# Generating controllable type-II Weyl points via periodic driving

## TL;DR

This paper proposes a method to generate and control type-II Weyl points in a topological semimetal model using quantum and classical fields, enabling potential applications in quantum optics and Floquet topological phases.

## Contribution

It introduces a way to realize controllable type-II Weyl points through a generalized Harper model with harmonic driving, including quantum treatment of the driving field.

## Key findings

- Type-II Weyl points can be generated by quantum treatment of the driving field.
- Tuning coupling strength controls Weyl point tilt and energy difference.
- Distinction between type-I and type-II Weyl points via Landau level structures.

## Abstract

Type-II Weyl semimetals are a novel gapless topological phase of matter discovered recently in 2015. Similar to normal (type-I) Weyl semimetals, type-II Weyl semimetals consist of isolated band touching points. However, unlike type-I Weyl semimetals which have a linear energy dispersion around the band touching points forming a three dimensional (3D) Dirac cone, type-II Weyl semimetals have a tilted cone-like structure around the band touching points. This leads to various novel physical properties that are different from type-I Weyl semimetals. In order to study further the properties of type-II Weyl semimetals and perhaps realize them for future applications, generating controllable type-II Weyl semimetals is desirable. In this paper, we propose a way to generate a type-II Weyl semimetal via a generalized Harper model interacting with a harmonic driving field. When the field is treated classically, we find that only type-I Weyl points emerge. However, by treating the field quantum mechanically, some of these type-I Weyl points may turn into type-II Weyl points. Moreover, by tuning the coupling strength, it is possible to control the tilt of the Weyl points and the energy difference between two Weyl points, which makes it possible to generate a pair of mixed Weyl points of type-I and type-II. We also discuss how to physically distinguish these two types of Weyl points in the framework of our model via the Landau level structures in the presence of an artificial magnetic field. The results are of general interest to quantum optics as well as ongoing studies of Floquet topological phases.