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 space-time 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 twofold 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.

Graphene as a two-dimensional topological semimetal has attracted much attention for its outstanding properties. In contrast, three-dimensional (3D) topological semimetals of carbon are still rare. Searching for such materials with salient physics has become a new direction in carbon research. Here, using first-principles calculations and tight-binding modeling, we propose a new class of Weyl semimetals based on three types of 3D graphene networks. In the band structures of these materials, two flat Weyl surfaces appear in the Brillouin zone, which straddle the Fermi level and are robust against external strain. Their unique atomic and electronic structures enable applications in correlated electronics, as well as in energy storage, molecular sieves, and catalysis. When the networks are cut, the resulting slabs and nanowires remain semimetallic with Weyl lines and points at the Fermi surfaces, respectively. Between the Weyl lines, flat surface bands emerge with possible strong magnetism. The robustness of these structures can be traced back to a bulk topological invariant, ensured by the sublattice symmetry, and to the one-dimensional Weyl semimetal behavior of the zigzag carbon chain.

Carbon, the basic building block of our universe, enjoys a vast number of allotropic structures. Owing to its bonding characteristic, most carbon allotropes possess the motif of hexagonal rings. Here, with first-principles calculations, we discover a new metastable three-dimensional carbon allotrope entirely composed of pentagon rings. The unique structure of this Pentagon Carbon leads to extraordinary electronic properties, making it a cornucopia of emergent topological fermions. Under lattice strain, Pentagon Carbon exhibits topological phase transitions, generating a series of novel quasiparticles, from isospin-1 triplet fermions to triply degenerate fermions and further to Hopf-link Weyl-loop fermions. Its Landau level spectrum also exhibits distinct features, including a huge number of almost degenerate chiral Landau bands, implying pronounced magneto-transport signals. Our work not only discovers a remarkable carbon allotrope with highly rare structural motifs, it also reveals a fascinating hierarchical particle genesis with novel topological fermions beyond the Dirac and Weyl paradigm.

Antiferromagnetic (AF) spin devices could be one of the representative components for applications of spintronics thanks to the numerous advantages such as resistance to magnetic field perturbation, stray field-free operation, and ultrahigh device operation speed. However, detecting and manipulating the spin of AF materials is still a major challenge due to the absence of a net magnetic moment and spin degeneracy in the band structure. Bipolar antiferromagnetic semiconductors are promising solutions to these problems. Herein, using density functional theory calculations, we present asymmetrical functionalized double MXenes (Cr₂TiC₂FCl) that behave as a novel bipolar antiferromagnetic semiconductor (BAFS) with vanishing magnetism, in which the valence band and conduction band around the Fermi level exhibit opposite spin directions. Remarkably, gate voltage can manipulate the spin orientation of the AF Cr₂TiC₂FCl and lead to a transition from BAFS to half-metal antiferromagnets (HMAF). Moreover, the mixed functionalized double MXenes with various F/Cl concentrations show the BAFS feature due to the different chemical environment for the Cr atom. Our results presented herein open a new strategy towards AF spintronics and the realization of the AF spin field effect transistor.

The search for topological semimetals is mainly focused on heavy-element compounds by following the footsteps of previous research on topological insulators, with less attention on light-element materials. However, the negligible spin orbit coupling with light elements may turn out to be beneficial for realizing topological band features. Here, using first-principles calculations, we propose a new two-dimensional light-element material—the honeycomb borophene oxide (h-B₂O), which has nontrivial topological properties. The proposed structure is based on the recently synthesized honeycomb borophene on an Al (111) substrate [W. Li, L. Kong, C. Chen, J. Gou, S. Sheng, W. Zhang, H. Li, L. Chen, P. Cheng and K. Wu, Sci. Bull., 2018, 63, 282–286]. The h-B₂O monolayer is completely flat, unlike the oxides of graphene or silicene. We systematically investigate the structural properties of h-B₂O, and find that it has very good stability and exhibits significant mechanical anisotropy. Interestingly, the electronic band structure of h-B₂O hosts a nodal loop centered around the Y point in the Brillouin zone, protected by the mirror symmetry. Furthermore, under moderate lattice strain, the single nodal loop can be transformed into two loops, each penetrating through the Brillouin zone. The loops before and after the transition are characterized by different × topological indices. Our work not only predicts a new two-dimensional material with interesting physical properties, but also offers an alternative approach to search for new topological phases in 2D light-element systems.