Landau levels in graphene in the presence of emergent gravity

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.     

Emergent Horava gravity in graphene

First of all, we reconsider the tight-binding model of monolayer graphene, in which the variations of the hopping parameters are allowed. We demonstrate that the emergent 2D$2D$ Weitzenbock geometry as well as the emergent U(1)$U\left(1\right)$ gauge field appear. The emergent gauge field is equal to the linear combination of the components of the zweibein. Therefore, we actually deal with the gauge fixed version of the emergent 2+1$2+1$   D$D$ teleparallel gravity. In particular, we work out the case, when the variations of the hopping parameters are due to the elastic deformations, and relate the elastic deformations with the emergent zweibein. Next, we investigate the tight-binding model with the varying intralayer hopping parameters for the multilayer graphene with the ABC$ABC$ stacking. In this case the emergent 2D$2D$ Weitzenbock geometry and the emergent U(1)$U\left(1\right)$ gauge field appear as well, and the emergent low energy effective field theory has the anisotropic scaling.     

Novel electric field effects on Landau levels in graphene

A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.     

Torsional Weyl-Dirac Electrodynamics

Issuing from a geometry with nonmetricity and torsion we build up a generalized classical electrodynamics. This geometrically founded theory is coordinate covariant, as well as gauge covariant in the Weyl sense. Photons having arbitrary mass, intrinsic magnetic currents, (magnetic monopoles), and electric currents exist in this framework. The field equations, and the equations of motion of charged (either electrically or magnetically) particles are derived from an action principle. It is shown that the interaction between magnetic monopoles is transmitted by massive photons. On the other hand, the photon is massive only in the presence of magnetic currents. We obtained a static spherically symmetric solution, describing either the Reissner-Nordstrom metric of an electric monopole, or the metric and field of a magnetic monopole. The latter must be massive. In the absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory.     

Valley filtering due to orbital magnetic moment in bilayer graphene

We investigate the effect of valley-dependent orbital magnetic moment on the transmission of quasiparticles through biased bilayer graphene npn and pnp junctions in the presence of out-of-plane magnetic field. It is shown that the valley-polarized Zeeman-like energy splitting, due to the interaction of orbital magnetic moment with magnetic field, can suppress the transmission of quasiparticles of one valley while transmitting those of the other valley. This valley-selective transmission property can be exploited for valley filtering. We demonstrate that the npn and pnp junction, respectively, filters off the $K^{\prime }$-valley and K-valley particles, with nearly perfect degree of filtration.     

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.     

Possible Mechanism of Plasticity Influenced by Magnetic Field

The strain energy of an edge dislocation in an external static magnetic field is determined by the theory of elasticity and electrodynamics according to the Volterra dislocation model for continuous media. The results show that the strain energy of the edge dislocation in paramagnetic states is increased due to static magnetic field and the increase in the energy of the dislocation is capable of influencing the dislocation depinning which leads to the change of plasticity. This gives an explanation on plasticity induced by magnetic field.     

Electromagnetic-field-induced suppression of transport through n-p junctions in graphene

We study electronic transport through an n-p junction in graphene irradiated by an electromagnetic field (EF). In the absence of EF one may expect the perfect transmission of quasiparticles flowing perpendicular to the junction. We show that the resonant interaction of propagating quasiparticles with the EF induces a dynamic gap between electron and hole bands in the quasiparticle spectrum of graphene. In this case the strongly suppressed quasiparticle transmission is only possible due to interband tunneling. The effect may be used to control transport properties of diverse structures in graphene, e.g., n-p-n transistors and quantum dots, by variation of the intensity and frequency of the external radiation.     

Aharonov-Bohm and non-inertial effects on a Klein-Gordon oscillator with potential in the cosmic string space-time with a spacelike dislocation

In this paper, we investigate the analogue effect to the Aharonov-Bohm effect for bound states in a relativistic quantum system described by the Klein-Gordon oscillator in the cosmic string space-time with a spacelike dislocation. We assume the topological defects have an internal magnetic flux and then analyze the effect on the relativistic energy eigenvalue subject to a Cornell-type potential and subsequently with a Coulomb-type potential. We show the presence of various potential parameters, the torsion parameter as well the cosmic string modify the energy spectrum.     

Gravity theory on Poisson manifold with R‐flux

A novel gravity theory based on Poisson Generalized Geometry is investigated. A gravity theory on a Poisson manifold equipped with a Riemannian metric is constructed from a contravariant version of the Levi‐Civita connection, which is based on the Lie algebroid of a Poisson manifold. Then, we show that in Poisson Generalized Geometry the R‐fluxes are consistently coupled with such a gravity. An R‐flux appears as a torsion of the corresponding connection in a similar way as an H‐flux which appears as a torsion of the connection formulated in the standard Generalized Geometry. We give an analogue of the Einstein‐Hilbert action coupled with an R‐flux, and show that it is invariant under both β‐diffeomorphisms and β‐gauge transformations.     

Scalar torsion and a new symmetry of general relativity

We reformulate the general theory of relativity in the language of Riemann–Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed with torsion. In this new framework, the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field. We show that in this formulation general relativity has a new kind of invariance, whose invariance group consists of a set of conformal and gauge transformations, called Cartan transformations. These involve both the metric tensor and the torsion vector field, and are similar to the well known Weyl gauge transformations. By making use of the concept of Cartan gauges, we show that, under Cartan transformations, the new formalism leads to different pictures of the same gravitational phenomena. We illustrate this fact by looking at the one of the classical tests of general relativity theory, namely the gravitational spectral shift. Finally, we extend the concept of space-time symmetry to Riemann–Cartan space-times with scalar torsion and obtain the conservation laws for auto-parallel motions in a static spherically symmetric vacuum space-time in a Cartan gauge, whose orbits are identical to Schwarzschild orbits in general relativity.     

Heisenberg groups and noncommutative fluxes

We develop a group-theoretical approach to the formulation of generalized abelian gauge theories, such as those appearing in string theory and M-theory. We explore several applications of this approach. First, we show that there is an uncertainty relation which obstructs simultaneous measurement of electric and magnetic flux when torsion fluxes are included. Next, we show how to define the Hilbert space of a self-dual field. The Hilbert space is Z₂-graded and we show that, in general, self-dual theories (including the RR fields of string theory) have fermionic sectors. We indicate how rational conformal field theories associated to the two-dimensional Gaussian model generalize to (4k + 2)-dimensional conformal field theories. When our ideas are applied to the RR fields of string theory we learn that it is impossible to measure the K-theory class of a RR field. Only the reduction modulo torsion can be measured.     

变形及电场作用对石墨烯电学特性影响的第一性原理计算

利用基于密度泛函理论的第一性原理方法,系统研究了变形、电场及共同作用对石墨烯电学特性影响的电子机理.研究表明,本征石墨烯的能隙及态密度值在费米能级处均为0,呈现出半金属特性;在一定的变形量下对石墨烯施加剪切、拉伸、扭转及弯曲变形作用,发现剪切和扭转变形对打开石墨烯能隙的作用明显;对本征石墨烯施加不同方向的电场,可知010电场方向对打开石墨烯能隙的作用效果最强.这是因为该电场方向下石墨烯C-C原子间的布居数正值较大,成键键能较高,而负值数值较小,反键键能较低;线性增加电场强度,石墨烯的能隙呈线性增长势;变形及电场共同作用下,外加电场提高了变形对打开石墨烯能隙的作用效果,但不及两种外场叠加的作用效果.     

Torsion effects on condensed matter: like a magnetic field but not so much

In this work, we study the effects of torsion due to a uniform distribution of topological defects (screw dislocations) on free spin/carrier dynamics in elastic solids. When a particle moves in such a medium, the effect of the torsion associated to the defect distribution is analogous to that of an applied magnetic field but with subtle differences. Analogue Landau levels are present in this system but they cannot be confined to two dimensions. In the case of spinless carriers, zero modes, which do not appear in the magnetic Landau levels, show up for quantized values of the linear momentum projected on the defects axis. Particles with spin are subjected to a Zeeman-like coupling between spin and torsion, which is insensitive to charge. This suggests the possibility of spin resonance experiments without a magnetic field for charged carriers or quasiparticles without electrical charge, like triplet excitons, for instance.     

磁致塑性效应下的位错动力学机制

基于磁致塑性效应探讨了磁场作用下位错受力和运动机制, 对磁场下的位错动力学机制进行了定性和定量分析. 选择氧化铝纳米颗粒强化铝基复合材料为实验对象, 在不同磁感应强度下(0–3 T范围)对试样进行磁场处理. 结果表明, 随着磁感应强度增加, 位错密度提高, 表现出塑性变形特征. 分析认为, 磁场力不足以驱动位错运动, 位错增殖诱因在于磁致塑性效应, 即磁场改变了顺磁性位错芯与障碍间自由基对中的电子自旋状态, 促使自由基对从强键结合单线态向弱键结合三重态转化, 位错穿越障碍时所需能量减小, 退钉扎趋势明显; 位错运动中的限速环节是位错在障碍处的停留, 磁场诱发的电子激发和原子重排速度很快, 表现出磁场作用的高效性. 磁场起作用的临界磁感应强度约为3 T, 低于3 T时磁场作用随磁场强度增加而变得明显, 高于3 T 后磁场效果会减小. 计算得到3 T 时位错运动速度是10^-3 m/s, 位错线长度比未加磁场时增加两个数量级, 位移与磁感应强度平方和磁场作用时间成正比. 实验和理论研究表明磁场具有改善材料塑性变形能力的显著作用.     

Aharonov-Bohm superperiod in a Laughlin quasiparticle interferometer

We report an Aharonov-Bohm superperiod of five magnetic flux quanta (5h/e) observed in a Laughlin quasiparticle interferometer, where an edge channel of the 1/3 fractional quantum Hall fluid encircles an island of the 2/5 fluid. This result does not violate the gauge invariance argument of the Byers-Yang theorem because the magnetic flux, in addition to affecting the Aharonov-Bohm phase of the encircling 1/3 quasiparticles, creates the 2/5 quasiparticles in the island. The superperiod is accordingly understood as imposed by the anyonic statistical interaction of Laughlin quasiparticles.     

A charged Taub-NUT metric with torsion: A new axially symmetric solution of the poincare gauge field theory

Within the framework of the Poincaré gauge field theory, McCrea has recently discovered a Taub-NUT-like metric with torsion. The metric is axially symmetric, whereas the torsion turns out to be SO(3)-symmetric. We find the corresponding solution with an additional electric charge.