Theory-Guided, Machine-Learning-Accelerated Discovery of a 3D Carbon Nested Nodal-Surface Semimetal

TL;DR

This paper introduces a symmetry-based design principle and machine learning approach to discover a new 3D carbon allotrope, Netsene, exhibiting nested nodal-surface topological semimetal properties with high carrier mobility.

Contribution

It develops a systematic method combining symmetry engineering and machine learning to discover novel topological materials, exemplified by Netsene, a stable 3D carbon nodal-surface semimetal.

Findings

Netsene is a dynamically and mechanically stable 3D carbon allotrope.

It hosts a complex nested nodal-surface system protected by non-symmorphic symmetries.

Netsene exhibits high Fermi velocities comparable to graphene.

Abstract

Extending the Dirac physics of two-dimensional (2D) graphene into three dimensions (3D) carbon allotropes with higher-dimensional band degeneracies remains a central challenge in topological materials science. Here, we propose a general symmetry-engineering principle that systematically transforms graphene's Dirac cone into a 3D nodal surface via controlled layering and registry shift, and employ this principle to guide a machine-learning-accelerated inverse design. By integrating a crystal diffusion variational autoencoder(CDVAE) with a Crystal Transformer, we discover a novel, dynamically and mechanically stable carbon allotrope named \textbf{Netsene} (bct-C$_{24}$), which crystallizes in the body-centered tetragonal \textit{I4/mcm} space group. First-principles calculations confirm that Netsene is a unique nested nodal-surface semimetal: it hosts a complex, double-bowl-shaped nodal-surface system around the Fermi level, protected by non-symmorphic symmetries, alongside Dirac-like linear crossings with Fermi velocities comparable to graphene ($\sim 9 \times 10^5$~m/s). Its non-trivial bulk topology manifests in drumhead surface states, including a nearly flat band. Netsene provides a structurally robust, bulk platform that unifies ultrahigh carrier mobility, topological nodal surfaces, and potential correlation physics, demonstrating the power of theory-guided, machine-learning-accelerated discovery for engineering topological quantum phases.