Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals

TL;DR

This paper introduces a new class of topological semimetals stabilized by off-centered symmetries in nonsymmorphic crystals, revealing how these symmetries enforce band degeneracies leading to point and line nodes.

Contribution

It provides a general framework for stabilizing band degeneracies using off-centered symmetries, especially in systems with strong spin-orbit coupling, expanding the understanding of topological semimetals.

Findings

Off-centered rotation/mirror symmetries induce band sticking in nonsymmorphic crystals.

Doublet pairs form due to partial translation, protecting topological nodes.

The framework applies to systems with strong spin-orbit coupling.

Abstract

Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been known that certain crystalline symmetries play an important role in protecting band degeneracy, a general recipe for stabilizing the degeneracy, especially in the presence of spin-orbit coupling, is still lacking. Here we show that a class of novel topological semimetals with point/line nodes can emerge in the presence of an off-centered rotation/mirror symmetry whose symmetry line/plane is displaced from the center of other symmorphic symmetries in nonsymmorphic crystals. Due to the partial translation perpendicular to the rotation axis/mirror plane, an off-centered rotation/mirror symmetry always forces two energy bands to stick together and form a doublet pair in the relevant invariant line/plane in momentum space. Such a doublet pair provides a basic building block for emerging topological semimetals with point/line nodes in systems with strong spin-orbit coupling.