We present a comprehensive theoretical study of the static spin response in HgTe quantum wells, revealing distinctive behavior for the topologically nontrivial inverted structure. Most strikingly, the q=0 (long-wave-length) spin susceptibility of the
undoped topological-insulator system is constant and equal to the value found for the gapless Dirac-like structure, whereas the same quantity shows the typical decrease with increasing band gap in the normal-insulator regime. We discuss ramifications for the ordering of localized magnetic moments present in the quantum well, both in the insulating and electron-doped situations. The spin response of edge states is also considered, and we extract effective Lande g-factors for the bulk and edge electrons. The variety of counter-intuitive spin-response properties revealed in our study arises from the systems versatility in accessing situations where the charge-carrier dynamics can be governed by ordinary Schrodinger-type physics, mimics the behavior of chiral Dirac fermions, or reflects the materials symmetry-protected topological order.
We have obtained analytical expressions for the q-dependent static spin susceptibility of monolayer transition metal dichalcogenides, considering both the electron-doped and hole-doped cases. Our results are applied to calculate spin-related physical
observables of monolayer MoS2, focusing especially on in-plane/out-of-plane anisotropies. We find that the hole-mediated RKKY exchange interaction for in-plane impurity-spin components decays with the power law $R^{-5/2}$ as a function of distance $R$, which deviates from the $R^{-2}$ power law normally exhibited by a two-dimensional Fermi liquid. In contrast, the out-of-plane spin response shows the familiar $R^{-2}$ long-range behavior. We also use the spin susceptibility to define a collective g-factor for hole-doped MoS2 systems and discuss its density-dependent anisotropy.
