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Register a new userCollisionless Hydrodynamics of Doped Graphene in a Magnetic Field
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The electrodynamics of a two-dimensional gas of massless fermions in graphene is studied by a collisionless hydrodynamic approach. A low-energy dispersion relation for the collective modes (plasmons) is derived both in the absence and in the presence of a perpendicular magnetic field. The results for graphene are compared to those for a standard two-dimensional gas of massive electrons. We further compare the results within the classical hydrodynamic approach to the full quantum mechanical calculation in the random phase approximation. The low-energy dispersion relation is shown to be a good approximation at small wave vectors. The limitations of this approach at higher order is also discussed.
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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-electron 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.
A doped graphene layer in the integer quantum Hall regime reveals a highly unusual particle-hole excitation spectrum, which is calculated from the dynamical polarizability in the random phase approximation. We find that the elementary neutral excitations in graphene in a magnetic field are unlike those of a standard two-dimensional electron gas (2DEG): in addition to the upper-hybrid mode, the particle-hole spectrum is reorganized in linear magneto-plasmons that disperse roughly parallel to $omega=v_F q$, instead of the usual horizontal (almost dispersionless) magneto-excitons. These modes could be detected in an inelastic light scattering experiment.
A weak perpendicular magnetic field, $B$, breaks the chiral symmetry of each valley in the electron spectrum of graphene, preserving the overall chiral symmetry in the Brillouin zone. We explore the consequences of this symmetry breaking for the interaction effects in graphene. In particular, we demonstrate that the electron-electron interaction lifetime acquires an anomalous $B$-dependence. Also, the ballistic zero-bias anomaly, $delta u(omega)$, where $omega$ is the energy measured from the Fermi level, emerges at a weak $B$ and has the form $delta u(B)sim B^2/omega^2$. Temperature dependence of the magnetic-field corrections to the thermodynamic characteristics of graphene is also anomalous. We discuss experimental manifestations of the effects predicted. The microscopic origin of the $B$-field sensitivity is an extra phase acquired by the electron wave-function resulting from the chirality-induced pseudospin precession.
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 is 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.
We develop a theory for graphene magnetotransport in the presence of carrier spin polarization as induced, for example, by the application of an in-plane magnetic field ($B$) parallel to the 2D graphene layer. We predict a negative magnetoresistance $sigma propto B^2$ for intrinsic graphene, but for extrinsic graphene we find a non-monotonic magnetoresistance which is positive at lower magnetic fields (below the full spin-polarization) and negative at very high fields (above the full spin-polarization). The conductivity of the minority spin band $(-)$ electrons does not vanish as the minority carrier density ($n_-$) goes to zero. The residual conductivity of $(-)$ electrons at $n_- = 0$ is unique to graphene. We discuss experimental implications of our theory.
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