bilayer graphene) is considered in a long-wave approximation near the Dirac points. It is proposed that the echo effect be used for the quantum memory of optical states in the far infrared.     

Two-dimensional quantum ring in a graphene layer in the presence of a Aharonov–Bohm flux

In this paper we study the relativistic quantum dynamics of a massless fermion confined in a quantum ring. We use a model of confining potential and introduce the interaction via Dirac oscillator coupling, which provides ring confinement for massless Dirac fermions. The energy levels and corresponding eigenfunctions for this model in graphene layer in the presence of Aharonov–Bohm flux in the centre of the ring and the expression for persistent current in this model are derived. We also investigate the model for quantum ring in graphene layer in the presence of a disclination and a magnetic flux. The energy spectrum and wave function are obtained exactly for this case. We see that the persistent current depends on parameters characterizing the topological defect.     

点缺陷扶手型石墨烯量子点的电子性质研究

基于有限差分方法, 数值求解了Dirac方程, 研究了垂直磁场下的点缺陷扶手型 石墨烯 量子点的能谱结构, 分析了尺寸大小对带隙的影响. 与无磁场时具有一定带隙 (带隙的大小与半径成反比) 的量子点相比, 在外加有限磁场下, 能谱中出现朗道能级, 最低朗道能级能量为零并与磁场强度无关, 并且朗道能级的简并度随着磁场的增加而增加. 进一步的计算表明, 最低朗道能级的简并度与磁场成线性关系, 与半径的平方成线性关系. 本文工作对基于石墨烯量子点的器件设计具有一定的指导意义.     

石墨烯量子磁输运性质的电场效应

最近研究发现石墨烯在一维周期性电学或磁学调制势下,其扩散电导率会出现Weiss振荡.本文进一步探索了面外加垂直磁场和面内加横向电场以及一维周期性弱调制电学势的多场耦合作用下,石墨烯的量子磁输运性质,结果表明:Weiss振荡振幅和电导率数值都随着静电场的增加而增加.有趣的是,当电场与磁场的比值达到某一临界值,即β_1=E/(ν_F·B)=1时,输运电导率的Weiss振荡突然消失.这一奇特现象在传统的二维电子气体中是不存在的,因此可以归因于石墨烯载流子外加电磁场的反常相对论性能谱.     

Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field

We show that the recently discovered double-valley splitting of the Landau levels in the quantum Hall effect in graphene can be explained as the perturbative orbital interaction of intravalley and intervalley microscopic orbital currents with a magnetic field. This effect is facilitated by the translationally noninvariant terms that correspond to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac fermions in quantum electrodynamics. We discuss recent data in view of these findings.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

The enigma of the quantum Hall effect in graphene

We apply Laughlin’s gauge argument to analyze the ν=0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν=0 quantized Hall effect. We argue that this ν=0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.     

Persistent currents in a graphene ring with armchair edges

A graphene nanoribbon with armchair edges is known to have no edge state. However, if the nanoribbon is in the quantum spin Hall state, then there must be helical edge states. By folding a graphene ribbon into a ring and threading it by a magnetic flux, we study the persistent charge and spin currents in the tight-binding limit. It is found that, for a broad ribbon, the edge spin current approaches a finite value independent of the radius of the ring. For a narrow ribbon, inter-edge coupling between the edge states could open the Dirac gap and reduce the overall persistent currents. Furthermore, by enhancing the Rashba coupling, we find that the persistent spin current gradually reduces to zero at a critical value beyond which the graphene is no longer a quantum spin Hall insulator.     

Theory of magnetic oscillations in Weyl semimetals

Weyl semimetals are a new class of Dirac material that possesses bulk energy nodes in three dimensions, in contrast to two dimensional graphene. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We find distinct behavior that can be used to identify materials containing three dimensional Dirac fermions. We derive expressions for the density of states, electronic specific heat, and the magnetization. We focus our attention on the quantum oscillations in the magnetization. We find phase shifts in the quantum oscillations that distinguish the Weyl semimetal from conventional three dimensional Schrödinger fermions, as well as from two dimensional Dirac fermions. The density of states as a function of energy displays a sawtooth pattern which has its origin in the dispersion of the three dimensional Landau levels. At the same time, the spacing in energy of the sawtooth spike goes like the square root of the applied magnetic field which reflects the Dirac nature of the fermions. These features are reflected in the specific heat and magnetization. Finally, we apply a simple model for disorder and show that this tends to damp out the magnetic oscillations in the magnetization at small fields.     

