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.     

Quantum limit in a quasi-one-dimensional conductor in a high tilted magnetic field

Recently, we have suggested Fermi-liquid–non-Fermi-liquid angular crossovers that may exist in quasi-one-dimensional (Q1D) conductors in high tilted magnetic fields (see A. G. Lebed, Phys. Rev. Lett. 115, 157001 (2015)). All calculations in the Letter were done by using the quasiclassical Peierls substitution method, whose applicability in high magnetic fields was questionable. Here, we solve a fully quantum mechanical problem and show that the main qualitative conclusions of the work cited above are correct. In particular, we show that in high magnetic fields, applied along one of the two main crystallographic axis, we have 2D electron spectrum, whereas, for directions of high magnetic fields far from the axes, we have 1D electron spectrum. The latter is known to promote non-Fermi-liquid properties. As a result, we expect the existence of Fermi-liquid–non-Fermi-liquid angular crossovers or phase transitions. Electronic parameters of Q1D conductor (Per)₂Pt(mnt)₂ show that such transitions can appear in feasible high magnetic fields of the order of H ? 20–25 T.     

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.     

Doped graphene in a quantizing magnetic field: Hall conductivity

The energy spectrum of electrons in doped graphene corresponding to the Landau levels in an external transverse magnetic field has been calculated in the low-energy approximation. The magnetic-field dependence of the electrical conductivity has been determined based on the derived dispersion relation of electrons in the doped graphene. The behavior of the conductivity has been analyzed for different impurity parameters, such as the hybridization potential and energy of adsorbed atoms.     

Magnetic quantum oscillations in a monolayer graphene under a perpendicular magnetic field

The de Haas-van Alphen(dHvA) oscillations of electronic magnetization in a monolayer graphene with structureinduced spin-orbit interaction(SOI) are studied.The results show that the dHvA oscillating centre in this system deviates from the well known(zero) value in a conventional two-dimensional electron gas.The inclusion of SOI will change the well-defined sawtooth pattern of magnetic quantum oscillations and result in a beating pattern.In addition,the SOI effects on Hall conductance and magnetic susceptibility are also discussed.     

Effect of a dc electric field on the high-frequency conductivity of a graphene superlattice

Longitudinal and transverse high-frequency conductivities of a graphene superlattice placed in an additional dc electric field are calculated. It is shown that in a sufficiently strong transverse field, the dependence of the longitudinal high-frequency conductivity of the superlattice on the ac field frequency changes. This effect is explained by the nonadditivity of the electronic spectrum of the investigated structure.     

Quantum and classical chaos in a thin film (heterostructure) in a tilted magnetic field

Classical and quantum dynamics of a spinless charged particle moving in a thin film placed in a tilted magnetic field is investigated. In the classical limit, nonlinear resonances and the condition of stochastization (Chirikov criterion) are studied. In the quantum case, a system of interacting resonances and an isolated resonance are analyzed. The energy spectrum is calculated numerically in the resonance approximation, and the statistics of the interlevel intervals is examined.State University, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 1–2, pp. 74–81, January–February, 1995.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

Quantum rings in tilted magnetic fields

The electronic states of semiconductor quantum rings (QRs) under tilted magnetic fields are studied in the framework of the effective mass and envelope function approximations. For an axial field, the orbital Zeeman contribution prevails leading to the well-known Aharanov–Bohm spectrum, but it slowly decreases as the magnetic field direction declines. For an in-plane field, only the diamagnetic shift survives and it leads to the formation of double quantum well solutions, this result being relevant for experimental techniques which use in-plane magnetic fields to determine the spin of QR ground states. We also investigate the magnetic response of partially overlapped QRs, which are characteristic of high-density samples of self-assembled rings, and find that the spectrum is quite sensitive to ring coupling.     

