Spin-orbit-free Weyl-loop and Weyl-point semimetals in a stable three-dimensional carbon allotrope

Abstract: Topological band theory has revolutionized our understanding of electronic structure of materials, in particular, a novel state - Weyl semimetal - has been predicted for systems with strong spin-orbit coupling (SOC). Here, a new class of Weyl semimetals, solely made of light elements with negligible SOC, is proposed. Our first-principles calculations show that conjugated p orbital interactions in a three-dimensional pure carbon network, termed interpenetrated graphene network, is sufficient to produce the same Weyl physics. This carbon allotrope has an exceptionally good structural stability. Its Fermi surface consists of two symmetry-protected Weyl loops with linear dispersion along perpendicular directions. Upon the breaking of inversion symmetry, each Weyl loop is reduced to a pair of Weyl points. The surface band of the network is nearly flat with a very large density of states at the Fermi level. It is reduced to Fermi arcs upon the symmetry breaking, as expected.

• The paper demonstrates that pure p orbital interactions in carbon induce Weyl semimetal phases without relying on spin-orbit coupling.
• It reveals robust structural stability with a cohesive energy of 7.62 eV/C and linear dispersions forming symmetry-protected Weyl loops.
• The study shows that breaking inversion symmetry transforms Weyl loops into Weyl points with Fermi arcs, enabling tunable topological transitions.

Spin-Orbit-Free Weyl Semimetals in a Carbon Allotrope

The study presented in the paper "Spin-orbit-free Weyl-loop and Weyl-point semimetals in a stable three-dimensional carbon allotrope" by Chen et al. contributes a notable advancement in the domain of topological materials by proposing a Weyl semimetal state in a spin-orbit-free framework. Through first-principles calculations, this research uncovers a new three-dimensional carbon allotrope, an interpenetrated graphene network, that exhibits Weyl physics typically associated with materials possessing strong spin-orbit coupling (SOC).

Key Contributions and Findings

The paper identifies a carbon allotrope where conjugated p orbital interactions are sufficient to realize Weyl physics, without reliance on materials with substantial SOC. The study emphasizes that the electronic structure, akin to Weyl semimetals, can arise through pure orbital effects. The allotrope is structurally stable, demonstrated by its Fermi surface comprising symmetry-protected Weyl loops, a hallmark of its topological nature. Upon breaking inversion symmetry, these loops reduce to Weyl points connected by Fermi arcs, well-characterized in topological semimetals.

Some significant points outlined in the paper include:

• Structural Stability: The carbon allotrope's cohesive energy of 7.62 eV/C, although slightly lower than diamond's, remains substantial, signifying its robust framework. It surpasses various known carbon structures like C60 and bct-C4 in stability.
• Electronic Band Structure: The band structure reveals linear dispersions along specific symmetry directions and Weyl loops crossing in the Brillouin Zone (BZ), suggesting near-flat surface bands with high density of states (DOS) at the Fermi level. This is verified by the calculated partial density of states primarily due to p orbitals.
• Symmetry Considerations: Chiral and mirror symmetries protect these Weyl loops. Breaking these symmetries transforms the loops into Weyl points, introducing Fermi arcs on the surface. The practical realization of Weyl points through manipulations like uniaxial strain and inversion symmetry breaking underscores the adaptability of this carbon allotrope to exhibit diverse electronic phenomena.

Theoretical Implications and Future Direction

The theoretical implications of this work broaden the scope of Weyl semimetals by demonstrating that degeneracy in band touching points can occur independently of SOC. This insight propels the search for topological materials into lighter element compositions, like carbon, expanding the potential material systems available for technological applications.

Practically, the manipulation of topological features, such as the shape and position of Weyl loops and points through strain or symmetry alterations, offers a pathway to engineer materials conducive to high-mobility transport characteristics, important for electronic and optoelectronic devices.

Moving forward, further exploration into spin-orbit-free systems will be vital, potentially embracing organic frameworks or transition metal systems with peculiar orbital arrangements. The ability to control topological transitions in such materials could pave the way for new applications, possibly in quantum computing or spintronics, where topologically protected states are advantageous.

In conclusion, the paper presents a compelling expansion of Weyl semimetal physics, promoting the potential of carbon-based materials in topological applications, and challenging existing notions related to the necessity of SOC in realizing these exotic quantum states.