Abstract:
Defect models have recently been declared dead (Watson 1997), because they predict microwave background and matter fluctuations grossly out of line with what we see. In this talk we apply the fact that many defects are automatically destroyed at the time of radiation-matter transition, thus resurrecting the defects model. Moreover, the resurrected version predicts a cosmological constant, explains the apparent excess of hot clusters and the non-Gaussianity observed in galaxy surveys. If this model is correct, then the MAP and PLANCK missions will not measure what people expect them to (oscillations); rather, they will measure a broad hump.

Abstract:
Graphene, being one-atom thick, is extremely sensitive to the presence of adsorbed atoms and molecules and, more generally, to defects such as vacancies, holes and/or substitutional dopants. This property, apart from being directly usable in molecular sensor devices, can also be employed to tune graphene electronic properties. Here we briefly review the basic features of atomic-scale defects that can be useful for material design. After a brief introduction on isolated $p_z$ defects, we analyse the electronic structure of multiple defective graphene substrates, and show how to predict the presence of microscopically ordered magnetic structures. Subsequently, we analyse the more complicated situation where the electronic structure, as modified by the presence of some defects, affects chemical reactivity of the substrate towards adsorption (chemisorption) of atomic/molecular species, leading to preferential sticking on specific lattice positions. Then, we consider the reverse problem, that is how to use defects to engineer graphene electronic properties. In this context, we show that arranging defects to form honeycomb-shaped superlattices (what we may call "supergraphenes") a sizeable gap opens in the band structure and new Dirac cones are created right close to the gapped region. Similarly, we show that substitutional dopants such as group IIIA/VA elements may have gapped quasi-conical structures corresponding to massive Dirac carriers. All these possible structures might find important technological applications in the development of graphene-based logic transistors.

Abstract:
The electrostatic behavior of a prototypical three-dimensional topological insulator Bi$_2$Se$_3$(111) is investigated by a scanning tunneling microscopy (STM) study of the distribution of Rb atoms adsorbed on the surface. The positively charged ions are screened by both free electrons residing in the topological surface state as well as band bending induced quantum well states of the conduction band, leading to a surprisingly short screening length. Combining a theoretical description of the potential energy with STM-based atomic manipulation, we demonstrate the ability to create tailored electronic potential landscapes on topological surfaces with atomic-scale control.

Abstract:
We present a brief overview of recently proposed detection schemes for axion, axion-like pseudoscalar particle and topological defect dark matter. We focus mainly on the possibility of using atomic and molecular systems for dark matter detection. For axions and axion-like particles, these methods are complementary probes to ongoing photon-axion interconversion experiments and astrophysical observations. For topological defects, these methods are complementary to conventional astrophysical search schemes based on gravitational signatures.

Abstract:
It is tempting to inflate along one of the many flat directions that arise in supersymmetric theories. The required flatness of the potential to obtain sufficient inflation and to not overproduce density fluctuations occurs naturally. However, the density perturbations (in the case of a single moduli field) that arise from inflaton quantum fluctuations are too small for structure formation. Here we propose that topological defects (such as cosmic strings), which arise during a phase transition near the end of moduli inflation can provide an alternative source of structure. The strings produced will be `fat', yet have the usual evolution by the time of nucleosynthesis. Possible models are discussed.

Abstract:
Quantum systems can provide outstanding performance in various sensing applications, ranging from bioscience to nanotechnology. Atomic-scale defects in silicon carbide are very attractive in this respect because of the technological advantages of this material and favorable optical and radio frequency spectral ranges to control these defects. We identified several, separately addressable spin-3/2 centers in the same silicon carbide crystal, which are immune to nonaxial strain fluctuations. Some of them are characterized by nearly temperature independent axial crystal fields, making these centers very attractive for vector magnetometry. Contrarily, the zero-field splitting of another center exhibits a giant thermal shift of -1.1 MHz/K at room temperature, which can be used for thermometry applications. We also discuss a synchronized composite clock exploiting spin centers with different thermal response.

Abstract:
We investigate cosmological structure formation seeded by topological defects which may form during a phase transition in the early universe. First we derive a partially new, local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced by topological defects or any other type of seeds. We then show that this system is well suited for numerical analysis of structure formation by applying it to seeds induced by fluctuations of a global scalar field. Our numerical results are complementary to previous investigations since we use substantially different methods. The resulting microwave background fluctuations are compatible with older simulations. We also obtain a scale invariant spectrum of fluctuations with about the same amplitude. However, our dark matter results yield a smaller bias parameter compatible with $b\sim 2$ on a scale of $20 Mpc$ in contrast to previous work which yielded to large bias factors. Our conclusions are thus more positive. According to the aspects analyzed in this work, global topological defect induced fluctuations yield viable scenarios of structure formation and do better than standard CDM on large scales.

Abstract:
We study the spin waves of the triangular skyrmion crystal that emerges in a two dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii-Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.

Abstract:
The scenario of a cosmology with topological defects is surveyed starting from the field theoretic aspects and ending with a description of large-scale structure formation and magnetic field generation. (Lectures delivered at ICTP, Trieste, July 1993.)

Abstract:
Spontaneous symmetry-breaking, where the ground state of a system has lower symmetry than the underlying Hamiltonian, is ubiquitous in physics. It leads to multiply-degenerate ground states, each with a different "broken" symmetry labeled by an order parameter. The variation of this order parameter in space leads to soliton-like features at the boundaries of different broken-symmetry regions and also to topological point defects. Bilayer graphene is a fascinating realization of this physics, with an order parameter given by its interlayer stacking coordinate. Bilayer graphene has been a subject of intense study because in the presence of a perpendicular electric field, a band gap appears in its electronic spectrum [1-3] through a mechanism that is intimately tied to its broken symmetry. Theorists have further proposed that novel electronic states exist at the boundaries between broken-symmetry stacking domains [4-5]. However, very little is known about the structural properties of these boundaries. Here we use electron microscopy to measure with nanoscale and atomic resolution the widths, motion, and topological structure of soliton boundaries and topological defects in bilayer graphene. We find that each soliton consists of an atomic-scale registry shift between the two graphene layers occurring over 6-11 nm. We infer the minimal energy barrier to interlayer translation and observe soliton motion during in-situ heating above 1000 {\deg}C. The abundance of these structures across a variety samples, as well as their unusual properties, suggests that they will have substantial effects on the electronic and mechanical properties of bilayer graphene.