On the theory of Nernst–Ettingshausen oscillations in monolayer and bilayer graphene

The Landau levels in graphene in crossed magnetic and electric fields are dependent on the electric field. However, this effect is not taken into account in many theoretical studies of graphene in crossed fields. In particular, it is not considered in the Nernst–Ettingshausen effect, in which the regime of crossed fields is realized. In this Letter, we considered the Nernst–Ettingshausen effect in monolayer and bilayer graphene, taking into account the dependence of Landau levels on the electric field. We showed that the magnitude and period of the Nernst coefficient oscillations depend on the electric field. This fact is important for the fundamental theory of Nernst–Ettingshausen effect in graphene and gives the new possibility for control of this effect using an applied electric field. The latter is very interesting for practical applications.     

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.     

Nernst-Ettingshausen effect in graphene

The Nernst-Ettingshausen effect corresponds to the regime of crossed magnetic and electric fields. In the current theoretical studies of this effect in graphene, the dependence of the Landau levels on the applied electric field is neglected. This dependence takes place in the case of the nonquadratic energy spectrum of the charge carriers. In this work, oscillations of the Nernst coefficient in graphene with a zero and nonzero band gap have been studied taking into account such dependence. The effect of the Coulomb interaction on these oscillations is considered.     

Dynamic Hall effect driven by circularly polarized light in a graphene layer

We report the observation of the circular ac Hall effect where the current is solely driven by the crossed ac electric and magnetic fields of circularly polarized radiation. Illuminating an unbiased monolayer sheet of graphene with circularly polarized terahertz radiation at room temperature generates--under oblique incidence--an electric current perpendicular to the plane of incidence, whose sign is reversed by switching the radiation helicity. Alike the classical dc Hall effect, the voltage is caused by crossed E and B fields which are, however rotating with the light's frequency.     

Effects of Crossed Electric and Magnetic Fields on Shallow Donor Impurity Binding Energy in a Parabolic Quantum Well

We have calculated variationally the ground state binding energy of a hydrogenic donor impurity in a parabolic quantum well in the presence of crossed electric and magnetic fields. These homogeneous crossed fields are such that the magnetic field is parallel to the heterostructure layers and the electric field is applied perpendicular to the magnetic field. The dependence of the donor impurity binding energy to the well width and the strength of the electric and magnetic fields are discussed. We hope that the obtained results will provide important improvements in device applications, especially for a suitable choice of both fields in the narrow well widths.     

耦合电磁场对石墨烯量子磁振荡的影响

我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应.我们发现,石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱,且当电场与磁场比值超过某一临界值时,量子磁振荡会突然消失,这与非相对论二维电子气的情况显著不同.这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释.此外,我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减.我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用,进而探测自旋轨道耦合引起的能隙.     

Observation of magnetoelectric linear birefringence

We report the first experimental observation of optical linear birefringence induced in molecular liquids by crossed electric and magnetic fields perpendicular to the direction of light propagation. The optical axes coincide with the external fields, and the strength is bilinear in the electric and magnetic fields.     

Towards a test of string theory using Rydberg atoms

The current controversy over the need for an experimental test of String Theory is considered. We report recent experiments on quasi-bound electrons in crossed electric and magnetic fields, in which states of very large electric dipole moment are excited. The excited electron is confined to one side of the atomic nucleus in the outer well of a controllable double-well potential. These states are discussed in relation to a recent theoretical proposal to test the spatial non-commutativity underpinning String Theory by studying Penning orbits of Rydberg atoms in crossed electric and magnetic fields.     

Orbital magnetic moment of a quantum well and a quantum dot in crossed magnetic and electric fields

A new physical effect, namely, oscillations of the orbital magnetic moment with a change in the electric field strength in two types of nanostructures, has been predicted. Explicit analytical expressions for the orbital magnetic moment of a quantum well and a quantum dot in crossed magnetic and electric fields have been derived. The oscillations of the orbital magnetic moment with a change in the electric and magnetic fields have been studied. The oscillation periods in both the electric and magnetic fields have been found and the limiting cases of the strong magnetic and quantum confinement effects have been considered.     

Analysis of the Zeeman effect on the energy spectrum in graphenes

An analysis of the Zeeman effect with a strong external magnetic field on the energy spectrum in graphene is presented. In general, the Hamiltonian of graphene in applied electric and magnetic fields is not of SO(1, 2) invariance even in the nearest-neighbor approximation because of the Zeeman coupling. But an approximate SO(1, 2) invariance can be obtained when the applied magnetic field is very strong. This approximate invariance can be used to relate the energy structure of graphene in the presence of both electric and magnetic fields to that when there is only magnetic field. Therefore, it can help explain the recently found quantum Hall conductance (4q ²/h)L for L = 0.1.     

