Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice

TL;DR

This paper investigates a square lattice model supporting various topological phases, revealing that hidden symmetries protect band degeneracies and influence phase transitions, including the emergence of quantum anomalous Hall effects.

Contribution

It identifies novel hidden symmetries that protect topological semimetal phases and their degeneracies in a square lattice system, providing new insights into symmetry protection mechanisms.

Findings

Hidden symmetries protect Weyl and flux topological semimetals.

Breaking hidden symmetries opens a band gap, inducing insulating phases.

Quantum anomalous Hall effect arises under specific parameters.

Abstract

We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and $2\pi$-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and $2\pi$-flux topological semimetal are protected by two distinct novel hidden symmetries, which both corresponds to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry.