The particle-hole excitation spectrum for doped graphene is calculated from the dynamical polarizability. We study the zero and finite magnetic field cases and compare them to the standard two-dimensional electron gas. The effects of electron-electro
n interaction are included within the random phase approximation. From the obtained polarizability, we study the screening effects and the collective excitations (plasmon, magneto-excitons, upper-hybrid mode and linear magneto-plasmons). We stress the differences with the usual 2DEG.
We investigate a generalized two-dimensional Weyl Hamiltonian, which may describe the low-energy properties of mechanically deformed graphene and of the organic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associated dispersion has generically
the form of tilted anisotropic Dirac cones. The tilt arises due to next-nearest-neighbor hopping when the Dirac points, where the valence band touches the conduction band, do not coincide with crystallographic high-symmetry points within the first Brillouin zone. Within a semiclassical treatment, we describe the formation of Landau levels in a strong magnetic field, the relativistic form of which is reminiscent to that of graphene, with a renormalized Fermi velocity due to the tilt of the Dirac cones. These relativistic Landau levels, experimentally accessible via spectroscopy or even a quantum Hall effect measurement, may be used as a direct experimental verification of Dirac cones in alpha-(BEDT-TTF)_2I_3.
We consider trial wavefunctions exhibiting SU(K) symmetry which may be well-suited to grasp the physics of the fractional quantum Hall effect with internal degrees of freedom. Systems of relevance may be either spin-unpolarized states (K=2), semicond
uctors bilayers (K=2,4) or graphene (K=4). We find that some introduced states are unstable, undergoing phase separation or phase transition. This allows us to strongly reduce the set of candidate wavefunctions eligible for a particular filling factor. The stability criteria are obtained with the help of Laughlins plasma analogy, which we systematically generalize to the multicomponent SU(K) case. The validity of these criteria are corroborated by exact-diagonalization studies, for SU(2) and SU(4). Furthermore, we study the pair-correlation functions of the ground state and elementary charged excitations within the multicomponent plasma picture.
Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry i
s more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.
