Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.     

Landau level spectrum for bilayer graphene in a tilted magnetic field

We consider a graphene bilayer in a constant magnetic field of arbitrary orientation, i.e., tilted with respect to the graphene plane. In the low energy approximation to the tight-binding model with Peierls substitution, we find the Landau level spectrum analytically in terms of spheroidal functions and the respective eigenvalues. We compare our result to the perpendicular and purely in-plane field cases. In the limit of perpendicular field we reproduce the known equidistant spectrum for Landau levels. In the opposite limit of large in-plane field this spectrum becomes two-fold degenerate, which is a consequence of Dirac point splitting induced by the in-plane field.     

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.     

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.     

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.     

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.     

Unusual microwave response of dirac quasiparticles in graphene

Recent experiments have proven that the quasiparticles in graphene obey a Dirac equation. Here we show that microwaves are an excellent probe of their unusual dynamics. When the chemical potential is small, the intraband response can exhibit a cusp around zero frequency Omega and this unusual line shape changes to Drude-like by increasing the chemical potential |mu|, with width linear in mu. The interband contribution at T=0 is a constant independent of Omega with a lower cutoff at 2mu. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap Delta. At a large magnetic field B, the diagonal and Hall conductivities at small Omega become independent of B but remain nonzero and show a structure associated with the lowest Landau level. This occurs because in the Dirac theory the energy of this level, E0 = +/-Delta, is field independent in sharp contrast to the conventional case.     

Dynamically generated anomalous magnetic moment in massless QED

In this paper we investigate the non-perturbative generation of an anomalous magnetic moment for massless fermions in the presence of an external magnetic field. In the context of massless QED in a magnetic field, we prove that the phenomenon of magnetic catalysis of chiral symmetry breaking, which has been associated in the literature with dynamical mass generation, is also responsible for the generation of a dynamical anomalous magnetic moment. As a consequence, the degenerate energy of electrons in Landau levels higher than zero exhibits Zeeman splitting. We explicitly report the splitting for the first Landau level and find the non-perturbative Lande g-factor and Bohr magneton. We anticipate that a dynamically generated anomalous magnetic moment will be a universal feature of theories with magnetic catalysis. Our findings can be important for condensed planar systems as graphene, as well as for highly magnetized dense systems as those forming the core of compact stars.     

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.     

Carrier scattering from dynamical magnetoconductivity in quasineutral epitaxial graphene

The energy dependence of the electronic scattering time is probed by Landau level spectroscopy in quasineutral multilayer epitaxial graphene. From the broadening of overlapping Landau levels we find that the scattering rate 1/τ increases linearly with energy ?. This implies a surprising property of the Landau level spectrum in graphene-the number of resolved Landau levels remains constant with the applied magnetic field. Insights are given about possible scattering mechanisms and carrier mobilities in the graphene system investigated.     

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.     

Extended Lagrangian formalisms for dyons and some applications to solid systems under external fields

We analyze the conditions of the electromagnetic potentials for systems with electric and magnetic charges and the Lagrangian theory with these potentials. The constructed Lagrangian function is valid for obtaining the field equations and the extended Lorentz force for dyonic charges for both relativistic particles in vacuum and non-relativistic entities in solids. In a second part, with the one-body Hamiltonian of independent particles in external fields, we explore some dual properties of the dyonic system under external fields. We analyze the possible diamagnetic (and ‘diaelectric’) response of magnetic monopoles under a weak and constant electromagnetic field and the theory of Landau levels in the case of magnetic charges under strong electromagnetic constant fields.     

Variational approach for the effects of periodic modulations on the spectrum of massless Dirac fermion

In the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic field. We analyze the influence of the lateral periodic modulations in one direction, created by these oscillating electric and magnetic fields, on Dirac like Landau levels depending on amplitudes and periods of the field modulations. We compare our theoretical results with those found within the framework of non-degenerate perturbation theory. We found that the technique presented here yields energies lower than that obtained by the perturbation calculation, and thus gives more stable solutions for the electronic spectrum of massless Dirac fermion subjected to a magnetic field perpendicular to graphene layer under the influence of additional periodic potentials.     

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.     

Transport property of inhomogeneous strained graphene

In analogy to real magnetic field, the pseudo-magnetic field (PMF) induced by inhomogeneous strain can also formthe Landau levels and edge states. In this paper, the transport properties of graphene under inhomogeneous strain arestudied. We find that the Landau levels have non-zero group velocity, and construct one-dimensional conducting channels.In addition, the edge states and the Landau level states in PMF are both fragile under disorder. We also confirm that thebackscattering of these states could be suppressed by applying a real magnetic filed (MF). Therefore, the transmissioncoefficient for each conducting channel can be manipulated by adjusting the MF strength, which indicates the applicationof switching devices.     

Gap opening in the zeroth Landau level in gapped graphene: pseudo-Zeeman splitting in an angular magnetic field

We present a theoretical study of gap opening in the zeroth Landau level in gapped graphene as a result of pseudo-Zeeman interaction. The applied magnetic field couples with the valley pseudospin degree of freedom of the charge carriers leading to the pseudo-Zeeman interaction. To investigate its role in transport at the charge neutrality point (CNP), we study the integer quantum Hall effect in gapped graphene in an angular magnetic field in the presence of pseudo-Zeeman interaction. Analytical expressions are derived for the Hall conductivity using the Kubo-Greenwood formula. We also determine the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that pseudo-Zeeman splitting leads to a minimum in the collisional conductivity at high magnetic fields and a zero plateau in the Hall conductivity. Evidence for activated transport at CNP is found from the temperature dependence of the collisional conductivity.     

Above-threshold dynamics of acoustic domains in liquid crystals

Owing to a nonquadratic spectrum, the Landau levels in graphene in crossed magnetic and electric fields should be affected by an electric field. Oscillations of magnetization in gapped and gapless graphene in crossed magnetic and electric fields are studied. The contribution of the Coulomb interaction to these oscillations is considered.     

Light-induced unconventional Landau levels of ultracold fermions in a trilayer honeycomb lattice

The spectrum of cold fermionic atoms is studied in a trilayer honeycomb optical lattice subjected to a perpendicular effective magnetic field,which is created with optical means. In the low energy approximation,the spectrum shows unconventional Landau levels,which are proportional to the 3/2 power of integer numbers. The zoro modes exist and the quasiparticles are chiral. It is also proposed to identify the unconventional Landau levels via probing the dynamic structure factor of the system with Bragg spectr...