Interacting chiral electrons at the 2D Dirac points: a review

Magnetic topological materials in two-dimensional: theory, material realization and application prospects

Two-dimensional (2D) magnetism and nontrivial band topology are both areas of research that are currently receiving significant attention in the study of 2D materials. Recently, a novel class of materials has emerged, known as 2D magnetic topological materials, which elegantly combine 2D magnetism and nontrivial topology. This field has garnered increasing interest, especially due to the emergence of several novel magnetic topological states that have been generalized into the 2D scale. These states include antiferromagnetic topological insulators/semimetals, second-order topological insulators, and topological half-metals. Despite the rapid advancements in this emerging research field in recent years, there have been few comprehensive summaries of the state-of-the-art progress. Therefore, this review aims to provide a thorough analysis of current progress on 2D magnetic topological materials. We cover various 2D magnetic topological insulators, a range of 2D magnetic topological semimetals, and the novel 2D topological half-metals, systematically analyzing the basic topological theory, the course of development, the material realization, and potential applications. Finally, we discuss the challenges and prospects for 2D magnetic topological materials, highlighting the potential for future breakthroughs in this exciting field.

Lieb-Schultz-Mattis Theorem in Higher Dimensions from Approximate Magnetic Translation Symmetry

We prove the Lieb-Schultz-Mattis theorem on the energy spectrum of a general two- or three-dimensional quantum many-body system with the U(1) particle number conservation and translation symmetry. Especially, it is demonstrated that the theorem holds in a system with long-range interactions. To this end, we introduce approximate magnetic translation symmetry under the total magnetic flux Φ=2π instead of the exact translation symmetry, and explicitly construct low energy variational states. The energy spectrum at Φ=2π is shown to agree with that at Φ=0 in the thermodynamic limit, which concludes the Lieb-Schultz-Mattis theorem.