Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field

We study symmetry breaking and gap generation for fermions in the 2D space of constant negative curvature (the Lobachevsky plane) in an external covariantly constant magnetic field in a four-fermion model. It is shown that due to the magnetic and negative curvature catalyses phenomena the critical coupling constant is zero and there is a symmetry breaking condensate in the chiral limit even in free theory. We analyze solutions of the gap equation in the cases of zero, weak, and strong magnetic fields. As a byproduct, we calculate the density of states and the Hall conductivity for noninteracting fermions that may be relevant for studies of graphene.     

Coulomb interactions of massless Dirac fermions in graphene; pair-distribution functions and exchange-driven spin-polarized phases

The quasi-2D electrons in graphene behave as massless fermions obeying a Dirac-Weyl equation in the low-energy regime near the two Fermi points. The stability of spin-polarized phases (SPP) in graphene is considered. The exchange energy is evaluated from the analytic pair-distribution functions, and the correlation energies are estimated via a closely similar four-component 2D electron fluid which has been investigated previously. SPPs appear for sufficiently high doping, when the exchange energy alone is considered. However, the inclusion of correlations is found to suppress the spin-phase transition in ideal graphene.     

Generally covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.     

Bonds and Fermi surfaces studied by photoelectron spectroscopy

Photoelectron spectroscopy with synchrotron radiation employing high energy and angular resolutions is a very efficient tool for experimental investigations of the electronic structure of solids and their surfaces. In addition to standard band-mapping applications, photoemission intensity and line-shape analyses provide valuable information about wave functions, bonds and interactions of a many-electron system. In this report we choose covalent semiconductor surfaces as well as metallic clean and nanostructured surfaces of layered materials to serve as model systems for assessing the spatial origin of photoelectrons and the three-dimensional shape of Fermi surfaces. Received: 11 July 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Modeling vacancies and hydrogen impurities in graphene: A molecular point of view

We have followed a ‘molecular’ approach to study impurity effects in graphene. This is thought as the limiting case of an infinitely large cluster of benzene rings. Therefore, we study several carbon clusters, with increasing size, from phenalene, including three benzene rings, up to coronene 61, with 61 benzene rings. The impurities considered were a chemisorbed H atom, a vacancy, and a substitutional proton. We performed HF and UHF calculations using the STO-3G basis set. With increasing cluster size in the absence of impurities, we find a decreasing energy gap, here defined as the HOMO-LUMO difference. In the case of H chemisorption or a vacancy, the gap does not decrease appreciably, whereas it is substantially reduced in the case of a substitutional proton. The presence of an impurity invariably induces an increase of the density of states near the HOMO level. We find a zero mode only in the case of a substitutional proton. In agreement with experiments, we find that both the chemisorbed H, the substitutional proton, and the C atom near a vacancy acquire a magnetic moment. The relevance of graphene clusters for the design of novel electronic devices is also discussed.     

Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime

The strong similarities between the light propagation in a curved spacetime and that in a medium with graded refractive index are found. It is pointed out that a curved spacetime is equivalent to an inhomogeneous vacuum for light propagation. The corresponding graded refractive index of the vacuum in a static spherically symmetrical gravitational field is derived. This result provides a simple and convenient way to analyse the gravitational lensing in astrophysics.     

First-principles calculations for magnetic properties of Mn-doped GaN nanotubes

Based on first-principles spin-density functional calculations, we investigate the electronic and magnetic properties of Mn-doped GaN nanotubes in which two of Ga atoms are substituted by Mn atoms. Similar to the case of Mn in bulk GaN, our calculations show that Mn atoms also act as an acceptor and all of the ground states for the Mn-doped GaNNTs are ferromagnetic. Moreover, the ferromagnetism is isotropic and independent of the chirality and diameter of the nanotubes. It is found that the most favorable configuration is the first-nearest neighbor Mn model, which is mainly mediated by both the hole-hole interaction and the dipole-dipole interaction.     

Casimir Energy in Hartle--Hawking State

We calculate the Casimir effect at finite temperature in Minkowski spacetime by using statistical method, the approximate expressions of the Casimir effect in the low and high temperature limits are also discussed. Then employing some general properties of the renormalized stress tensor, we obtain the Casimir energy stress tensor in Hattie-Hawking state.     

Spontaneous Emission of an Inertial Multi-Level Atom in a Spacetime with a Reflecting Plane Boundary

We calculate the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy for a multi-level hydrogen atom in the multipolar coupling scheme in a spacetime with a reflecting boundary. Our results show that, due to the presence of the boundary, the polarizations of the atom in the parallel direction and in the normal direction are weighted differently in terms of their contributions to the spontaneous emission rate, which is an oscillating function of the atom distance from the boundary. The possible experimental implications of our result are briefly discussed.     

