Symmetry-protected four double-Weyl fermions and their topological phase transitions in nonmagnetic crystals

TL;DR

This paper classifies symmetry conditions for four double-Weyl fermions in nonmagnetic crystals, identifies a candidate material, and explores strain-induced topological phase transitions.

Contribution

It establishes symmetry constraints for four double-Weyl points, identifies a candidate material, and analyzes their topological phase transitions under strain.

Findings

28 space groups can host four symmetry-protected double-Weyl points.

Identified THRLN-C$_{32}$ as an ideal material candidate.

Strain induces transitions from four-DWP state to Weyl complexes, conventional WPs, or trivial insulator.

Abstract

Realizing Weyl semimetals (WSMs) with the minimal number of Weyl points (WPs) fundamentally simplifies extracting intrinsic topological responses. While a minimum of four conventional ($|C|=1$) WPs in nonmagnetic crystals is well-established, the exact symmetry requirements and material realization for the unique configuration of four unconventional double-Weyl points (DWPs, $|C|=2$) remain unresolved. Here, we establish rigorous crystalline symmetry constraints restricting the existence of exactly four symmetry-protected DWPs to merely 28 space groups in both nonmagnetic spinless and spinful systems. Guided by this classification, we identify an $sp$$^2$--$sp$$^3$ hybridized chiral carbon allotrope, THRLN-C$_{32}$, as an ideal candidate hosting precisely this four-DWP configuration near the Fermi level. These $C_4$-protected DWPs project extended or closed-loop Fermi arcs onto the surface Brillouin zone, providing unambiguous spectroscopic signatures. Furthermore, external strain drives profound topological phase transitions encapsulated in a unified evolution landscape: the pristine four-DWP state dissociates into two exotic three-terminal Weyl complexes, degenerates into eight conventional $|C|=1$ WPs, or collapses into a trivial insulator. This work provides a definitive theoretical framework for minimal double-WSMs in nonmagnetic spinful systems and introduces an optimal material platform for investigating strain-tunable topological quantum phenomena.