Topological Hopf and chain link semimetal states and their application to Co2MnGa (Theory and Materials Prediction) (1712.00055v1)

Abstract: Topological semimetals can be classified by the connectivity and dimensionality of the band cross- ing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimet- al are 0D points, whereas the band crossings of a nodal-line semimetal are 1D closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topolog- ical surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.

Analysis of Topological Hopf and Chain Link Semimetal States

The paper "Topological Hopf and chain link semimetal states and their application to Co$_2$MnGa (Theory and Materials Prediction)" explores the theoretical prediction and computational analysis of novel topological semimetal states. In this work, Chang et al. propose new classes of semimetal states characterized by three-dimensional (3D) band crossings, specifically focusing on nontrivial topological structures like Hopf links and nodal chains.

The classification of topological semimetals traditionally relies on the dimensionality of band crossing manifolds at the Fermi level. For instance, Dirac and Weyl semimetals are characterized by zero-dimensional (0D) point-like crossings, while nodal-line semimetals are defined by one-dimensional (1D) loops. This paper introduces 3D band crossings protected by spatial symmetries, emphasizing asymmetric links, such as Hopf links or coupled chains, which are enabled through the presence of perpendicular crystalline mirror planes.

A key highlight of the paper is the theoretical proposal and computational verification of the ferromagnetic full Heusler compound Co$_2$MnGa as a candidate material manifesting these novel topological states. First-principles band structure calculations are employed to elucidate that Co$_2$MnGa hosts both Hopf-linked and chain-like bulk band crossings alongside unconventional surface states. The findings are robust against spin-orbit coupling (SOC) effects due to the weak SOC present, and the predicted features remain stable across various symmetry-preserving perturbations.

The paper further elucidates that these 3D band structures are linked to nontrivial topological surface states. In particular, the Hopf links lead to surface states that are coupled, filling the intersections of their projections in the Brillouin zone. The authors utilize symmetries and mirror eigenvalues to define distinct topological invariants, explaining the protection and stability of these band features.

From a practical perspective, the theoretical identification and characterization of Co$_2$MnGa provide a promising pathway to experimentally realize exotic topological semimetals with nontrivial band topology. The rich electronic structure revealed in Co$_2$MnGa suggests potential applications in spintronics and quantum computing, where topologically protected states can contribute to robust electronic behaviors even in the presence of environmental perturbations.

The theoretical implications of this work extend the understanding of topological phases, challenging the current classification paradigms. The introduction of these 3D link structures could impact the broader condensed matter research community's approach to exploring and categorizing new material systems. Future research may explore how these topological characteristics manifest in transport properties, catalyzing technological innovations and offering new functionalities in electronic device designs.

Overall, this paper effectively integrates topological theory with realistic materials prediction, altering the framework for considering topological protection in higher dimensions and providing a fertile ground for further investigation into complex topological systems.