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This work is an analytic theoretical study of a 2D semiconductor with a Fermisurface that is split by the Zeeman coupling of electron spins to an externalmagnetic field in the presence of electron-electron interactions. For the firsttime, we calculate the spin susceptibility for long-range and finite-rangeinteractions diagrammatically, and find a resonant peak structure at the Kohnanomaly already in first-order perturbation theory. In contrast to thedensity-density correlator that is suppressed due to the large electrostaticenergy required to stabilize charge density order, the spin susceptibility doesnot suffer from electrostatic screening effects, thus favouringspin-density-wave order in 2D semiconductors. Our results impose significantconsequences for determining magnetic phases in 2D semiconductors. For example,a strongly enhanced Kohn anomaly may result in helical ordering of magneticimpurities due to the RKKY interaction. Furthermore, the spin degree of freedomcan equally represent a layer pseudospin in the case of bilayer materials. Inthis case, the external "magnetic field" is a combination of layer bias andinterlayer hopping. The sharp peak of the 2D static spin susceptibility maythen be responsible for dipole-density-wave order in bilayer materials at largeenough electron-phonon coupling.

Spin susceptibility in interacting two-dimensional semiconductors and bilayer systems at first order: Kohn anomalies and spin density wave ordering