Dielectric function, screening, and plasmons in 2D graphene

The dynamical dielectric function of two dimensional graphene at arbitrary wave vector $q$ and frequency $\omega$, $\epsilon(q,\omega)$, is calculated in the self-consistent field approximation. The results are used to find the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in 2D graphene layer within the random phase approximation. At long wavelengths ($q\to 0$) the plasmon dispersion shows the local classical behavior $\omega_{cl} = \omega_0 \sqrt{q}$, but the density dependence of the plasma frequency ($\omega_0 \propto n^{1/4}$) is different from the usual 2D electron system ($\omega_0 \propto n^{1/2}$). The wave vector dependent plasmon dispersion and the static screening function show very different behavior than the usual 2D case.Comment: 6 pages, 3 figure

Conserved cosmological structures in the one-loop superstring effective action

A generic form of low-energy effective action of superstring theories with one-loop quantum correction is well known. Based on this action we derive the complete perturbation equations and general analytic solutions in the cosmological spacetime. Using the solutions we identify conserved quantities characterizing the perturbations: the amplitude of gravitational wave and the perturbed three-space curvature in the uniform-field gauge both in the large-scale limit, and the angular-momentum of rotational perturbation are conserved independently of changing gravity sector. Implications for calculating perturbation spectra generated in the inflation era based on the string action are presented.Comment: 5 pages, no figure, To appear in Phys. Rev.

Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. Considering the general curvature ($K$) and the cosmological constant ($\Lambda$) in the background medium, the perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in general scales. In the first part, we elaborate these Newtonian correspondences. In the second part, using the identified gauge-invariant variables with correct Newtonian correspondences, we present the relativistic results with general pressures in the background and perturbation. We present the general super-sound-horizon scale solutions of the above mentioned variables valid for general $K$, $\Lambda$, and generally evolving equation of state. We show that, for vanishing $K$, the super-sound-horizon scale evolution is characterised by a conserved variable which is the perturbed three-space curvature in the comoving gauge. We also present equations for the multi-component hydrodynamic situation and for the rotation and gravitational wave.Comment: 16 pages, no figure, To appear in Gen. Rel. Gra

A conserved variable in the perturbed hydrodynamic world model

We introduce a scalar-type perturbation variable $\Phi$ which is conserved in the large-scale limit considering general sign of three-space curvature ($K$), the cosmological constant ($\Lambda$), and time varying equation of state. In a pressureless medium $\Phi$ is {\it exactly conserved} in all scales.Comment: 4 pages, no figure, To appear in Phys. Rev.

Velocity renormalization and anomalous quasiparticle dispersion in extrinsic graphene

Using many-body diagrammatic perturbation theory we consider carrier density- and substrate-dependent many-body renormalization of doped or gated graphene induced by Coulombic electron-electron interaction effects. We quantitatively calculate the many-body spectral function, the renormalized quasiparticle energy dispersion, and the renormalized graphene velocity using the leading-order self-energy in the dynamically screened Coulomb interaction within the ring diagram approximation. We predict experimentally detectable many-body signatures, which are enhanced as the carrier density and the substrate dielectric constant are reduced, finding an intriguing instability in the graphene excitation spectrum at low wave vectors where interaction completely destroys all particle-like features of the noninteracting linear dispersion. We also make experimentally relevant quantitative predictions about the carrier density and wave-vector dependence of graphene velocity renormalization induced by electron-electron interaction. We compare on-shell and off-shell self-energy approximations within the ring diagram approximation, finding a substantial quantitative difference between their predicted velocity renormalization corrections in spite of the generally weak-coupling nature of interaction in graphene.Comment: 9 pages, 6 figure

Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings

We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.Comment: 5 pages, revtex, no figure

Third-order cosmological perturbations of zero-pressure multi-component fluids: Pure general relativistic nonlinear effects

Present expansion stage of the universe is believed to be mainly governed by the cosmological constant, collisionless dark matter and baryonic matter. The latter two components are often modeled as zero-pressure fluids. In our previous work we have shown that to the second-order cosmological perturbations, the relativistic equations of the zero-pressure, irrotational, multi-component fluids in a spatially near flat background effectively coincide with the Newtonian equations. As the Newtonian equations only have quadratic order nonlinearity, it is practically interesting to derive the potential third-order perturbation terms in general relativistic treatment which correspond to pure general relativistic corrections. Here, we present pure general relativistic correction terms appearing in the third-order perturbations of the multi-component zero-pressure fluids. We show that, as in a single component situation, the third-order correction terms are quite small (~ 5 x10^{-5} smaller compared with the relativistic/Newtonian second-order terms) due to the weak level anisotropy of the cosmic microwave background radiation. Still, there do exist pure general relativistic correction terms in third-order perturbations which could potentially become important in future development of precision cosmology. We include the cosmological constant in all our analyses.Comment: 20 pages, no figur

The Origin of Structures in Generalized Gravity

In a class of generalized gravity theories with general couplings between the scalar field and the scalar curvature in the Lagrangian, we can describe the quantum generation and the classical evolution of both the scalar and tensor structures in a simple and unified manner. An accelerated expansion phase based on the generalized gravity in the early universe drives microscopic quantum fluctuations inside a causal domain to expand into macroscopic ripples in the spacetime metric on scales larger than the local horizon. Following their generation from quantum fluctuations, the ripples in the metric spend a long period outside the causal domain. During this phase their evolution is characterized by their conserved amplitudes. The evolution of these fluctuations may lead to the observed large scale structures of the universe and anisotropies in the cosmic microwave background radiation.Comment: 5 pages, latex, no figur

Valley dependent many-body effects in 2D semiconductors

We calculate the valley degeneracy ($g_v$) dependence of the many-body renormalization of quasiparticle properties in multivalley 2D semiconductor structures due to the Coulomb interaction between the carriers. Quite unexpectedly, the $g_v$ dependence of many-body effects is nontrivial and non-generic, and depends qualitatively on the specific Fermi liquid property under consideration. While the interacting 2D compressibility manifests monotonically increasing many-body renormalization with increasing $g_v$, the 2D spin susceptibility exhibits an interesting non-monotonic $g_v$ dependence with the susceptibility increasing (decreasing) with $g_v$ for smaller (larger) values of $g_v$ with the renormalization effect peaking around $g_v\sim 1-2$. Our theoretical results provide a clear conceptual understanding of recent valley-dependent 2D susceptibility measurements in AlAs quantum wells.Comment: 5 pages, 3 figure

Collective modes of monolayer, bilayer, and multilayer fermionic dipolar liquid

Motivated by recent experimental advances in creating polar molecular gases in the laboratory, we theoretically investigate the many body effects of two-dimensional dipolar systems with the anisotropic and $1/r^3$ dipole-dipole interactions. We calculate collective modes of 2D dipolar systems, and also consider spatially separated bilayer and multilayer superlattice dipolar systems. We obtain the characteristic features of collective modes in quantum dipolar gases. We quantitatively compare the modes of these dipolar systems with the modes of the extensively studied usual two-dimensional electron systems, where the inter-particle interaction is Coulombic.Comment: 11 pages, 7 figure