Orbital magnetization and anomalous Hall effect in interacting Weyl semimetals

Abstract

Ferromagnetic Weyl semi-metals exhibit an anomalous Hall effect, a consequence of their topological properties. In the non-interacting case, the derivative of the orbital magnetization with respect to chemical potential is proportional to this anomalous Hall effect, the Středa formula. Motivated by compounds such as Mn3Sn, here we investigate how interactions modeled by a Hubbard U impact on both quantities when the Fermi energy is either aligned with the Weyl nodes or away from them. Using Dynamical Mean-Field Theory, we first find interaction-induced Mott-and band-insulating transitions. In the Weyl semimetal regime, away from insulators, interactions lead to an increase in the imbalance between the densities of spin species induced by a Zeeman term h. This increased imbalance leads to an increase of the anomalous Hall effect that can also be understood from the displacement of the Weyl nodes and topological arguments. This interaction-induced spin imbalance also compensates the reduction in orbital magnetization of each spin species that comes from smaller quasiparticle weight. In the small inteaction regime, the combined effects lead to an orbital magnetization that depends weakly on interaction and still changes linearly with chemical potential at small doping. In the intermediate and strong correlation regimes, the localization due to interaction affects strongly the orbital magnetization, which becomes small. A quasiparticle picture explains the anomalous Hall effect but does not suffice for the orbital magnetization. We propose a modified Středa formula to relate anomalous Hall effect and orbital magnetization in the weak correlation limit. We also identify mirror and particle-hole symmetries of the lattice model that explain, respectively, the vanishing of the anomalous Hall effect at h = 0 for all U and of the orbital magnetization at half-filling, µ = 0, for all U and h. arXiv:1807.07508v2 [cond-mat.str-el]

Quasiparticle Properties under Interactions in Weyl and Nodal Line Semimetals

“…One possible explanation of the above movement of WPs is due to the mean-field analysis in the weak-interaction regime, as discussed in Refs. 16,33 . Specifically, the Hubbard interaction can be decoupled as…”

“…On the other hand, the stability of WPs under the Hubbard interaction (below a critical U) may be protected by the space-inversion symmetry of this model. Now, a few remarks are in order concerning the nature of the metal-insulator transition in our WSM models 33 . The gap in WSM1 model opens after the WPs merge at the X point, especially when the non-interacting WPs are very close to each other, a small U could open the gap.…”

“…4). For large U the insulating phase should be a Mott insulator, which can be identified by checking whether the imaginary part of the self-energy at low frequency diverges 33 . The numerical results of the imaginary part are shown in Fig.…”

“…Finally, we would like to discuss the effect of quasi-particle weight Z which is ignored in our mean-field analysis 33 . In the presence of the Hubbard interaction, the single-particle band structure is renormalized by the factor Z.…”

Photonic spin Hall effect on the surfaces of type-I and type-II Weyl semimetals

“…They are a prototypical representative of the gapless topological materials, and have been experimentally discovered in three-dimensional condensed matters including MoTe 2 , WTe 2 , NbAs, TaP, TaAs, and so forth [3][4][5][6]. WSMs are privileged for many intriguing topographies such as anomalous Hall effect [1,7], surface states with Fermi arcs [4,5], large second harmonic generation [2,8], and circular photogalvanic effect [9,10], etc. The Weyl nodes in WSMs can be anisotropic and tilted away from the vertical axis [11].…”