Tuning the Chern number and Berry curvature with spin-orbit coupling and magnetic textures

Abstract

We obtain the band structure of a particle moving in a magnetic spin texture, classified by its chirality and structure factor, in the presence of spin-orbit coupling. This rich interplay leads to a variety of novel topological phases characterized by the Berry curvature and their associated Chern numbers. We suggest methods of experimentally exploring these topological phases by Hall drift measurements of the Chern number and Berry phase interferometry to map the Berry curvature.

Mean field study of the topological Haldane-Hubbard model of spin-12fermions

“…However, the gaps always remain nonzero but are difficult to resolve by eye, as we illustrate in the insets. The existence of these 'almost band touching' points can be understood if we appeal to a 'projection' approach 54,55 which assumes that the bands in the magnetically ordered state can be constructed by studying fermions moving adiabatically in the background of the tetrahedral order, while having their spins perfectly polarized along the local Zeeman field axes.…”

“…In the projection approach, we ignore the explicit underlying tetrahedral order, instead assuming its effects are encoded in the emergent Berry phase factors 54,55 for fermions as they traverse closed loops on the honeycomb lattice. Fermions hopping in a closed three-site loop will pick up a Berry phase of ±π/2 corresponding to half the solid angle subtended by any three of the four spins of the tetrahedral.…”

“…(ii) Using the converged mean field solution, we compute the band structure and Berry curvature of the various magnetically ordered insulating phases. In the tetrahedral phase, we find that a naïve application of a commonly employed projection approach, which assumes that the itinerant fermions in the ordered phase move adiabatically with spins projected along the local Zeeman field axes, 54,55 while it is generally a useful approach, is inadequate in this case to understand the band dispersion since it produces spurious band touchings due to an artificial restoration of time-reversal symmetry. Our numerical mean field calculations in the tetrahedral phase show that these band touchings in fact get gapped out, and a Berry curvature computation yields robust topological bands with high Chern numbers.…”

Large anomalous Nernst effect in a skyrmion crystal

“…Regarding the AHE in skyrmionic systems, quantum AHE (QAHE), i.e. the AHE with a quantized AHC with an integer C n called Chern number of n -th band, has recently been predicted in some SkX models where the conduction electron spins are exchange-coupled to the SkX either strongly 15 or weakly 16 , preceded by a report of QAHE in a meron (half-skyrmion) crystal 17 . In this paper we focus on the case Hamamoto et al picked out 15 , because of its particularly large implying the possibility of large ANE as well, thanks to the close relation between AHE and ANE 2 18 , and that is the main point we confirmed in this study.…”