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

TL;DR

This paper proposes a feasible method to realize and study both type-I and type-II Weyl points in three-dimensional cold atom systems, enabling direct observation of their Lifshitz phase transition.

Contribution

It introduces a new experimental scheme using current spin-orbit coupling technology to realize and tune Weyl points in ultracold atomic gases.

Findings

Identification of three degenerate points with distinct Chern numbers.

Demonstration of continuous transition from type-I to type-II Weyl points.

Provision of a platform for experimental study of Weyl point topological transitions.

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.