Topological Semimetals from first-principles

Abstract: We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands. Different types of topological semimetals can be distinguished based on the degeneracy of the band crossings, their codimension (e.g., point or line nodes), as well as the crystal space group symmetries on which the protection of stable band crossings relies. The dispersion near the band crossing is a further discriminating characteristic. These properties give rise to a wide range of distinct semimetal phases such as Dirac or Weyl semimetals, point or line node semimetals, and type-I or type-II semimetals. In this review we give a general description of various families of topological semimetals with an emphasis on proposed material realizations from first-principles calculations. The conceptual framework for studying topological gapless electronic phases is reviewed, with a particular focus on the symmetry requirements of energy band crossings, and the relation between the different families of topological semimetals is elucidated. In addition to the paradigmatic Dirac and Weyl semimetals, we pay particular attention to more recent examples of topological semimetals, which include nodal line semimetals, multifold fermion semimetals, triple-point semimetals. Less emphasis is placed on their surface state properties, responses to external probes, and recent experimental developments.

Insightful Overview of "Topological Semimetals from first-principles"

The paper titled "Topological Semimetals from first-principles," authored by Heng Gao and collaborators, presents a comprehensive review of recent advances in the theoretical understanding and prediction of topological semimetals (TSMs). The authors focus on gapless electronic phases characterized by topologically stable band crossings, offering a complex and detailed taxonomy based on degeneracy, codimension, symmetries, and dispersion characteristics.

The key distinguishing attributes of various TSMs are meticulously outlined, including Degenerate Point Nodes and Line Nodes, and protection mechanisms governed by crystal symmetries. The paper delves into several prominent subcategories of semimetal phases like Dirac and Weyl semimetals, nodal line semimetals, multifold fermion semimetals, and triple-point semimetals, providing crucial insight into their theoretical frameworks and the material realizations proposed through first-principles calculations.

Notably, the paper places an emphasis on symmetry, one of the central unifying themes in the study of TSMs. Symmetry considerations provide foundational insight, relating structural material characteristics to electronic properties and enabling the classification and protection of the various band crossings observed in these materials. Specifically, symmetry requirements, such as those of the crystal and compositional structure, are shown to determine band degeneracies and crossings, elucidating the relationships between different families of TSMs.

The authors highlight the significance of density functional theory (DFT) in the single-particle approximation for exploring weakly correlated systems. They note that DFT is integral to advancing predictions for new materials exhibiting topological properties. The paper includes predictions of TSMs based on first-principles calculations, identifying potential candidate materials that manifest these exotic topological phases, such as Weyl semimetal TaAs and Dirac nodal line semimetal ZrSiS.

In discussing Dirac and Weyl semimetals, the paper underscores the importance of topological invariants like the Chern number, which protects the stability of Weyl points as monopoles of Berry curvature in momentum space. The review draws critical attention to Dirac semimetals and their symmetry-reliant occurrences, emphasizing the role of rotation symmetries and nonsymmorphic space groups.

The paper further explores new territory by addressing generalized classes of TSMs beyond traditional Dirac and Weyl fermions. These include and highlight multifold band crossings with novel and unconventional fermions and triple-point semimetals characterized by symmetry-protected band degeneracies.

The implications of these findings are substantial, providing avenues for novel quantum transport phenomena and potential applications across spintronics, quantum computation, and catalysis that rely on the unique topological states of matter. Future directions highlighted in the paper point towards systematic searches for new topological materials, leveraging computational techniques and symmetry analysis to uncover ideal candidates for technological development.

Overall, this paper stands as an authoritative source guiding researchers towards understanding, predicting, and harnessing TSMs' unique properties. It paves the way towards advanced materials that hold promise for disruptive advancements in technology domains influenced by quantum mechanics and material science.