Line nodes, Dirac points and Lifshitz transition in 2D nonsymmorphic photonic crystals

Topological phase transitions, which have fascinated generations of physicists, are always demarcated by gap closures. In this work, we propose very simple 2D photonic crystal lattices with gap closure points, i.e. band degeneracies protected by nonsymmorphic symmetry. Our photonic structures are relatively easy to fabricate, consisting of two inequivalent dielectric cylinders per unit cell. Along high symmetry directions, they exhibit line degeneracies protected by glide reflection symmetry, which we explicitly demonstrate for $pg,pmg,pgg$ and $p4g$ nonsymmorphic groups. In the presence of time reversal symmetry, they also exhibit point degeneracies (Dirac points) protected by a $Z_2$ topological number associated with crystalline symmetry. Strikingly, the robust protection of $pg$-symmetry allows a Lifshitz transition to a type II Dirac cone across a wide range of experimentally accessible parameters, thus providing a convenient route for realizing anomalous refraction. Further potential applications include a stoplight device based on electrically induced strain that dynamically switches the lattice symmetry from $pgg$ to the higher $p4g$ symmetry. This controls the coalescence of Dirac points and hence the group velocity within the crystal.Comment: 11 pages, 8 figures, 3 table

Domain wall brane in a reduced Born-Infeld-f(T)f(T) theory

The Born-Infeld $f(T)$ theory is reduced from the Born-Infeld determinantal gravity in Weitzenb\"ock spacetime. We investigate a braneworld scenario in this theory and obtain an analytic domain wall solution by utilizing the first-order formalism. The model is stable against the linear tensor perturbation. It is shown that the massless graviton is localized on the brane, but the continuous massive gravitons are non-localized and will generate a tiny correction with the behavior of ${1}/{(k r)^{3}}$ to the Newtonian potential. The four-dimensional teleparallel gravity is recovered as an effective infrared theory on the brane. As a physical application, we consider the (quasi-)localization property of spin-1/2 Dirac fermion in this model.Comment: 9 pages, 2 figures, published versio