# Exploring topological double-Weyl semimetals with cold atoms in optical lattices

## TL;DR

This paper proposes a cold atom optical lattice setup to realize and detect double-Weyl semimetals, exploring their topological properties, phase transitions, and experimental detection methods.

## Contribution

It introduces a feasible model for simulating double-Weyl semimetals with cold atoms and details methods to detect their topological features and phase transitions.

## Key findings

- Double-Weyl points behave as Berry flux sinks and sources stabilized by C_{4h} symmetry.
- Splitting of double-Weyl points into single-Weyl points under C_4 breaking.
- Detection of topological phases via atomic transfer fractions, Wannier center shifts, and spin polarization.

## Abstract

We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose to realize a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of \$pm2$ behave as sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the \$C_{4h}$ point-group symmetry. By applying a realizable \$C_4$ breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the \$C_4$ breaking term, which contains a topological and a normal insulating phases and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with the time-of-flight imaging; (iii) the band topology of the \$C_4$ symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.