Optical Hall conductivity in bulk and nanostructured graphene beyond the Dirac approximation

We present a perturbative method for calculating the optical Hall conductivity in a tight-binding framework based on the Kubo formalism. The method involves diagonalization only of the Hamiltonian in absence of the magnetic field, and thus avoids the computational problems usually arising due to the huge magnetic unit cells required to maintain translational invariance in presence of a Peierls phase. A recipe for applying the method to numerical calculations of the magneto-optical response is presented. We apply the formalism to the case of ordinary and gapped graphene in a next-nearest neighbour tight-binding model as well as graphene antidot lattices. In both case, we find unique signatures in the Hall response, that are not captured in continuum (Dirac) approximations. These include a non-zero optical Hall conductivity even when the chemical potential is at the Dirac point energy. Numerical results suggest that this effect should be measurable in experiments.Comment: 7 pages, 4 figures, accepted in Physical Review

Rigorous perturbation theory versus variational methods in the spectral study of carbon nanotubes

Recent two-photon photo-luminescence experiments give accurate data for the ground and first excited excitonic energies at different nanotube radii. In this paper we compare the analytic approximations proved in \cite{CDR}, with a standard variational approach. We show an excellent agreement at sufficiently small radii.Comment: Accepted for publication in Contemporary Mathematic

Correlation and dimensional effects of trions in carbon nanotubes

We study the binding energies of singlet trions, i.e. charged excitons, in carbon nanotubes. The problem is modeled, through the effective-mass model, as a three-particle complex on the surface of a cylinder, which we investigate using both one- and two-dimensional expansions of the wave function. The effects of dimensionality and correlation are studied in detail. We find that the Hartree-Fock approximation significantly underestimates the trion binding energy. Combined with band structures calculated using a non-orthogonal nearest neighbour tight binding model, the results from the cylinder model are used to compute physical binding energies for a wide selection of carbon nanotubes. In addition, the dependence on dielectric screening is examined. Our findings indicate that trions are detectable at room temperature in carbon nanotubes with radius below 8{\AA}

The Faraday effect revisited: General theory

This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron approximation is assumed. At zero temperature and zero frequency, if the Fermi energy lies in a spectral gap, we rigorously prove the Widom-Streda formula. For free electrons, the transverse conductivity can be explicitly computed and coincides with the classical result. In the general case, using magnetic perturbation theory, the conductivity tensor is expanded in powers of the strength of the magnetic field $B$. Then the linear term in $B$ of this expansion is written down in terms of the zero magnetic field Green function and the zero field current operator. In the periodic case, the linear term in $B$ of the conductivity tensor is expressed in terms of zero magnetic field Bloch functions and energies. No derivatives with respect to the quasi-momentum appear and thereby all ambiguities are removed, in contrast to earlier work.Comment: Final version, accepted for publication in J. Math. Phy

On the existence of impurity bound excitons in one-dimensional systems with zero range interactions

We consider a three-body one-dimensional Schr\"odinger operator with zero range potentials, which models a positive impurity with charge $\kappa > 0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$ there exists a unique bound state whose binding energy behaves like $\kappa^4$, and we explicitly compute its leading coefficient. On the other hand, if $\kappa$ is larger than some critical value then the system has no bound states

Moebius sequence : a multidisciplinary clinical approach

Background: Moebius Sequence (MS) is a rare disorder defined by bilateral congenital paralysis of the abducens and facial nerves in combination with various odontological, craniofacial, ophthalmological and orthopaedic conditions. The aetiology is still unknown; but both genetic (de novo mutations) and vascular events in utero are reported. The purpose of present study was through a multidisciplinary clinical approach to examine children diagnosed with Moebius-like symptoms. Ten children underwent odontological, ophthalmological, obstetric, paediatric, orthopaedic, genetic, radiological and photographical evaluation. Five patients maintained the diagnosis of MS according to the diagnostic criteria. Results: All five patients had bilateral facial and abducens paralysis confirmed by ophthalmological examination. Three of five had normal brain MR imaging. Two had missing facial nerves and one had missing abducens nerves. The Strengths and Difficulties Questionnaire (SDQ) showed normal scores in three of five patients. Interestingly, two of five children were born to mothers with uterine abnormalities (unicornuate/bicornuate uterus). In the odontological examination three of five showed enamel hypomineralisation. All five had abnormal orofacial motor function and maxillary prognathism. Two patients had adactyly, syndactyly and brachydactyly. None of the five patients had Poland anomaly, hip dislocation or dysplasia but all had a mild degree of scoliosis. We observed congenital club-feet, calcaneovalgus deformities, macrodactyly of one or more toes or curly toes. Pedobarography showed plantar pressures within normal ranges. Conclusions: Adherence to standard diagnostic criteria is central in the diagnosis of MS. An accurate diagnosis is the basis for correct discussion of other relevant concomitant symptoms of MS, genetic testing and evaluation of prognosis. The multidisciplinary approach and adherence to diagnostic criteria taken in present study increases the knowledge on the relationship between genotype, phenotype and symptomatology of MS. © 2017 The Author(s)

Strong pressure-energy correlations in van der Waals liquids

Strong correlations between equilibrium fluctuations of the configurational parts of pressure and energy are found in the Lennard-Jones liquid and other simple liquids, but not in hydrogen-bonding liquids like methanol and water. The correlations, that are present also in the crystal and glass phases, reflect an effective inverse power-law repulsive potential dominating fluctuations, even at zero and slightly negative pressure. In experimental data for supercritical Argon, the correlations are found to be approximately 96%. Consequences for viscous liquid dynamics are discussed.Comment: Phys. Rev. Lett., in pres

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page