Spontaneous Emission of an Atom in a Spacetime with Two Parallel Reflecting Boundaries

We consider an inertial two-level atom in interaction with a real massless scalar quantum field in a spacetime between two parallel reflecting plane boundaries, and calculate the contributions of vacuum fluctuations and radiation reaction to the rate of change of the atomic energy. Our results show that there exists a regime of the separation L between the two boundaries such that the excited atom＇s spontaneous emission is impossible. There also exist certain values of the atom＇s position such that the corrections due to the presence of boundaries balance each other, so that the atom＇s spontaneous emission rate is the same as if there were no boundaries at all.     

Statistical-Mechanical Entropy of a Black Hole with a Global Monopole to All Orders in Planck Length

Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle, we calculate the statistical entropy of the scalar field in the global monopole black hole spacetime without any artificial cutoff. It is shown that the entropy is proportional to the horizon area.     

Electronic Raman Scattering in Graphene

Linear dispersion near the Dirac points in the band structure of graphenes can give rise to novel physical properties. We calculate the electronic contribution to the Raman spectra in graphenes, which also shows novel features. In the clean limit, the Raman spectrum in the undoped graphene is linear （with a universal slope against impurity scattering） at low energy due to the linear dispersion near the Dirae points, and it peaks at a position corresponding to the van Hove singularity in the band structure. In a doped graphene, the electronic Raman absorption is forbidden up to a vertical inter-band particle-hole gap. Beyond the gap the spectrum follows the undoped case. In the presence of impurities, absorption within the gap （in the otherwise clean case） is induced, which is identified as the intra-band contribution. The Drude-like intra-band contribution is seen to be comparable to the higher energy inter-band Raman peak. The results are discussed in connection to experiments.     

Photoluminescence from a gold nanotip in an accelerated reference frame

Photoluminescence from a gold nanotip, which is induced by surface plasmons propagating over a curved tapered nanotip surface is considered in a co-moving accelerated reference frame. Similar to the surface-enhanced Raman scattering (SERS) effect, nonlinear optical mixing of the surface plasmons with the Unruh quanta is supposed to be enhanced by many orders of magnitude.     

Radiative Energy Shifts of an Atom Coupled to the Derivative of a Scalar Field near a Reflecting Boundary

We study the radiative energy level shifts of a two-level atom in dipole coupling to the derivative of a massless scalar quantum field in a spacetime with a perfectly reflecting boundary, and calculate the contributions of vacuum fluctuations and radiation reaction to the level shift. It is found that the energy level shift of the excited state is an oscillating function of the atom＇s distance from the boundary and it can either be positive or negative, while that of the ground state is always positive. The most remarkable feature is that the energy level shift of the ground state behaves like 1/z^4 when the atom＇s distance from the boundary, z, is very large as compared to the transition wavelength of the atom, while it behaves like 1/z^3 when z is very small     

Radiative Energy Shifts of an Accelerated Multilevel Atom Coupled to the Derivative of a Scalar Field

We study the energy level shifts of an accelerated multilevel atom in dipole coupling to the derivative of a quantum massless scalar field and separately calculate the contributions of vacuum fluctuations and radiation reaction to the shifts. It is found that, in contrast to the case of a monopole-like interaction, both the vacuum fluctuations and radiation reaction contributions are changed by acceleration, and they all contain non-thermal correction terms. Our results suggest that the effect of acceleration on the energy shifts is dependent on the type of the interaction between the atom and the quantum field.     

Black hole thermodynamics and the factor of 2 problem

We show that the recent tunneling formulas for black hole radiation in static, spherically symmetric spacetimes follow as a consequence of the first law of black hole thermodynamics and the area-entropy relation based on the radiation temperature. A tunneling formula results even if the radiation temperature is different from the one originally derived by Hawking and this is discussed in the context of the recent factor of 2 problem. In particular, it is shown that if the radiation temperature is higher than the Hawking temperature by a factor of two, thermodynamics then leads to a tunneling formula which is exactly the one recently found to be canonically invariant.     

Dynamics of superhorizon photons during inflation with vacuum polarization

We study asymptotic dynamics of photons propagating in the polarized vacuum of a locally de Sitter Universe. The origin of the vacuum polarization is fluctuations of a massless, minimally coupled, scalar, which we model by the one-loop vacuum polarization tensor of scalar electrodynamics. We show that late time dynamics of the electric field on superhorizon scales approaches that of an Airy oscillator. The magnetic field amplitude, on the other hand, asymptotically approaches a nonvanishing constant (plus an exponentially small oscillatory component), which is suppressed with respect to the initial (vacuum) amplitude. This implies that the asymptotic photon dynamics is more intricate than that of a massive photon obeying the local Proca equation.     

Tunnelling Radiation of Charged and Magnetized Massive Particles from BTZ Black Holes

We investigate the tunnelling radiation of charged and magnetized massive particles from a Banados-Teitelboim- Zanelli （BTZ） black hole by extending the Parikh-Wilczek tunnelling framework. In order to calculate the emission rate, we reconstruct the electromagnetic field tensor and the Lagrangia~n of the field corresponding to the source with electric and magnetic charges, and treat the charges as an equivalent electric charge for simplicity in the later calculation. The result supports Parikh-Wilczek＇s conclusion, that is, the Hawking thermal radiation actually deviates from perfect thermality and agrees with an underlying unitary theory.