Weyl semimetals in optical lattices: moving and merging of Weyl points, and hidden symmetry at Weyl points.

Jing-Min Hou,Wei Chen

doi:10.1038/srep33512

Jing-Min Hou, Wei Chen

Open Access

https://doi.org/10.1038/srep33512

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Abstract

We propose to realize Weyl semimetals in a cubic optical lattice. We find that there exist three distinct Weyl semimetal phases in the cubic optical lattice for different parameter ranges. One of them has two pairs of Weyl points and the other two have one pair of Weyl points in the Brillouin zone. For a slab geometry with (010) surfaces, the Fermi arcs connecting the projections of Weyl points with opposite topological charges on the surface Brillouin zone is presented. By adjusting the parameters, the Weyl points can move in the Brillouin zone. Interestingly, for two pairs of Weyl points, as one pair of them meet and annihilate, the originial two Fermi arcs coneect into one. As the remaining Weyl points annihilate further, the Fermi arc vanishes and a gap is opened. Furthermore, we find that there always exists a hidden symmetry at Weyl points, regardless of anywhere they located in the Brillouin zone. The hidden symmetry has an antiunitary operator with its square being −1.

Highlights

It is a difficult task to investigate moving and merging of Weyl points and topological phase transitions in real solid materials, the parameters of which can not be tuned in a wide ranges
Based on a mapping method, we discover the hidden symmetry at each Weyl point in the Brillouin zone and discuss its relation with topological phase transitions
When the Weyl points with opposite topological charges meet, they merge and annihilate, which leads to a topological phase transition

Summary

Introduction

It is a difficult task to investigate moving and merging of Weyl points and topological phase transitions in real solid materials, the parameters of which can not be tuned in a wide ranges. It is intriguing to study moving and merging of Weyl points, and topological phase transitions in optical lattices. The hopping-accompanying phase has been realized with periodic lattice shaking[31,32] and laser-assisted tunneling techniques[33,34,35,36] Another important progress in experiments is the measurement of Zak phase of topological Bloch bands in optical lattices[37], which provides a path to detect topological characters in optical lattices. Fermi arcs connect the projections of Weyl poionts on the surface Brillouin zone and evolve with the moving of Weyl points. For the Weyl semimetal phase with two pairs of Weyl points, there are two Fermi arcs connect projections of Weyl points with opposite charges on the surface Brillouin zone. Based on a mapping method, we discover the hidden symmetry at each Weyl point in the Brillouin zone and discuss its relation with topological phase transitions

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