Lieb Lattice Altermagnetism Enables Novel Topological States and Dirac Point Gaps

Altermagnetism, a relatively unexplored form of magnetism, is attracting growing interest due to its potential for creating novel quantum materials, and recent work by Xingmin Huo from Beihang University, Xingchuan Zhu from Nanjing University of Science and Technology, and Chang-An Li expands our understanding of this phenomenon on the Lieb lattice. The team demonstrates a versatile approach to designing altermagnetic models, revealing a strong connection between altermagnetism and the emergence of higher-order topological states, a cutting-edge area of condensed matter physics. Their investigations show that altermagnetic arrangements reconstruct topological edge states and, crucially, induce gaps within them, leading to the appearance of corner modes in open systems. This research, also involving contributions from Shiping Feng from Beijing Normal University, Song-Bo Zhang from Hefei National Laboratory and University of Science and Technology of China, and Shengyuan A. Yang from The Hong Kong Polytechnic University, establishes that altermagnetism provides a unique and robust pathway for engineering these exotic topological states, surpassing the capabilities of conventional magnetism.

Topological Materials And Magnetic Phenomena

This compilation details substantial research in condensed matter physics, focusing on topological materials, magnetism, and related phenomena. Core themes include the theoretical prediction and characterization of topological insulators, topological semimetals, and higher-order topological insulators, alongside investigations into their potential applications. A significant portion of the work explores magnetic materials, spin-orbit coupling, spin transport, and spintronic devices, including research on altermagnetism and magnetic skyrmions. Further studies investigate strongly correlated electron systems, unconventional superconductivity, quantum spin liquids, and the use of computational methods like Density Functional Theory to understand material properties.

Research also encompasses non-Hermitian physics, disordered systems, and two-dimensional materials such as graphene and transition metal dichalcogenides. The consistent use of computational modeling highlights its importance in advancing our understanding of these complex materials. Applying a symmetry operation combining rotation and time reversal, the team generated a basis respecting altermagnetic symmetry. By carefully considering spin orientations within the cluster, researchers identified 13 distinct arrangements, forming the basis for constructing the Lieb lattice. These bases were then arranged on a square lattice, creating a Hamiltonian incorporating exchange and hopping terms. Through this process, the study generated seven unique magnetic configurations compatible with the Lieb lattice structure.

Researchers then examined the resulting Hamiltonians to confirm spin-split band structures, a key indicator of altermagnetism. The team extended this approach to construct g-wave altermagnetic models, demonstrating the method’s versatility. This work systematically constructs both d-wave and g-wave altermagnetic arrangements, building upon the unique symmetries of the Lieb lattice. This detailed exploration establishes a foundation for investigating the interplay between altermagnetism and topological phenomena. Experiments reveal that incorporating these altermagnetic configurations into the topological Lieb lattice induces higher-order topological states when the magnetic moments align in the plane.

Specifically, the team demonstrates the emergence of corner modes within gaps created by the in-plane magnetic moments, realizing a higher-order topological phase. The research confirms that this induction of higher-order topology is universally applicable across all altermagnetic configurations constructed on the Lieb lattice. By applying symmetry constraints, the team successfully generated seven distinct altermagnetic arrangements and verified that these models exhibit spin-split band structures, a key characteristic of altermagnetism. Importantly, the study reveals that these altermagnetic configurations induce higher-order topological states, evidenced by the emergence of corner modes within gaps at Dirac points in open square geometries. This effect, consistently observed across all constructed altermagnetic models, distinguishes them from conventional magnetic arrangements like ferromagnetism and ferrimagnetism. Future work may investigate the impact of different symmetry-breaking perturbations on the stability and properties of these higher-order topological states. This research highlights the potential of altermagnetism for engineering novel topological states of matter and offers a pathway for designing materials with tailored electronic properties.