Tuning the topological properties of Heusler alloys via band structure engineering.

Heusler alloys have proven to be an efficient and versatile platform, hosting a wide variety of topological states of matter, including the anomalous Hall effect, skyrmions, chiral anomaly, Dirac and Weyl fermions, and the transverse Nernst thermoelectric effect, thermal spintronics, and topological surface states. Their tunable electronic structure and diverse ground-state properties make them ideal candidates for realising topological semimetals with optimised spin orbit coupling strength, band gaps, and related parameters. Recent studies on transition-metal-based Heusler alloys have revealed nontrivial band topology and remarkable transport responses such as the anomalous Hall and Nernst effects (AHE and ANE). In this family, topological states often arise from band inversion driven by crystal symmetry, suggesting that external stimuli can induce topological phase transitions. Moreover, the presence of transition metal elements introduces magnetism, breaking time-reversal symmetry and, when combined with the band topology, producing a finite Berry curvature that contributes to intrinsic anomalous Hall conductivity (AHC). Maximising AHC requires careful tuning of the band topology via some external stimuli, such as strain or chemical alloying. Therefore, a comprehensive understanding of the mechanisms governing band structure evolution is essential for shifting the transport behaviour of Heusler alloys from extrinsic to intrinsic regimes. In this regard, we demonstrate the recent advancements in the regime of band structure engineering techniques for enhancing the magnetic, topological and transport properties in Heusler compounds from a basic physics point of view towards their application in spintronics and quantum topological devices.