Geometric semimetals and their simulation in synthetic matter

TL;DR

This paper introduces geometric semimetals, a new class of three-dimensional gapless systems with nontrivial band geometry, protected by symmetries but topologically trivial, and discusses their potential realization in synthetic matter experiments.

Contribution

It proposes geometric semimetals as a novel class of gapless systems with nontrivial band geometry, expanding the understanding of topological phases.

Findings

Geometric semimetals are protected by generalized chiral and rotation symmetries.

They exhibit nonzero quantum metric trace, possibly quantized.

Potential realization in synthetic-matter experiments is discussed.

Abstract

Topological semimetals, such as the Weyl and Dirac semimetals, represent one of the most active research fields in modern condensed matter physics. The peculiar physical properties of these systems mainly originate from their underlying symmetries, emergent relativistic dispersion, and band topology. In this Letter, we present a different class of gapless systems in three dimensions, dubbed $\textit{geometric semimetals}$. These semimetals are protected by the generalized chiral and rotation symmetries, but are topologically trivial. Nevertheless, we show that their band geometry is nontrivial, as evidenced by the nonzero quantum metric trace with possible quantization. The possible realization in synthetic-matter experiments is also discussed.