Quantum Hall effect in back-gated InAs/GaSb heterostructures under a tilted magnetic field

We investigate the quantum Hall effect (QHE) in the InAs/GaSb hybridized electron–hole system grown on a conductive InAs substrate which act as a back-gate. In these samples, the electron density is constant and the hole density is controlled by the gate-voltage. Under a magnetic field perpendicular to the sample plane, the QHE appears along integer Landau-level (LL) filling factors of the net-carriers, where the net-carrier density is the difference between the electron and hole densities. In addition, longitudinal resistance maxima corresponding to the crossing of the extended states of the original electron and hole LLs make the QHE regions along integer-ν_net discontinuous. Under tilted magnetic fields, these R_xx maxima disappear in the high magnetic field region. The results show that the in-plane magnetic field component enhances the electron–hole hybridization and the formation of minigaps at LL crossings.     

Absolute negative conductivity in graphene with the Hubbard interaction in a magnetic field

The current-voltage and current-magnetic field characteristics for a graphene with the electron Hubbard interaction at low temperatures have been calculated in terms of the average electron method. The characteristics obtained have been analyzed as a function of the frequency of the external ac electric field and the magnetic field strength. The portion with an absolute negative conductivity has been revealed.     

On phase transitions of semimetals in a strong magnetic field

A simple model of semimetals in a strong magnetic field is studied in the Hartree-Fock approximation by taking into account both the excitonic and liquid-gas type transitions simultaneously.     

Quantum magnetostriction oscillations in a two-dimensional antiferromagnet with spin-phonon interaction in a magnetic field

The ground state of a two-dimensional antiferromagnet with S=1/2 interacting with acoustic phonons in a magnetic field was studied by the quantum Monte Carlo method in the nonadiabatic approximation. Oscillations of the amplitude of the root-mean-square displacement of ions and the average phonon occupation number in a magnetic field were found. Local maxima were revealed in the distribution functions of site magnetic moments and ion displacements. The saturation magnetization was calculated as a function of the spin-phonon coupling constant.     

Excited states of two-dimensional hydrogen atom in tilted magnetic field: Quantum chaos

The aim of the current work is the research of the influence of a tilted magnetic field direction on the spectrum and the energy level spacing distribution of a two-dimensional (2D) hydrogen atom and of an exciton in GaAs/Al_0.33Ga_0.67As quantum well. It was discovered that the quantum chaos (QC) is initiated with an increasing angle α between the magnetic field direction and the normal to the atomic plane. It is characterized by the repulsion of levels leading to the eliminating of the shell structure and by changing the spectrum statistical properties. The statement about the initiation of chaos and its dominance over regular motion with increasing angle α is confirmed by the results of our calculations of the classical dynamics presented in this paper. The evolution of the spatial distribution of the square of the absolute value of the wave function at an increasing angle α was observed. The differences of calculated dependencies of energies for various excited states on the tilt angle at a wide range of the magnetic field strength were described.     

Angular magnetoresistance oscillations in bilayers in tilted magnetic fields

Angular magnetoresistance oscillations (AMRO) were originally discovered in organic conductors and then found in many other layered metals. It should be possible to observe AMRO to semiconducting bilayers as well. Here we present an intuitive geometrical interpretation of AMRO as the Aharonov–Bohm interference effect, both in real and momentum spaces, for balanced and imbalanced bilayers. Applications to the experiments with bilayers in tilted magnetic fields in the metallic state are discussed. We speculate that AMRO may be also observed when each layer of the bilayer is in the composite-fermion state.     

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.     

RKKY interaction in three-dimensional tilted Dirac and Weyl semimetals

We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities of the tilted Dirac and Weyl semimetals in three dimensions. In accordance with the untilted scenario, the RKKY interaction contains three terms, namely the Heisenberg term, the Ising term, and the Dzyaloshinsky-Moriya term. The main influence of tilt on the RKKY Hamiltonian is a modulation to the oscillation frequencies of range functions. Our results enrich the knowledge of the magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.