Weyl semimetals are quantum materials where the electronic band structure leads to the presence of Weyl fermions as emergent quasiparticles. These materials exhibit unique topological properties and feature phenomena such as surface Fermi arcs and the chiral anomaly, making them of great interest in condensed matter physics and potential applications in quantum computing.
Symmetry-protected topological (SPT) states are phases of matter that possess non-trivial topological properties, protected by the presence of certain symmetries, and unlike traditional topological insulators, they become indistinguishable from a trivial state when these symmetries are broken. These states have garnered significant interest due to their robust edge states that could be utilized in quantum computing and other technologies that require stable quantum properties, immune to localized perturbations.
Non-Abelian anyons are exotic quasiparticles that arise in certain two-dimensional systems and have the unique property that interchanging them results in a change to the system's quantum state that depends on the order of the exchanges. This property makes non-Abelian anyons promising candidates for fault-tolerant quantum computation, as they can potentially perform operations that are inherently robust against local errors.
A Van Hove singularity is a feature in the electronic density of states of a solid where there is a divergent or non-analytic point due to the topology of the topology of the energy bands. This singularity can significantly influence the physical properties of materials, like superconductivity and magnetism, by enhancing electron interactions at specific energy levels.