Chiral Dirac-like fermion in spin-orbit-free antiferromagnetic semimetals

Group Theory on Quasisymmetry and Protected Near Degeneracy

In solid state systems, group representation theory is powerful in characterizing the behavior of quasiparticles, notably the energy degeneracy. While conventional group theory is effective in answering yes-or-no questions related to symmetry breaking, its application to determining the magnitude of energy splitting resulting from symmetry lowering is limited. Here, we propose a theory on quasisymmetry and near degeneracy, thereby expanding the applicability of group theory to address questions regarding large-or-small energy splitting. Defined within the degenerate subspace of an unperturbed Hamiltonian, quasisymmetries form an enlarged symmetry group eliminating the first-order splitting. This framework ensures that the magnitude of splitting arises as a second-order effect of symmetry-lowering perturbations, such as external fields and spin-orbit coupling. We systematically tabulate the quasisymmetry groups within 32 crystallographic point groups and find all the possible unitary quasisymmetry group structures regarding double degeneracy. Applying our theory to the realistic material AgLa, we predict a "quasi-Dirac semimetal" phase characterized by two tiny-gap band anticrossings.

Structural and Electronic Chirality in Inorganic Crystals: from Construction to Application

Chirality represents a fundamental characteristic inherent in nature, playing a pivotal role in the emergence of homochirality and the origin of life. While the principles of chirality in organic chemistry are well-documented, the exploration of chirality within inorganic crystal structures continues to evolve. This ongoing development is primarily due to the diverse nature of crystal/amorphous structures in inorganic materials, along with the intricate symmetrical and asymmetrical relationships in the geometry of their constituent atoms. In this review, we commence with a summary of the foundational concept of chirality in molecules and solid states matters. This is followed by an introduction of structural chirality and electronic chirality in three-dimensional and two-dimensional inorganic materials. The construction of chirality in inorganic materials is classified into physical photolithography, wet-chemistry method, self-assembly, and chiral imprinting. Highlighting the significance of this field, we also summarize the research progress of chiral inorganic materials for applications in optical activity, enantiomeric recognition and chiral sensing, selective adsorption and enantioselective separation, asymmetric synthesis and catalysis, and chirality-induced spin polarization. This review aims to provide a reference for ongoing research in chiral inorganic materials and potentially stimulate innovative strategies and novel applications in the realm of chirality.

Landau Theory of Altermagnetism

We formulate a Landau theory for altermagnets, a class of collinear compensated magnets with spin-split bands. Starting from the nonrelativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters, and the effect of nonzero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO_{2}, MnTe, and CuF_{2} that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity, and magnetoelastic and magneto-optical probes. Finally, we comment on generalizations of our framework to a wider family of exotic magnetic systems derived from the zero spin-orbit coupled limit.

Observation of plaid-like spin splitting in a noncoplanar antiferromagnet

Spatial, momentum and energy separation of electronic spins in condensed-matter systems guides the development of new devices in which spin-polarized current is generated and manipulated1-3. Recent attention on a set of previously overlooked symmetry operations in magnetic materials4 leads to the emergence of a new type of spin splitting, enabling giant and momentum-dependent spin polarization of energy bands on selected antiferromagnets5-10. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet manganese ditelluride (MnTe2), the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic (AFM) ground state. Such an unconventional spin pattern, further found to diminish at the high-temperature paramagnetic state, originates from the intrinsic AFM order instead of spin-orbit coupling (SOC). Our finding demonstrates a new type of quadratic spin texture induced by time-reversal breaking, placing AFM spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials.