Existence and topological stability of Fermi points in multilayered graphene

We study the existence and topological stability of Fermi points in a graphene layer and stacks with many layers. We show that the discrete symmetries (spacetime inversion) stabilize the Fermi points in monolayer, bilayer and multilayer graphene with orthorhombic stacking. The bands near $k=0$ and $\epsilon=0$ in multilayers with the Bernal stacking depend on the parity of the number of layers, and Fermi points are unstable when the number of layers is odd. The low energy changes in the electronic structure induced by commensurate perturbations which mix the two Dirac points are also investigated.Comment: 6 pages, 6 figures. Expanded version as will appear in PR

Superfluid analogies of cosmological phenomena

Superfluid 3He-A gives example of how chirality, Weyl fermions, gauge fields and gravity appear in low energy corner together with corresponding symmetries, including Lorentz symmetry and local SU(N). This supports idea that quantum field theory (Standard Model or GUT) is effective theory describing low-energy phenomena. * Momentum space topology of fermionic vacuum provides topological stability of universality class of systems, where above properties appear. * BCS scheme for 3He-A incorporates both ``relativistic'' infrared regime and ultraviolet ``transplanckian'' range: subtle issues of cut-off in quantum field theory and anomalies can be resolved on physical grounds. This allows to separate ``renormalizable'' terms in action, treated by effective theory, from those obtained only in ``transPlanckian'' physics. * Energy density of superfluid vacuum within effective theory is ~ E_{Planck}^4. Stability analysis of ground state beyond effective theory leads to exact nullification of vacuum energy: equilibrium vacuum is not gravitating. In nonequilibrium, vacuum energy is of order energy density of matter. * 3He-A provides experimental prove for anomalous nucleation of fermionic charge according to Adler-Bell-Jackiw. * Helical instability in 3He-A is described by the same equations as formation of magnetic field by right electrons in Joyce-Shaposhnikov scenario. * Macroscopic parity violating effect and angular momentum paradox are both desribed by axial gravitational Chern-Simons action. * High energy dispersion of quasiparticle spectrum allow to treat problems of vacuum in presence of event horizon, etc.Comment: draft of review for Physics Reports, RevTex file, 113 pages, 26 figures; new sections and references are adde

Design of crystal-like aperiodic solids with selective disorder--phonon coupling

Functional materials design normally focuses on structurally-ordered systems because disorder is considered detrimental to many important physical properties. Here we challenge this paradigm by showing that particular types of strongly-correlated disorder can give rise to useful characteristics that are inaccessible to ordered states. A judicious combination of low-symmetry building unit and high-symmetry topological template leads to aperiodic "procrystalline" solids that harbour this type of topological disorder. We identify key classes of procrystalline states together with their characteristic diffraction behaviour, and establish a variety of mappings onto known and target materials. Crucially, the strongly-correlated disorder we consider is associated with specific sets of modulation periodicities distributed throughout the Brillouin zone. Lattice dynamical calculations reveal selective disorder-phonon coupling to lattice vibrations characterised by these same periodicities. The principal effect on the phonon spectrum is to bring about dispersion in energy rather than wave-vector, as in the poorly-understood "waterfall" effect observed in relaxor ferroelectrics. This property of procrystalline solids suggests a mechanism by which strongly-correlated topological disorder might allow new and useful functionalities, including independently-optimised thermal and electronic transport behaviour as required for high-performance thermoelectrics.Comment: 4 figure

Nonradiating Photonics with Resonant Dielectric Nanostructures

Nonradiating sources of energy have traditionally been studied in quantum mechanics and astrophysics, while receiving a very little attention in the photonics community. This situation has changed recently due to a number of pioneering theoretical studies and remarkable experimental demonstrations of the exotic states of light in dielectric resonant photonic structures and metasurfaces, with the possibility to localize efficiently the electromagnetic fields of high intensities within small volumes of matter. These recent advances underpin novel concepts in nanophotonics, and provide a promising pathway to overcome the problem of losses usually associated with metals and plasmonic materials for the efficient control of the light-matter interaction at the nanoscale. This review paper provides the general background and several snapshots of the recent results in this young yet prominent research field, focusing on two types of nonradiating states of light that both have been recently at the center of many studies in all-dielectric resonant meta-optics and metasurfaces: optical {\em anapoles} and photonic {\em bound states in the continuum}. We discuss a brief history of these states in optics, their underlying physics and manifestations, and also emphasize their differences and similarities. We also review some applications of such novel photonic states in both linear and nonlinear optics for the nanoscale field enhancement, a design of novel dielectric structures with high-$Q$ resonances, nonlinear wave mixing and enhanced harmonic generation, as well as advanced concepts for lasing and optical neural networks.Comment: 22 pages, 9 figures, review articl

Topological semimetal in a fermionic optical lattice

Optical lattices play a versatile role in advancing our understanding of correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard and hexagonal optical lattices opens up a new thrust towards discovering novel quantum states of matter, which have no prior analogs in solid state electronic materials. Here, we demonstrate that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. The new quantum state is characterized by a parabolic band-degeneracy point with Berry flux $2\pi$, in sharp contrast to the $\pi$ flux of Dirac points as in graphene. We prove that the appearance of this topological liquid is universal for all lattices with D$_4$ point group symmetry as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states.Comment: 6 pages, 3 figures and Supplementary Informatio

Easily retrievable objects among the NEO population

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth’s neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of Δv. Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs