Nodal surface semimetals: Theory and material realization

TL;DR

This paper provides a comprehensive theoretical framework for understanding nodal surface semimetals, classifies different types based on symmetry protections, and predicts real material examples through first-principles calculations.

Contribution

It introduces new classes of nodal surface semimetals protected by crystalline symmetries, including magnetic systems, and predicts material realizations.

Findings

Nodal surfaces can be protected by spacetime inversion and sublattice symmetries.

Spin-orbit coupling can destroy or preserve certain nodal surfaces depending on symmetry.

First-principles calculations predict specific materials hosting nodal surfaces.

Abstract

We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence bands cross on closed nodal surfaces in the Brillouin zone. We propose different classes of nodal surfaces, both in the absence and in the presence of spin-orbit coupling (SOC). In the absence of SOC, a class of nodal surfaces can be protected by spacetime inversion symmetry and sublattice symmetry and characterized by a $\mathbb{Z}_2$ index, while another class of nodal surfaces are guaranteed by a combination of nonsymmorphic two-fold screw-rotational symmetry and time-reversal symmetry. We show that the inclusion of SOC will destroy the former class of nodal surfaces but may preserve the latter provided that the inversion symmetry is broken. We further generalize the result to magnetically ordered systems and show that protected nodal surfaces can also exist in magnetic materials without and with SOC, given that certain magnetic group symmetry requirements are satisfied. Several concrete nodal-surface material examples are predicted via the first-principles calculations. The possibility of multi-nodal-surface materials is discussed.