石墨烯量子磁输运性质的电场效应

最近研究发现石墨烯在一维周期性电学或磁学调制势下, 其扩散电导率会出现Weiss振荡. 本文进一步探索了面外加垂直磁场和面内加横向电场以及一维周期性弱调制电学势的多场耦合作用下, 石墨烯的量子磁输运性质, 结果表明: Weiss振荡振幅和电导率数值都随着静电场的增加而增加. 有趣的是, 当电场与磁场的比值达到某一临界值, 即时, 输运电导率的Weiss振荡突然消失. 这一奇特现象在传统的二维电子气体中是不存在的, 因此可以归因于石墨烯载流子外加电磁场的反常相对论性能谱. 关键词：石墨烯; 静电场; Weiss振荡; 磁输运性质     

石墨烯量子磁输运性质的电场效应

最近研究发现石墨烯在一维周期性电学或磁学调制势下, 其扩散电导率会出现Weiss振荡. 本文进一步探索了面外加垂直磁场和面内加横向电场以及一维周期性弱调制电学势的多场耦合作用下, 石墨烯的量子磁输运性质, 结果表明: Weiss振荡振幅和电导率数值都随着静电场的增加而增加. 有趣的是, 当电场与磁场的比值达到某一临界值, 即时, 输运电导率的Weiss振荡突然消失. 这一奇特现象在传统的二维电子气体中是不存在的, 因此可以归因于石墨烯载流子外加电磁场的反常相对论性能谱. 关键词：石墨烯; 静电场; Weiss振荡; 磁输运性质     

Bound states in disclinated graphene with Coulomb impurities in the presence of a uniform magnetic field

In this contribution, we study the effects caused by an impurity on the quantum dynamics of massive excitations in a disclinated graphene in the presence of an external magnetic field. Within a continuum approach, the problem is mathematically modeled by the definition of a special vector potential containing all the information about the topology and the interacting fields. The presence of disclination is introduced by a term in the Dirac equation that translates the appearance of a phase associated with the transport of the spinor around the apex of the cone. We solve exactly the Dirac equation for this problem and the eigenvalues are obtained. We observe the influence of the disclination on the spectrum of energy and the allowed values of magnetic field.     

石墨烯莫尔超晶格

石墨烯莫尔超晶格来源于六方氮化硼衬底对石墨烯的二维周期势调控. 由于这种外加的周期势对石墨烯能带具有显著的调制作用, 近年来引发了人们广泛的关注. 利用氮化硼衬底上外延的单晶石墨烯薄膜, 我们系统研究了基底调制下的莫尔超晶格以及相关的物理特性. 首先, 我们在电子端和空穴端都观测到了超晶格狄拉克点, 并且超晶格狄拉克点同本征狄拉克点类似, 都表现出绝缘体的特性. 在低温强磁场下, 可以观测到到单层石墨烯和双层石墨烯的量子霍尔效应. 并且, 从朗道扇形图中, 可以清晰的看到磁场下形成的超晶格朗道能级. 此外, 利用红外光谱的方法研究了强磁场下石墨烯超晶格体系不同朗道能级之间的跃迁, 发现这种跃迁满足有质量狄拉克费米子的行为, 对应38 meV的本征能隙. 在此基础上, 我们在380 meV位置发现一个同超晶格能量对应的光电导峰. 通过利用旋量势中三个不同的势分量对光电导峰进行拟合, 发现赝自旋杂化势起主导作用. 进一步研究表明赝自旋杂化势强度随载流子浓度的增大显著降低, 表明电子-电子相互作用引起的旋量势的重构.     

Quantum Hall states near the charge-neutral Dirac point in graphene

We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors nu=+/-1 depend only on the perpendicular component of the field with respect to the graphene plane, indicating that they are not spin related. A nonlinear magnetic field dependence of the activation energy gap at filling factor nu=1 suggests a many-body origin. We therefore propose that the nu=0 and +/-1 states arise from the lifting of the spin and sublattice degeneracy of the n=0 Landau level, respectively.     

Topological aspects of graphene

Topological aspects of the electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i) Presence of the pair of massless Dirac dispersions, which is the origin of anomalous properties including a peculiar quantum Hall effect (QHE), is not accidental to honeycomb, but is generic for a class of two-dimensional lattices that interpolate between square and π-flux lattices. Topological stability guarantees persistence of the peculiar QHE. (ii) While we have the massless Dirac dispersion only around E=0, the anomalous QHE associated with the Dirac cone unexpectedly persists for a wide range of the chemical potential. The range is bounded by van Hove singularities, at which we predict a transition to the ordinary fermion behaviour accompanied by huge jumps in the QHE with a sign change. (iii) We establish a coincidence between the quantum Hall effect in the bulk and the quantum Hall effect for the edge states, which is another topological effect. We have also explicitly shown that the E=0 edge states in honeycomb in zero magnetic field persist in magnetic field. (iv) We have also identified a topological origin of the fermion doubling in terms of the chiral symmetry.