Cubic 3D Chern photonic insulators with orientable large Chern vectors

Time Reversal Symmetry (TRS) broken topological phases provide gapless surface states protected by topology, regardless of additional internal symmetries, spin or valley degrees of freedom. Despite the numerous demonstrations of 2D topological phases, few examples of 3D topological systems with TRS breaking exist. In this article, we devise a general strategy to design 3D Chern insulating (3D CI) cubic photonic crystals in a weakly TRS broken environment with orientable and arbitrarily large Chern vectors. The designs display topologically protected chiral and unidirectional surface states with disjoint equifrequency loops. The resulting crystals present the following characteristics: First, by increasing the Chern number, multiple surface states channels can be supported. Second, the Chern vector can be oriented along any direction simply changing the magnetization axis, opening up larger 3D CI/3D CI interfacing possibilities as compared to 2D. Third, by lowering the TRS breaking requirements, the system is ideal for realistic photonic applications where the magnetic response is weak.

Particle Physics Phenomenology

The most important milestones in particle physics are put in a historical perspective. We follow a century of scattering experiments, from Rutherford to LHC. We introduce successively the concept of the atomic nucleus, the study of β‎-decay and the proposal of the neutrino, the first internal symmetries, the Fermi theory and the Yukawa meson. In parallel we present the technical achievements in accelerator and detector technologies which made these advances possible. We end with the discovery of strange particles, the flavour SU(3) unitary symmetry, and the introduction of the quarks. This chapter follows a descriptive rather than a deductive approach and summa- rises many aspects of particle physics phenomenology which preceded the discovery of the Standard Model.

Fundamental Theory of Torsion Gravity

In this work, we present the general differential geometry of a background in which the space–time has both torsion and curvature with internal symmetries being described by gauge fields, and that is equipped to couple spinorial matter fields having spin and energy as well as gauge currents: torsion will turn out to be equivalent to an axial-vector massive Proca field and, because the spinor can be decomposed in its two chiral projections, torsion can be thought as the mediator that keeps spinors in stable configurations; we will justify this claim by studying some limiting situations. We will then proceed with a second chapter, where the material presented in the first chapter will be applied to specific systems in order to solve problems that seems to affect theories without torsion: hence the problem of gravitational singularity formation and positivity of the energy are the most important, and they will also lead the way for a discussion about the Pauli exclusion principle and the concept of macroscopic approximation. In a third and final chapter, we are going to investigate, in the light of torsion dynamics, some of the open problems in the standard models of particles and cosmology which would not be easily solvable otherwise.

Cubic 3D Chern photonic insulators with orientable large Chern vectors

Time Reversal Symmetry (TRS) broken topological phases provide gapless surface states protected by topology, regardless of additional internal symmetries, spin or valley degrees of freedom. Despite the numerous demonstrations of 2D topological phases, few examples of 3D topological systems with TRS breaking exist. In this article, we devise a general strategy to design 3D Chern insulating (3D CI) cubic photonic crystals in a weakly TRS broken environment with orientable and arbitrarily large Chern vectors. The designs display topologically protected chiral and unidirectional surface states with disjoint equifrequency loops. The resulting crystals present the following novel characteristics: First, by increasing the Chern number, multiple surface states channels can be supported. Second, the Chern vector can be oriented along any direction simply changing the magnetization axis, opening up larger 3D CI/3D CI interfacing possibilities as compared to 2D. Third, by lowering the TRS breaking requirements, the system is ideal for realistic photonic applications where the magnetic response is weak.

Probing stacking configurations in a few layered MoS2 by low frequency Raman spectroscopy

Novel two-dimensional (2D) layered materials, such as MoS2, have recently gained a significant traction, chiefly due to their tunable electronic and optical properties. A major attribute that affects the tunability is the number of layers in the system. Another important, but often overlooked aspect is the stacking configuration between the layers, which can modify their electro-optic properties through changes in internal symmetries and interlayer interactions. This demands a thorough understanding of interlayer stacking configurations of these materials before they can be used in devices. Here, we investigate the spatial distribution of various stacking configurations and variations in interlayer interactions in few-layered MoS2 flakes probed through the low-frequency Raman spectroscopy, which we establish as a versatile imaging tool for this purpose. Some interesting anomalies in MoS2 layer stacking, which we propose to be caused by defects, wrinkles or twist between the layers, are also reported here. These types of anomalies, which can severely affect the properties of these materials can be detected through low-frequency Raman imaging. Our findings provide useful insights for understanding various structure-dependent properties of 2D materials that could be of great importance for the development of future electro-optic devices, quantum devices and energy harvesting systems.

Classification of topological phases with finite internal symmetries in all dimensions

We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.

Timeless State of Gravity: Possible Solution for Cosmological Constant problem

We study a localization of gravity through the matching point between non-inertial frames and local inertial frames. This localization of gravity is done through defining relative gravitational red-shift. This lead to an emergence of a timeless state in a mathematically consistent way. In this timeless state of gravity, we find a geometric interpretation of the speed of light and mass. The experimental support of the timeless state is the quantum entanglement and internal symmetries that are independent of time. Therefore gravity would be responsible for measurements independent of time including quantum entanglement. Based on the Gravity/Gauge equivalence in the timeless state, we conjecture that the universe emerged from a black hole with a global $SU(3)\times SU(2)\times U(1)$ symmetry on its event horizon that produces gauge fields Electromagnetism, weak and strong nuclear force through localization of this global symmetry. Through the localization in the gravity field, the timeless measurements such as spin will be correlated with the varying of timeless measurement which is relative gravitational red-shift. We present a gravitational or geometric interpretation of spin-0, spin-1, and spin-1/2 states. We present an interpretation of why do we measure matter rather than anti-matter. We found that the Higgs scalar field is represented by the gravitational red-shift at every point in the space around the black hole. We derive the numerical value of the cosmological constant that agrees with experimental observations.

From Conception to Kamchatka

In the early 1980s, scientists were astounded to discover a new phase of matter, the quasicrystal—a material that exhibits internal symmetries incompatible with a regularly repeating pattern. In The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter, Paul Steinhardt recounts his first encounters with quasicrystals and his decades-long search for a naturally formed example.