Type-II Weyl Points in Three-Dimensional Cold Atom Optical Lattices

Abstract

Topological Lifshitz phase transition characterizes an abrupt change of the topology of the Fermi surface through a continuous deformation of parameters. Recently, Lifshitz transition has been predicted to separate two types of Weyl points: type-I and type-II (or called structured Weyl points), which has attracted considerable attention in various fields. Although recent experimental investigation has seen a rapid progress on type-II Weyl points, it still remains a significant challenge to observe their characteristic Lifshitz transition. Here, we propose a scheme to realize both type-I and type-II Weyl points in three-dimensional ultracold atomic gases by introducing an experimentally feasible configuration based on current spin-orbit coupling technology. In the resultant Hamiltonian, we find three degenerate points: two Weyl points carrying a Chern number $-1$ and a four-fold degenerate point carrying a Chern number $2$. Remarkably, by continuous tuning of a convenient experimental knob, all these degenerate points can transition from type-I to type-II, thereby providing an ideal platform to study different types of Weyl points and directly probe their Lifshitz phase transition.

10 pages, 5 figures

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• Electromagnetic Scattering Laws in Weyl Systems
• Tilted disordered Weyl semimetals
• Exploring topological double-Weyl semimetals with cold atoms in optical lattices
• Realising Type II Weyl Points in an Optical Lattice
• On the renormalization of Coulomb interactions in two-dimensional tilted Dirac fermions
• Weyl Bogoliubov excitations in Bose-Hubbard extension of Weyl semimetal
• Exotic Topological States with Raman-Induced Spin-Orbit Coupling