Landau levels in graphite intercalation compounds

The first calculation of the magnetic energy level structure of a graphite intercalation compound is presented. The calculational technique exploits the staging symmetry through the k_z-axis zone folding of the magnetic energy levels of the graphite π-bands. The results are applicable to the interpretation of the magnetoreflection and de Haas-van Alphen type experiments in intercalated graphite.     

Exact diagonalization of Landau levels in Bernal graphite

The magneto-electronic structure of Bernal graphite is derived by the Peierls tight-binding model. Seven important atomic interactions are taken into account and the corresponding Hamiltonian matrix is rearranged as a band-like form for efficient calculation. The results derived from this exact diagonalization method demonstrate that interlayer interactions play remarkable roles in Landau level structures.     

Tight-binding description of Landau levels of graphite in tilted magnetic fields

The electronic structure of Bernal-stacked graphite subject to tilted magnetic fields is studied theoretically. The minimal nearest-neighbor tight-binding model with the Peierls substitution is employed to describe the structure of Landau levels. We show that, while the orbital effect of the in-plane component of the magnetic field is negligible for massive Dirac fermions in the vicinity of the K point of the graphite Brillouin zone, at the H point it leads to the experimentally observable splitting of Landau levels, which grows approximately linearly with the in-plane field intensity.     

Landau level spectroscopy of ultrathin graphite layers

Far infrared transmission experiments are performed on ultrathin epitaxial graphite samples in a magnetic field. The observed cyclotron resonance-like and electron-positron-like transitions are in excellent agreement with the expectations of a single-particle model of Dirac fermions in graphene, with an effective velocity of c=1.03 x 10(6) m/s.     

Density-induced interchange of anisotropy axes at half-filled high Landau levels

We observe density-induced 90 degrees rotations of the anisotropy axes in transport measurements at half-filled high Landau levels in the two dimensional electron system, where stripe states are proposed ( nu = 9/2, 11/2, etc.). Using a field effect transistor, we find the transition density to be 2.9x10(11) cm(-2) at nu = 9/2. Hysteresis is observed in the vicinity of the transition. We construct a phase boundary in the filling factor magnetic field plane in the regime 4.4相似文献   

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ν=±4 being the most stable in the quantum Hall effect measurement, instead of ν=±8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ν=±4 is, down to very low fields, weakly dependent on the strength of the magnetic field.     

Landau levels in disordered alloys

The electronic structure of a substitutionally disordered alloy in a uniform magnetic field has been studied on a simple model of scattering potentials (zero range potentials). The coherent potential and single-site aproximation have been employed. It turned out that in wide energy region the Dingle temperature, characterizing the decay of the amplitude of de Haas — van Alphen oscillations, is determined by the part of self-energy which does not depend on magnetic field. The field dependent part is important only for a few Landau levels at the bottom of the band. The results can be applied to simple metals and semi-metals.     

Landau levels and Riemann zeros

The number N(E) of complex zeros of the Riemann zeta function with positive imaginary part less than E is the sum of a "smooth" function N[over ](E) and a "fluctuation." Berry and Keating have shown that the asymptotic expansion of N[over ](E) counts states of positive energy less than E in a "regularized" semiclassical model with classical Hamiltonian H=xp. For a different regularization, Connes has shown that it counts states "missing" from a continuum. Here we show how the "absorption spectrum" model of Connes emerges as the lowest Landau level limit of a specific quantum-mechanical model for a charged particle on a planar surface in an electric potential and uniform magnetic field. We suggest a role for the higher Landau levels in the fluctuation part of N(E).     

Thermal scattering in surface Landau levels

We review the application of surface Landau level studies to measurement of the point by point thermal phonon scattering on the Fermi surfaces of metals. Results of such measurements in Cu are presented, and compared critically with those of other experiments and with theoretical calculations. Some new and preliminary results on thermal scattering in Al, In and Bi are discussed.     

