Unified Analysis of Cosmological Perturbations in Generalized Gravity

In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the scalar field and the scalar curvature in the Lagrangian, thus includes broad classes of generalized gravity theories resulting from recent attempts for the unification. We analyze both the scalar-type mode and the gravitational wave in analogous ways. For both modes the large scale evolutions are characterized by the same conserved quantities which are valid in the Einstein's gravity. This unified and simple treatment is possible due to our proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure

Compressibility of graphene

We develop a theory for the compressibility and quantum capacitance of disordered monolayer and bilayer graphene including the full hyperbolic band structure and band gap in the latter case. We include the effects of disorder in our theory, which are of particular importance at the carrier densities near the Dirac point. We account for this disorder statistically using two different averaging procedures: first via averaging over the density of carriers directly, and then via averaging in the density of states to produce an effective density of carriers. We also compare the results of these two models with experimental data, and to do this we introduce a model for inter-layer screening which predicts the size of the band gap between the low-energy conduction and valence bands for arbitary gate potentials applied to both layers of bilayer graphene. We find that both models for disorder give qualitatively correct results for gapless systems, but when there is a band gap at charge neutrality, the density of states averaging is incorrect and disagrees with the experimental data.Comment: 10 pages, 7 figures, RevTe

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

Optical and transport gaps in gated bilayer graphene

We discuss the effect of disorder on the band gap measured in bilayer graphene in optical and transport experiments. By calculating the optical conductivity and density of states using a microscopic model in the presence of disorder, we demonstrate that the gap associated with transport experiments is smaller than that associated with optical experiments. Intrinsic bilayer graphene has an optical conductivity in which the energy of the peaks associated with the interband transition are very robust against disorder and thus provide an estimate of the band gap. In contrast, extraction of the band gap from the optical conductivity of extrinsic bilayer graphene is almost impossible for significant levels of disorder due to the ambiguity of the transition peaks. The density of states contains an upper bound on the gap measured in transport experiments, and disorder has the effect of reducing this gap which explains why these experiments have so far been unable to replicate the large band gaps seen in optical measurements.Comment: 5 pages, 5 figures, RevTeX. Published versio

Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetryin the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.Comment: accepted in Phys. Rev.

Cosmological perturbations in a gravity with quadratic order curvature couplings

We present a set of equations describing the evolution of the scalar-type cosmological perturbation in a gravity with general quadratic order curvature coupling terms. Equations are presented in a gauge ready form, thus are ready to implement various temporal gauge conditions depending on the problems. The Ricci-curvature square term leads to a fourth-order differential equation for describing the spacetime fluctuations in a spatially homogeneous and isotropic cosmological background.Comment: 5 pages, no figure, To appear in Phys. Rev.

The causal structure of dynamical charged black holes

We study the causal structure of dynamical charged black holes, with a sufficient number of massless fields, using numerical simulations. Neglecting Hawking radiation, the inner horizon is a null Cauchy horizon and a curvature singularity due to mass inflation. When we include Hawking radiation, the inner horizon becomes space-like and is separated from the Cauchy horizon, which is parallel to the out-going null direction. Since a charged black hole must eventually transit to a neutral black hole, we studied the neutralization of the black hole and observed that the inner horizon evolves into a space-like singularity, generating a Cauchy horizon which is parallel to the in-going null direction. Since the mass function is finite around the inner horizon, the inner horizon is regular and penetrable in a general relativistic sense. However, since the curvature functions become trans-Planckian, we cannot saymore about the region beyond the inner horizon, and it is natural to say that there is a 'physical' space-like singularity. However, if we assume an exponentially large number of massless scalar fields, our results can be extended beyond the inner horizon. In this case, strong cosmic censorship and black hole complementarity can be violated.Comment: 23 pages, 23 figure

Cosmological Gravitational Wave in a Gravity with Quadratic Order Curvature Couplings

We present a set of equations describing the cosmological gravitational wave in a gravity theory with quadratic order gravitational coupling terms which naturally arise in quantum correction procedures. It is known that the gravitational wave equation in the gravity theories with a general $f(R)$ term in the action leads to a second order differential equation with the only correction factor appearing in the damping term. The case for a $R^{ab} R_{ab}$ term is completely different. The gravitational wave is described by a fourth order differential equation both in time and space. However, curiously, we find that the contributions to the background evolution are qualitatively the same for both terms.Comment: 4 pages, revtex, no figure