Starting from crystal, electronic and magnetic structures of Heusler compounds, this paper studies the new topological materials related to Heusler compounds and their topological properties, such as anomalous Hall effect, skyrmions, chiral anomaly, Dirac fermion, Weyl fermion, transverse Nernst thermoelectric effect, thermal spintronics and topological surface states. It can be discovered that the topological state of Heusler compound can be well protected due to its high symmetry, thus producing rich topological properties. Heusler materials belonged to Weyl semimetals usually have strong anomalous Hall effect, and the Heusler materials with doping or Anomalous Nernst Effect (ANE) usually have higher thermoelectric figure of merit. These anomalous effects are closely related to the strong spin–orbit interaction. In application, people can use the non-dissipative edge state of quantum anomalous Hall effect to develop a new generation of low-energy transistors and electronic devices. The conversion efficiency of thermoelectric materials can be improved by ANE, and topological superconductivity can be used to promote the progress of quantum computation.
Berry curvature and the anomalous Hall effect in Heusler compounds