New physics in high Landau levels

Recent magneto-transport experiments on ultra-high mobility 2D electron systems in GaAs/AlGaAs heterostructures have revealed the existence of whole new classes of correlated many-electron states in highly excited Landau levels. These new states, which appear only at extremely low temperatures, are distinctly different from the familiar fractional quantum Hall liquids of the lowest Landau level. Prominent among the recent findings are the discoveries of giant anisotropies in the resistivity near half-filling of the third and higher Landau levels and the observation of re-entrant integer quantum Hall states in the flanks of these same levels. This contribution will survey the present status of this emerging field.     

Infrared spectroscopy of Landau levels of graphene

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to sqrt[B], and the deduced band velocity is (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.     

Optical transitions and cyclotron resonance at Landau levels split by a periodic potential

The structure of the electron spectrum is investigated and selection rules are found for transitions between magnetic subbands in a surface 2D superlattice of quantum dots in a perpendicular magnetic field. The photon absorption probabilities are calculated, and the profiles of the absorption lines are determined for allowed and forbidden direct dipole transitions between subbands split off from different Landau levels. Zh. éksp. Teor. Fiz. 114, 1795–1803 (November 1998)     

Condensation of states at the Landau levels and disorder-independent transport in a random system

I consider an electron on a square lattice, formed by random strenght point potentials, in the presence of a magnetic field, orthogonal to the lattice. When the number of magnetic flux quanta per unit cell is less than one, then an infinite density of extended disorder independent states condenses at each Landau level and provides the possibility for resistivity minima in a disordered system.     

Exciton spectrum for two-dimensional electron systems at fractional occupation numbers of the Landau levels

It is shown that q absorption lines arise in two-dimensional crystal lattices at a rational fractional number p/q of magnetic-field flux quanta per electron. The absorption lines correspond to different exciton formation energies and are determined by the electron-hole Coulomb interaction. The number of the absorption lines is calculated for electron densities corresponding to the fractional quantum Hall effect.     

Discrete coherent states for higher Landau levels

We consider the quantum dynamics of a charged particle evolving under the action of a constant homogeneous magnetic field, with emphasis on the discrete subgroups of the Heisenberg group (in the Euclidean case) and of the SL(2,R)$SL(2,\mathbb{R})$ group (in the Hyperbolic case). We investigate completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results follow from identifying the completeness problem with known results from the theory of Gabor frames. The results for the hyperbolic setting follow by using a combination of methods from coherent states, time-scale analysis and the theory of Fuchsian groups and their associated automorphic forms.     

Mesoscopic superposition states in relativistic Landau levels

We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily superpositions of coherent states involving the particle orbital quanta in a well-defined mesoscopic regime. We demonstrate that these mesoscopic superpositions have a purely relativistic origin and disappear in the nonrelativistic limit.     

Collapse of Landau levels in gated graphene structures

We describe a new regime of magnetotransport in two-dimensional electron systems in the presence of a narrow potential barrier. In such systems, the Landau level states, which are confined to the barrier region in strong magnetic fields, undergo a deconfinement transition as the field is lowered. Transport measurements on a top-gated graphene device are presented. Shubnikov-de Haas (SdH) oscillations, observed in the unipolar regime, are found to abruptly disappear when the strength of the magnetic field is reduced below a certain critical value. This behavior is explained by a semiclassical analysis of the transformation of closed cyclotron orbits into open, deconfined trajectories.     

Hillock formation on ion-irradiated graphite surfaces

Abstract

Scanning probe microscopy experiments show that ion irradiation of (0001) graphite results in the formation of isolated defects comprising of a few tens of atoms. We use molecular dynamics simulations and density-functional theory calculations to study the formation probabilities of these defects. We identify different defect structures which correspond to experimentally observed hillocks on graphite surfaces. We find that the predominant source of defects are vacancies and interlayer interstitials, and identify a three-atom carbon ring defect on the graphite surface.