Polarization jumps by breaking symmetries of two-dimensional Weyl semimetals

TL;DR

This paper investigates how symmetry-breaking in 2D Weyl semimetals causes polarization jumps, revealing a universal relation with Weyl node displacement, and extends understanding of polarization behavior in gapless topological systems.

Contribution

It demonstrates that polarization jumps occur in 2D Weyl semimetals when symmetry is broken, characterized by the Weyl dipole, providing a universal description applicable to such materials.

Findings

Polarization exhibits a jump when a symmetry-breaking gap opens.

The jump is universally described by the Weyl dipole.

Results apply broadly to 2D Weyl semimetals.

Abstract

The electric polarization as a bulk quantity is described by the modern theory of polarization in insulating systems and cannot be defined in conducting systems. Upon a gradual change of a parameter in the system, the polarization always varies smoothly as long as the gap remains open. In this paper, we focus on the two-dimensional Weyl semimetal, which hosts Weyl nodes protected by symmetries, and study the behavior of the polarization when a symmetry-breaking term $M$ is introduced and a gap opens. We show that there can be a jump between $M\to0^+$ and $M\to0^-$ limits. We find that the jump is universally described by the ``Weyl dipole" representing how the Weyl nodes with monopole charges are displaced in the reciprocal space. Our result is applicable to general two-dimensional Weyl semimetals.