重叠的环形电场和非均匀磁场质谱分析器的离子光学性质及其二级象差

本文讨论了由环形电场和非均匀磁场形成的重叠场的离子光学问题。运用变分原理(费马原理)给出离子轨迹方程,分析了这种普遍的重叠场作为质谱分析器的离子光学性质及其二级象差。本文的结果和公式对于文献上关于二级象差的理论作了进一步的概括与推广,因而具有普遍性。这对于设计与研究重叠场质谱分析器具有一定的意义。 关键词：     

Electric- and magnetic-field-tuned Landau levels and Hall conductivity in AA-stacked bilayer graphene

We theoretically study the combined effect of magnetic and electric fields on the Landau levels and Hall conductivity in AA-stacked bilayer graphene. From the analytic expressions derived, we obtain explicit criterions for determining the zero-energy Landau level and different level crossings in the graphene bilayer. For providing a scheme of experimental verification, we further explore the quantum Hall effect in such a biased bilayer. It is found that the zero-conductance Hall plateau in this system can vanish at certain specific combinations of magnetic and electric fields, accompanying with the occurrence of resonance Hall conductivity steps.     

Photodetachment of H<Superscript>−</Superscript> ion in crossed gradient electric and magnetic fields

We study the photodetachment of H ^? ion in crossed gradient electric and magnetic fields and put forward an analytical formula for calculating the photodetachment cross-section. Compared to the photodetachment of H ^? ion in a gradient electric field, the Hamiltonian of the detached electron has three degrees of freedom, which makes the dynamical behaviour of the detached electron complex. Photodetachment cross-section for various external fields and the laser polarization are calculated and displayed. A comparison with the photodetachment cross-section in crossed uniform electric and magnetic fields or in a single gradient electric field has been made. The agreement of our results with the above two special cases suggests the correctness of our calculation. Our study may have some potential applications in the photodetachment microscopy experiment or in ion detection.     

Semiconductor electrons in electric and magnetic fields

Optical properties of semiconductors in the simultaneous presence of electric and magnetic fields are reviewed, with particular emphasis on the possibilities of modulation techniques. First, the problem of an electron in crossed and parallel fields is solved in the one-level effective mass approximation (EMA), and the results are used to interpret the experimental interband transitions in Ge, with due account of the degenerate character of the valence band in this material. The limitations of the one-level EMA are discussed, and the two-level model is introduced, which correctly describes the experimentally observed transition from a magnetic type to an electric type of motion in increasing transverse electric field. Possibilities to observe electric field effects in cyclotron resonance transitions are discussed in this approximation. Finally, the three-level model is used to describe properly both orbital and spin properties of conduction electrons. It is demonstrated that in a small-gap semiconductor with large spin-orbit interaction a sufficiently strong transverse electric field destroys the Landau orbital quantization but not the Pauli spin quantization. Possible experimental consequences of this situation are discussed. Influence of finite dimensions of the sample on the character of the electron motion in crossed and parallel fields is examined. A possibility to achieve the semiconductor-semimetal transition in a symmetryinduced zero-gap semiconductor in crossed field configuration is predicted and described, taking into account the Luttinger effects in the magnetic level structure.     

Effect of crossed electric and magnetic fields on donor impurity binding energy

By using an appropriate coordinate transformation, we have calculated variationally the ground state binding energy of a hydrogenic donor impurity in a quantum well in the presence of crossed electric and magnetic fields which are applied tilted at an angle to the layers. The dependence of the donor impurity binding energy on the well width, on the strength of the electric and magnetic fields, on the impurity position and on the directions of the external fields is discussed. PACS 71.55.Eq; 71.55.-i     

Magnetothermoelectric transport in modulated and unmodulated graphene

We draw motivation from recent experimental studies and present a comprehensive study of magnetothermoelectric transport in a graphene monolayer within the linear response regime. We employ the modified Kubo formalism developed for thermal transport in a magnetic field. Thermopower as well as thermal conductivity as a function of the gate voltage of a graphene monolayer in the presence of a magnetic field perpendicular to the graphene plane is determined for low magnetic fields (～1 T) as well as high fields (～8 T). We include the effects of screened charged impurities on thermal transport. We find good qualitative and quantitative agreement with recent experimental work on the subject. In addition, in order to analyze the effects of modulation, which can be induced by various means, on the thermal transport in graphene, we evaluate the thermal transport coefficients for a graphene monolayer subjected to a periodic electric modulation in a magnetic field. The results are presented as a function of the magnetic field and the gate voltage.     

Pattern formation in reaction-diffusion system in crossed electric and magnetic fields

We consider a reaction-diffusion system in crossed electric and magnetic fields lying on the reaction plane. It is shown that a charge separation along the direction normal to the reaction plane resulting in a diffusional flux may cause a differential flow induced chemical instability and stationary pattern formation on a homogeneous steady state. This pattern is generically different from a Turing pattern modified by the crossed fields. The special role of magnetic field is emphasized. Our theoretical analysis is corroborated by numerical simulation on a reaction-diffusion system in three dimensions.     

Is a Fermi-Dirac distribution function for a non-equilibrium electron gas in high crossed electric and magnetic fields possible?

We generalize our investigation of the electron distribution function of anelectron gas interacting with phonons and moving in high crossed electric and magnetic fields. We consider the case of a degenerate gas: we look for conditions under which the distribution function is of a Fermi-Dirac type with an electric and magnetic field dependent temperature.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters $E_r}$ and $\Ga/2$ of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of $10^{-9}-10^{-12}$ for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.