Conical intersections for light and matter waves

Abstract

We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective Dirac equation, with electron spin replaced by a "fermionic" half-integer pseudospin. However, in many systems such as metamaterials, modal symmetries result in the formation of higher order conical intersections with integer or "bosonic" pseudospin. The ability to engineer lattices with these qualitatively different singular dispersion relations opens up many applications, including superior slab lasers, generation of orbital angular momentum, zeroindex metamaterials, and quantum simulation of exotic phases of relativistic matter.

Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems

“…where the integral is again taken similarly to Eq. (8). For the spectrum (2), we find [30] w 2 = 0, |sk y | < |m|…”

“…k ∈ π a [−1, 1] becomes a parameter and the winding numbers of each domain are calculated over the 1D Brillouin zone defined by k ⊥ ∈ 2π a √ 3 (−1, 1) using Eqs. (8) and (10) for the field (S4) (see also Section I above). Figure S5 shows k-distributions of the direction angle Re φ and the phase Arg B of the B-field (S4), as well as the corresponding winding numbers w 1 (k ) and w 2 (k ) for γ = 0.4.…”

“…Both types of phenomena have been studied in the context of quantum as well as classical waves, and both are deeply tied to the geometrical features of spectral degeneracies. In the Hermitian case, the common degeneracies are Dirac points: linear bandcrossings (generically, in a 3D parameter space), which separate distinct topological phases and mark the birth or destruction of topological edge modes [7,8]. Non-Hermitian systems, however, exhibit a distinct class of spectral degeneracies known as exceptional points (EPs), which are branch points in a 2D parameter space where the Hamiltonian becomes non-diagonalizable [4,9,10].…”

Realization of a magneto-optical near-zero index medium by an unpaired Dirac point

“…This provides a practical method for using all-dielectric photonic structures to realize NZ index media, which have numerous exotic capabilities such as geometry-insensitive wave-guiding [7]. Although the type of band-crossing point utilized in these schemes [8][9][10][11][12][13] is sometimes called "Dirac-like", due to the conical dispersion, it is not actually described by a Dirac Hamiltonian, as evidenced by the fact that the cone is attached to an inseparable flat band [14,15]. The underlying photonic crystals in these studies are Tsymmetric, and so are the effective media, which have NZ refractive index but no magneto-optical activity.…”

Nonlinear optical response of the α−T3 model due to the nontrivial topology of the band dispersion

“…It is also found that the nonlinear optical conductivity of graphene would topologically be enhanced in the presence of spin-orbit coupling [38][39][40]. Inspired by these properties of graphene, there is a growing interest in studying similar structures for potential use in nanoelectronics [41].…”