Realizing type-II Weyl points in an optical lattice

Abstract

The recent discovery of the Lorentz symmetry-violating 'Type II' Weyl semimetal phase has renewed interest in the study of Weyl physics in condensed matter systems. However, tuning the exceptional properties of this novel state has remained a challenge. Optical lattices, created using standing laser beams, provide a convenient platform to tune tunnelling parameters continuously in time. In this paper, we propose a generalised two level system exhibiting type II Weyl points that can be realised using ultra-cold atoms in an optical lattice. The system is engineered using a three-dimensional lattice with complex π phase tunnelling amplitudes. Various unique properties of the type II Weyl semimetal such as open Fermi surface, anomalous chirality and topological Fermi arcs can be probed using the proposed optical lattice scheme. Introduction-In-spite of its theoretical proposal as early as 1929 [1], Weyl Fermion, one of the intriguing particles predicted in the development of quantum field theory, has not been observed as an elementary particle. However, these massless particles have been recently detected in condensed matter experiments as low energy collective excitations, or quasi-particles, in a Weyl SemiMetal (WSM) that supports Fermi-arc topological surface states [2-4]. As described by quantum field theory that is intrinsically relativistic, Weyl Fermions are Lorentz covariant. Nevertheless, Lorentz symmetry can be violated in condensed matter systems, resulting in 'type II' Weyl semimetal phase, that has no equivalent in quantum field theory. This newly proposed type-II WSM phase [5,6], has been experimentally observed in materials such as MoTe2 [7][8][9][10] and LaAlGe [11], and has been predicted to exist in other materials such as diphosphides of Mo and W [12]. Compared to the type I WSM phase, the type II phase exhibits many novel properties such as non-vanishing finite density of states at Fermi level [5] and anomalous chiral Landau levels [13][14][15]. These properties together with the topologically protected Fermi arc surface states, apart from being interesting in fundamental physics, may be useful in the realisation of quantum computation and high efficiency circuitry.

Topological metal bands with double-triple-point fermions in optical lattices

“…The 2D spin-orbit coupling and topological bands have been generated in an optical Raman lattice [54,55]. In addition, several schemes have been suggested to realize topological semimetal bands with Weyl fermions [56][57][58][59][60][61][62][63][64][65][66] and double-Weyl fermions [67,68]. Moreover, it has been proposed that the spin-1 triplepoint fermions can emerge in some topological metal bands in cold atom systems [24][25][26], which can even be simulated in parameter space [69,70].…”

Weyl points and Fermi arcs in a chiral phononic crystal

“…In addition to the standard Weyl points possessing a point-like Fermi surface (referred to as type-I), another type of Weyl point was more recently recognized, which has a conical Fermi surface (referred to as type-II) 13,[19][20][21] . Since the Weyl point or Weyl cone in Weyl semimetals represents a special dispersion of electrons moving in periodic potentials, the question naturally arises as to whether a similar dispersion or the Weyl point for classical waves propagating in artificial periodic structures exists [8][9][10][11][12][13][22][23][24][25][26][27][28] . Lu et al were the first to report the existence of Weyl points and the associated one-way SWs in photonic crystals based on double-gyroid structures 8,9 .…”

Type-II Dirac Photons at Metasurfaces

“…Among all classical wave systems, the topological photonic system has received the most attention due to its foreseeable impact in technology and because the characterization can be carried out using standard equipment. For example, three-dimensional (3D) Dirac points (DPs) and Weyl points have been created in dielectric photonic crystals [15,[19][20][21]. Recently, the design of type-II DPs using photonic crystals has been theoretically predicted [34][35][36], but the existence of these DPs has not yet been demonstrated experimentally.…”