Symmetry-protected coexistence of a nodal surface and multiple types of Weyl fermions in $P6_3$-$\text{B}_{30}$

TL;DR

This paper predicts that the boron allotrope P6_3-B30 hosts coexisting topological states, including a nodal surface and various Weyl fermions, offering a platform for multidimensional topological physics exploration.

Contribution

It introduces P6_3-B30 as a stable, spinless topological semimetal with coexisting nodal surface and multiple Weyl fermions protected by crystal symmetries.

Findings

P6_3-B30 hosts a symmetry-enforced nodal surface at k_z=π.

Multiple types of Weyl fermions are present at high-symmetry points.

Surface states show Fermi arcs connecting Weyl nodes.

Abstract

The coexistence of topological states with different dimensionalities in a single crystalline system offers a unique platform to study the interplay of distinct fermionic excitations. Here, integrating first-principles calculations with symmetry analysis, we propose the three-dimensional boron allotrope $P6_3$-$\text{B}_{30}$ as an ideal, structurally stable candidate for exploring multidimensional topological physics. Benefiting from the practically negligible spin-orbit coupling of the light-element framework, $P6_3$-$\text{B}_{30}$ operates as a pristine spinless topological semimetal. We show that the combined time-reversal and twofold screw symmetry ($\mathcal{T}S_{2z}$) enforces a robust two-dimensional nodal surface on the $k_z = \pi$ plane via a Kramers-like degeneracy. Concurrently, the system hosts a diverse set of zero-dimensional Weyl fermions -- including an unconventional double-Weyl point ($\mathcal{C} = -2$), conventional Type-I WPs ($\mathcal{C} = -1$), and completely tilted Type-II WPs ($\mathcal{C} = +1$) -- emerging at the high-symmetry points $\Gamma$ and K, as well as along the H-K path, protected by $C_6$ and $C_3$ crystalline rotational symmetries. Crucially, the substantial momentum-space separation between the nodal surface and Weyl points allows for their unambiguous independent resolution. Calculations of the (100) surface states reveal distinct, nontrivial Fermi arcs connecting Weyl nodes of opposite chirality. This work establishes $P6_3$-$\text{B}_{30}$ as a compelling material platform for investigating the physics of multidimensional hybrid topological fermions and their interplay.